https://github.com/BapMel/mesocalc
Tip revision: fcb46321b1b824ebbb95eeaf5f554ccdb2015965 authored by Baptiste Mélès on 20 February 2025, 11:42:15 UTC
version de Christine Proust, 19/05/2017
version de Christine Proust, 19/05/2017
Tip revision: fcb4632
mesocalc.html
<?xml version="1.0" encoding="utf-8"?>
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Strict//EN"
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
<html xmlns="http://www.w3.org/1999/xhtml" xml:lang="fr">
<head>
<title>MesoCalc</title>
<meta name="author" content="Baptiste Mélès"/>
<meta name="description" content="MesoCalc is a Mesopotamian
calculator." />
<meta http-equiv="Content-Type" content="text/html;charset=UTF-8"/>
<meta http-equiv="Content-Language" content="fr"/>
<!--
MesoCalc, a Mesopotamian Calculator written by Baptiste Mélès
<baptiste.meles@normalesup.org>.
Copyright (C) 2013 Baptiste Mélès
This program is free software: you can redistribute it and/or modify
it under the terms of the GNU General Public License as published by
the Free Software Foundation, either version 3 of the License, or
(at your option) any later version.
This program is distributed in the hope that it will be useful, but
WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
General Public License for more details.
You should have received a copy of the GNU General Public License
along with this program. If not, see <http://www.gnu.org/licenses/>.
-->
<!-- This is the source code of MesoCalc, a Mesopotamian calculator.
Welcome to readers.
The code is divided into three successive parts:
1. the CSS style sheet (for aesthetics);
2. the JavaScript source code (for algorithmics);
3. the HTML code (for user interface).
Why JavaScript? So that people can:
1. easily use the program online (whatever their operating system or
terminal may be), and
2. download it as a single file, use it offline.
For historical reasons, the code mixes English and French words. It was
first written with French words. I hope that it will not disturb you.
-->
<style type="text/css">
/* *************************************************************
* CSS Style Sheet
**************************************************************** */
body {
background-color: #FFEECC;
font-size: 10pt;
margin: 2em;
font-family: Verdana, Charcoal, Geneva, "Luxi Sans", sans-serif;
}
div#tout {
margin-top: 1em;
margin-bottom: 1em;
padding-bottom: 1em;
margin-left: auto;
margin-right: auto;
font-size: 13px;
background-color: white;
width: 800px;
}
div#nav {
float: left;
height: 100%;
width: 15em;
position: fixed;
}
div.titre {
padding-left: 1em;
margin-bottom: .5em;
border-bottom: 1px solid #000;
}
.encart {
background: #eee;
border: 2px solid #ddd;
border-radius: 0 20px 0 0;
padding: 5px 25px 7px 25px;
margin: 30px 0;
}
div#corps {
margin-left: 16em;
margin-right: 3em;
}
table, th, td {
border: 1px solid black;
border-spacing: 0px;
border-collapse: collapse;
padding: 3px;
background: white;
}
div.center {
margin-left: auto;
margin-right: auto;
}
table.invisible, table.invisible td, table.invisible th {
text-align: center;
border: 0px;
}
table.center {
margin-left: auto;
margin-right: auto;
}
table.encadre td, table.encadre th {
text-align: center;
border : 0px;
}
input {
font-family: monospace;
}
.system {
color: #0080C0;
font-weight: bold;
}
.result_line {
font-weight: bold;
background-color: white;
border: 1px;
padding: 0 2em;
}
div#nav
a {
color: maroon;
text-decoration: none;
}
h1 a, h1 a:visited {
text-decoration: none;
color: #8080FF;
}
div#nav p {
margin-left: 1em;
}
div#nav ul {
padding-left: 2em;
}
div#corps p {
margin-top: 1em;
margin-bottom: 1em;
text-indent: 3em;
text-align: justify;
}
div#titre {
color: #8080FF;
text-align: center;
margin-left: auto;
margin-right: auto;
width: 30em;
padding-bottom: 2em;
}
.encadre {
border: 1px solid black;
}
div#titre p {
color: maroon;
font-size: 2em;
font-weight: normal;
padding: 0;
margin: 0;
}
h1 {
font-size: 4em;
padding: 0;
margin: 0;
}
h2 {
color: navy;
font-size: 3em;
margin-top: 1.5em;
margin-bottom: 1em;
}
h3 {
color: navy;
padding-left: 1em;
font-size: 1.5em;
margin-top: 2em;
margin-bottom: 1em;
}
h4 {
color: navy;
padding-left: 3em;
font-size: 1.2em;
margin-top: 2.5em;
margin-bottom: 1.5em;
}
hr.petit {
color: gray;
background-color: gray;
height: 0px;
width: 10em;
border: 0;
}
div.retrait, ul {
}
div.cadre {
border: 1px solid black;
}
.highlight
{
color: red;
}
</style>
</head>
<body onload="main();">
<script type="text/javascript">
//<![CDATA[
<!--
////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////
// JAVASCRIPT CODE OF MESOCALC
////////////////////////////////////////////////////////////////
////////////////////////////////////////////////////////////////
// In the following, "sexa" means "sexagesimal number" and "deci" means
// "decimal number".
// Remark: One of JavaScript's limitations is that numbers can not be
// greater than 9007199254740992 (which is 2^53, or
// 53.37.35.32.22.29.43.36.32). This is a real issue, for Mesopotamian
// mathematics really use numbers which are greater than this one. Thus,
// we have to go through this limitation. This can be done by
// considering numbers not as numbers, but as strings. As a consequence,
// computations must not be done by JavaScript in decimal notation.
// Personal reminder: in Google Chrome's JavaScript debugger, use
// console.log() to test functions. Example:
//
// for (i = 1; i <= 100; i++) console.log(Deci_to_sexa_absolute(i))
////////////////////////////////////////////////////////////////
// Initialization function
////////////////////////////////////////////////////////////////
function main () {
// In this function are initialized, at first load of the HTML page,
// some general variables.
// This boolean says if the calculator is used in floating or
// absolute mode.
sexa_floating = true;
// This boolean values are useful to switch on/off the display of some
// tables.
affiche_table_inverse = false;
affiche_table_carres = false;
affiche_table_racines_carrees = false;
affiche_table_racines_cubiques = false;
// Typical answers (especially for error messages)
nu = "<em>nu</em> (Undefined).";
not_sexa = "Use a sexagesimal integer.";
not_sexas = "Use sexagesimal integers.";
not_deci = "Use a decimal integer.";
negative = "Negative result.";
// For iterated operations: n-ary additions, n-ary
// multiplications... For example, when you compute an addition, you
// first see just two operand boxes. But if you compute the result,
// then a third box will appear, and so on.
nb_additions = 2;
addenda = new Array;
nb_soustractions = 2;
subtrahenda = new Array;
nb_multiplications = 2;
multiplicanda = new Array;
nb_add_longueurs = 2;
addenda_longueurs = new Array;
// Measuring units and their respective ratios.
length_unit = [
["danna", "30"],
["uš", "1.0"],
["ninda", "12"],
["kuš", "30"],
["šusi", "1"]
];
surface_unit = [
["gan", "1.40"],
["sar", "1.0"],
["gin", "3.0"],
["še", "1"]
];
volume_unit = [
["gan", "1.40"],
["sar", "1.0"],
["gin", "3.0"],
["še", "1"]
];
capacity_unit = [
["gur", "5"],
["bariga", "6"],
["ban", "10"],
["sila", "1.0"],
["gin", "3.0"],
["še", "1"]
];
weight_unit = [
["gu", "1.0"],
["mana", "1.0"],
["gin", "3.0"],
["še", "1"]
];
// Exhaustive list of regular numbers up to 20 places. This list was
// constructed by Mathieu Ossendrijver.
regulars_list = new Array(
"1", "1.0.2.16.16.29.22.46.42.59.1.28.55.30.39.44.38.24",
"1.0.2.52.46.55.36.34.38.17.20.45.46.22.4.48", "1.0.4.3.53.47.20.37.30",
"1.0.5.51.34.18.13.35.22.37.35.3.45.52.48.43.27.24.26.40",
"1.0.6.20.19.30.40.21.17.57.1.46.29.37.52.48.54",
"1.0.6.56.52.25.18.9.8.42.7.56.55.40.48",
"1.0.8.8.4.6.6.44.42.19.32.40.50.23.26.15",
"1.0.9.55.51.54.41.19.24.29.18.36.36.5.37.30",
"1.0.11.1.14.27.12.48.21.56.2.41.16.48",
"1.0.12.49.7.26.12.44.53.0.14.48.53.20",
"1.0.15.5.53.2.27.45.36.27.38.52.48",
"1.0.15.42.31.16.40.11.12.37.32.22.42.57.46.40", "1.0.16.53.53.20",
"1.0.19.10.48.12.10.18.44.0.40.3", "1.0.19.47.28.55.18.26.33.36",
"1.0.20.58.55.48.44.33.37.58.7.30",
"1.0.23.15.59.57.27.50.9.52.30.6.17.57.25.45.7.1.52.30",
"1.0.23.52.43.9.41.45.36",
"1.0.25.4.14.53.33.50.12.58.19.1.6.31.19.58.49.41.15",
"1.0.26.52.33.3.42.25.12.46.42.58.33.20.47.25.3.7.30",
"1.0.27.58.14.0.57.36",
"1.0.29.46.37.22.58.58.22.52.1.35.50.20.34.34.4.26.40",
"1.0.32.4.1.30.13.30", "1.0.33.52.32.12.50.40.44.26.40",
"1.0.36.10.5.38.37.4.24.56.7.5.23.26.15",
"1.0.36.46.56.41.33.16.42.28.8.53.20",
"1.0.37.58.43.42.19.54.30.57.34.6.5.37.30",
"1.0.39.41.29.32.30.27.23.23.5.8.7.19.55.2.0.57.36", "1.0.40.53.20",
"1.0.43.11.9.21.30.21.21.2.32.22.22.46.42.51.43.29.16.48",
"1.0.43.48.4.40.28.41.47.13.39.41.42.0.20.44.9.36", "1.0.45",
"1.0.47.17.58.41.44.48.48.1.15.45.2.12.17.44.26.52.48",
"1.0.47.54.56.30.48.17.4.16.3.46.20.41.51.21.36",
"1.0.49.6.56.42.41.7.58.7.30",
"1.0.50.55.57.58.57.15.34.9.33.15.3.42.13.20",
"1.0.51.25.4.45.18.21.33.55.29.32.49.30.6.13.30.40.30",
"1.0.52.2.5.4.37.7.45.33.39.32.53.22.33.36",
"1.0.53.14.10.9.11.19.45.51.17.20.21.1.13.49.41.15",
"1.0.53.51.11.34.50.10.0.55.28.45.39.5.40.44.26.40",
"1.0.55.3.18.48.37.20.24.2.40.35.33.32.41.43.7.30",
"1.0.56.9.30.23.3.12.58.12.29.43.17.45.36",
"1.0.56.46.33.35.19.6.9.9.15.17.40.13.16.42.28.8.53.20",
"1.0.57.58.44.16.47.24.26.40", "1.1.0.17.12.27.14.36.25.39.59.36.57.36",
"1.1.0.54.18.10.7.41.21.2.0.32", "1.1.2.6.33.45",
"1.1.4.25.11.18.19.26.28.3.40.33.2.15", "1.1.5.2.19.31.59.55.23.31.12",
"1.1.6.14.40.0.36.7.3.11.36.5.37.30", "1.1.9.10.37.42.4.1.55.12",
"1.1.13.19.12.41.28.19.12", "1.1.15.8.57.21.1.12.36.39.10.37.2.13.20",
"1.1.17.28.4.31.21.10.7.30",
"1.1.18.5.20.41.4.42.29.51.18.44.16.47.24.26.40",
"1.1.19.17.56.37.0.18.45",
"1.1.21.37.13.12.51.2.13.14.49.10.42.28.49.41.15",
"1.1.22.14.31.54.4.26.40",
"1.1.23.27.12.45.6.39.26.50.47.16.40.11.43.7.30",
"1.1.25.11.15.39.39.50.13.55.37.26.58.25.24.58.17.28.19.12",
"1.1.26.24", "1.1.29.20.55.43.59.3.18.34.4.56.28.16.50.59.42.43.12",
"1.1.30.33.45", "1.1.32.24.0.34.1.26.8.46.9.59.3.18.4.46.25.11.6.40",
"1.1.32.53.27.10.46.7.24.37.16.41.50.58.56.57.45.12.57.36",
"1.1.33.30.52.43.11.23.17.4.15.49.10.27.22.45.7.12",
"1.1.34.43.46.55.13.8.49.6.5.37.30", "1.1.36.34.9.57.26.28.30.50.10.25",
"1.1.37.41.6.38.25.35.36.22.49.47.33.2.35.31.12",
"1.1.38.54.5.46.48.13.15.40.40.48.21.16.59.45.3.30.56.15",
"1.1.39.31.34.58.31.17.38.26.10.22.13.20",
"1.1.40.44.36.17.43.48.24.20.42.36.0.12.51.14.24.50.37.30",
"1.1.41.51.37.30.50.30.22.56.9.5.35.13.55.12",
"1.1.42.29.8.30.30.35.28.46.7.14.8.28.26.40", "1.1.43.42.13.20",
"1.1.46.2.25.21.35.2.22.59.14.36.40.19.12",
"1.1.46.39.58.53.45.17.7.2.47.2.24", "1.1.47.53.8.40.18.45",
"1.1.50.13.30.11.48.11.2.54.43.18.27.1.41.15",
"1.1.50.51.6.16.38.55.20.3.50.24",
"1.1.52.4.21.0.36.34.8.28.59.47.41.43.7.30",
"1.1.53.55.15.8.6.57.29.53.7.2.50.28.0.33.20",
"1.1.55.2.30.40.20.34.56.38.24",
"1.1.56.53.30.7.12.52.6.8.9.18.56.21.4.11.51.6.40",
"1.1.59.14.12.5.59.25.26.24", "1.2.1.5.19.4.1.58.31.6.40",
"1.2.3.26.10.34.44.41.0.5.37.30", "1.2.4.3.54.41.35.31.1.43.42.13.20",
"1.2.5.17.25.4.28.3.59.3.45",
"1.2.7.38.26.7.45.40.29.54.45.17.35.30.41.18.30.56.15",
"1.2.8.16.12.48", "1.2.9.29.48.9.40.29.26.25.55.22.7.41.51.54.50.37.30",
"1.2.12.28.48", "1.2.15.27.56.25.47.2.36.3.0.30.10.38.3.37.57.30.14.24",
"1.2.16.41.40.18.45", "1.2.18.33.18.34.26.57.13.22.44.36.32.35.33.20",
"1.2.19.41.0.52.43.46.49.32.4.1.2.20.13.17.11.2.24",
"1.2.20.54.49.45.24.33.40.42.55.11.43.7.30",
"1.2.21.32.44.29.54.43.51.20.48.39.4.1.58.31.6.40",
"1.2.22.46.35.34.54.33.22.13.18.2.48.45",
"1.2.23.54.22.28.24.24.48.5.6.54.53.42.22.27.50.24",
"1.2.24.32.19.2.5.9.39.36.50.13.17.39.59.49.43.42.13.20",
"1.2.25.46.13.39.45.11.6.40",
"1.2.28.8.1.13.58.38.15.43.21.12.24.25.20.38.24",
"1.2.28.46.0.21.53.28.25.22.41.49.34.4.48", "1.2.30",
"1.2.32.21.57.10.36.13.39.46.29.2.37.49.26.24",
"1.2.32.59.58.52.55.36.4.53.4.7.40.48", "1.2.34.14.3.31.48.59.3.45",
"1.2.36.36.10.19.27.2.11.11.54.20.55.51.57.30.56.15",
"1.2.37.14.14.36.21.24.31.33.53.16.48",
"1.2.38.28.24.16.22.1.34.5.21.32.32.29.24.50.37.30",
"1.2.40.20.41.34.28.2.43.0.31.53.7.35.51.33.45",
"1.2.41.28.47.33.20.50.22.50.52.48",
"1.2.43.21.10.14.48.16.45.12.45.25.55.33.20",
"1.2.45.43.37.45.3.55.0.28.48",
"1.2.46.21.47.34.51.51.40.39.6.13.39.45.11.6.40", "1.2.47.36.8.3.20",
"1.2.49.58.45.12.40.44.30.50.41.43.7.30", "1.2.50.36.57.37.36.42.40",
"1.2.51.51.23.8.16.25.2.3.2.48.45", "1.2.54.52.24.57.36",
"1.2.57.59.44.26.21.41.15.48.39.45.59.44.9.23.35.45.18.45",
"1.2.59.8.9.36",
"1.3.1.1.3.56.26.25.48.49.11.39.49.56.26.0.29.37.46.40",
"1.3.3.24.11.33.59.3.45", "1.3.5.17.13.33.22.47.26.17.46.40",
"1.3.6.25.46.38.23.19.39.39.13.4.3.6.58.27.8.55.40.48",
"1.3.7.40.30.52.43.37.5.58.27.23.6.54.50.37.30",
"1.3.8.18.54.3.17.9.54.14.19.15.33.20",
"1.3.9.33.40.31.35.44.17.14.58.1.20.51.33.45",
"1.3.10.42.18.15.15.43.6.41.10.45.4.52.39.14.41.16.48",
"1.3.11.20.43.16.21.43.31.51.32.50.57.38.14.49.36", "1.3.12.35.33.20",
"1.3.14.59.7.14.54.7.14.25.8.43.18.43.39.38.52.48",
"1.3.15.37.34.52.9.53.31.41.43.50.56.15.21.36", "1.3.16.52.30",
"1.3.19.16.13.38.29.10.50.1.18.54.24.47.48.28.48",
"1.3.19.54.43.52.5.17.46.56.43.55.46.33.36",
"1.3.21.9.44.4.27.50.48.2.48.45",
"1.3.23.3.17.53.54.38.43.4.57.8.11.21.28.53.20",
"1.3.23.33.37.27.11.37.27.50.18.16.41.33.51.29.4.27.11.15",
"1.3.24.12.10.17.18.40.34.57.33.41.45.36",
"1.3.25.27.15.34.34.18.5.15.55.33.41.53.46.54.15.28.7.30",
"1.3.26.5.49.33.47.15.25.57.47.27.33.13.24.56.17.46.40",
"1.3.27.20.57.5.38.53.45.2.47.17.2.26.33.27.25.18.45",
"1.3.28.29.54.9.0.51.0.38.0.57.36", "1.3.30.23.41.7.29.22.57.46.40",
"1.3.32.47.55.28.22.42.56.44.9.36",
"1.3.33.26.33.55.33.0.34.24.35.33.20", "1.3.34.41.50.9.22.30",
"1.3.37.6.14.16.35.15.4.13.49.44.24.50.37.30",
"1.3.37.44.55.20.49.55.12", "1.3.39.0.16.40.37.37.20.49.35.5.51.33.45",
"1.3.42.3.34.16.19.12", "1.3.46.22.30.43.12",
"1.3.48.16.49.44.23.45.38.10.48.33.34.48.53.20",
"1.3.50.41.44.42.39.33.2.48.45",
"1.3.51.20.34.2.47.24.16.5.57.1.7.29.22.57.46.40",
"1.3.52.36.11.28.32.49.31.52.30",
"1.3.54.24.27.10.17.45.53.31.28.52.0.48.38.13.28.54.45.20",
"1.3.55.1.16.15.53.9.48.47.56.13.39.15.1.45.28.7.30",
"1.3.55.40.8.13.49.37.46.40",
"1.3.56.55.50.46.59.26.5.27.54.14.51.52.12.25.18.45",
"1.3.58.5.19.58.57.9.54.1.11.38.8.41.18.44.7.17.45.36",
"1.3.58.44.13.48.48.59.49.30.26.30.35.51.28.30.43.12", "1.4",
"1.4.2.25.21.35.20.17.49.50.57.34.51.12.42.23.36.57.36",
"1.4.3.4.18.3.19.0.56.50.30.8.49.27.33.7.12", "1.4.4.20.9.22.30",
"1.4.6.45.40.48.43.2.43.8.49.53.35.36.24.20.9.36",
"1.4.7.24.39.54.59.21.45.16.56.28.43.23.31.12",
"1.4.8.40.36.22.31.11.41.8.50.51.33.45",
"1.4.10.35.35.22.20.4.42.7.15.51.2.30",
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kings = {
Nabopolassar: "Nabopolassar",
Nebuchadnezzar: "Nebuchadnezzar",
EvilMerodach: "Evil-Merodach",
Neriglissar: "Neriglissar",
Nabonidus: "Nabonidus",
Cyrus: "Cyrus",
Cambyses: "Cambyses",
Bardiya: "Bardiya",
NebuchadnezzarIII: "Nebuchadnezzar III",
Darius: "Darius",
NebuchadnezzarIV: "Nebuchadnezzar IV",
Darius: "Darius",
Xerxes: "Xerxes",
Artaxerxes: "Artaxerxes",
DariusII: "Darius II",
ArtaxerxesII: "Artaxerxes II",
ArtaxerxesIII: "Artaxerxes III",
Arses: "Arses",
DariusIII: "Darius III"
};
kings_order = [ "Nabopolassar", "Nebuchadnezzar", "EvilMerodach",
"Neriglissar", "Nabonidus", "Cyrus", "Cambyses", "Bardiya",
"NebuchadnezzarIII", "Darius", "NebuchadnezzarIV", "Darius",
"Xerxes", "Artaxerxes", "DariusII", "ArtaxerxesII",
"ArtaxerxesIII", "Arses", "DariusIII" ];
// This calendar was designed and sent by Bruno Gombert in June 2016,
// after R. A. Parker and W. H. Dubberstein, /Babylonian Chronology,
// 626 B.C.-A.D. 45/, Studies in Ancient Oriental Civilization 24, 1942.
calendar =
{Nabopolassar: [ {1: "5/4/-626", 2: "5/5/-626", 3: "4/6/-626", 4:
"3/7/-626", 5: "2/8/-626", 6: "31/8/-626", 7: "29/9/-626", 8:
"29/10/-626", 9: "27/11/-626", 10: "27/12/-626", 11: "25/1/-625", 12:
"24/2/-625"}, {1: "24/3/-625", 2: "23/4/-625", 3: "23/5/-625", 4:
"21/6/-625", 5: "21/7/-625", 6: "19/8/-625", 7: "18/9/-625", 8:
"18/10/-625", 9: "16/11/-625", 10: "16/12/-625", 11: "14/1/-624", 12:
"12/2/-624"}, {1: "14/3/-624", 2: "12/4/-624", 3: "12/5/-624", 4:
"10/6/-624", 5: "10/7/-624", 6: "8/8/-624", 7: "7/9/-624", 8:
"7/10/-624", 9: "6/11/-624", 10: "5/12/-624", 11: "4/1/-623", 12:
"2/2/-623", b12: "3/3/-623"}, {1: "2/4/-623", 2: "1/5/-623", 3:
"31/5/-623", 4: "29/6/-623", 5: "29/7/-623", 6: "27/8/-623", 7:
"26/9/-623", 8: "26/10/-623", 9: "25/11/-623", 10: "24/12/-623", 11:
"23/1/-622"}, {1: "22/3/-622", 2: "21/4/-622", 3: "20/5/-622", 4:
"18/6/-622", 5: "18/7/-622", 6: "16/8/-622", 7: "15/9/-622", 8:
"15/10/-622", 9: "14/11/-622", 10: "13/12/-622", 11: "12/1/-621", 12:
"11/2/-621"}, {1: "11/3/-621", 2: "9/4/-621", 3: "9/5/-621", 4:
"7/6/-621", 5: "6/7/-621", 6: "5/8/-621", b6: "3/9/-621", 7:
"3/10/-621", 8: "2/11/-621", 9: "2/12/-621", 10: "1/1/-620", 11:
"30/1/-620", 12: "1/3/-620"}, {1: "30/3/-620", 2: "28/4/-620", 3:
"28/5/-620", 4: "26/6/-620", 5: "25/7/-620", 6: "24/8/-620", 7:
"22/9/-620", 8: "22/10/-620", 9: "21/11/-620", 10: "21/12/-620", 11:
"19/1/-619", 12: "18/2/-619"}, {1: "19/3/-619", 2: "18/4/-619", 3:
"17/5/-619", 4: "16/6/-619", 5: "15/7/-619", 6: "13/8/-619", 7:
"12/9/-619", 8: "12/10/-619", 9: "10/11/-619", 10: "10/12/-619", 11:
"8/1/-618", 12: "7/2/-618", b12: "8/3/-618"}, {1: "7/4/-618", 2:
"7/5/-618", 3: "5/6/-618", 4: "5/7/-618", 5: "3/8/-618", 6: "1/9/-618",
7: "1/10/-618", 8: "31/10/-618", 9: "29/11/-618", 10: "28/12/-618", 11:
"27/1/-617", 12: "25/2/-617"}, {1: "26/3/-617", 2: "25/4/-617", 3:
"24/5/-617", 4: "23/6/-617", 5: "23/7/-617", 6: "21/8/-617", 7:
"20/9/-617", 8: "19/10/-617", 9: "18/11/-617", 10: "17/12/-617", 11:
"15/1/-616", 12: "14/2/-616"}, {1: "15/3/-616", 2: "14/4/-616", 3:
"13/5/-616", 4: "12/6/-616", 5: "12/7/-616", 6: "11/8/-616", b6:
"9/9/-616", 7: "9/10/-616", 8: "7/11/-616", 9: "7/12/-616", 10:
"5/1/-615", 11: "3/2/-615", 12: "5/3/-615"}, {1: "3/4/-615", 2:
"3/5/-615", 3: "1/6/-615", 4: "1/7/-615", 5: "31/7/-615", 6:
"30/8/-615", 7: "28/9/-615", 8: "28/10/-615", 9: "26/11/-615", 10:
"26/12/-615", 11: "24/1/-614", 12: "22/2/-614"}, {1: "24/3/-614", 2:
"22/4/-614", 3: "21/5/-614", 4: "20/6/-614", 5: "20/7/-614", 6:
"19/8/-614", 7: "18/9/-614", 8: "17/10/-614", 9: "16/11/-614", 10:
"15/12/-614", 11: "13/1/-613", 12: "12/2/-613", b12: "12/3/-613"}, {1:
"11/4/-613", 2: "10/5/-613", 3: "8/6/-613", 4: "8/7/-613", 5:
"7/8/-613", 6: "5/9/-613", 7: "5/10/-613", 8: "4/11/-613", 9:
"3/12/-613", 10: "2/1/-612", 11: "31/1/-612", 12: "2/3/-612"}, {1:
"31/3/-612", 2: "30/4/-612", 3: "29/5/-612", 4: "27/6/-612", 5:
"27/7/-612", 6: "26/8/-612", 7: "24/9/-612", 8: "24/10/-612", 9:
"22/11/-612", 10: "22/12/-612", 11: "21/1/-611", 12: "19/2/-611"}, {1:
"21/3/-611", 2: "19/4/-611", 3: "19/5/-611", 4: "17/6/-611", 5:
"16/7/-611", 6: "15/8/-611", b6: "13/9/-611", 7: "13/10/-611", 8:
"11/11/-611", 9: "11/12/-611", 10: "10/1/-610", 11: "9/2/-610", 12:
"10/3/-610"}, {1: "9/4/-610", 2: "8/5/-610", 3: "7/6/-610", 4:
"6/7/-610", 5: "5/8/-610", 6: "3/9/-610", 7: "2/10/-610", 8:
"1/11/-610", 9: "30/11/-610", 10: "30/12/-610", 11: "29/1/-609", 12:
"27/2/-609"}, {1: "28/3/-609", 2: "27/4/-609", 3: "26/5/-609", 4:
"25/6/-609", 5: "24/7/-609", 6: "23/8/-609", 7: "21/9/-609", 8:
"20/10/-609", 9: "19/11/-609", 10: "18/12/-609", 11: "17/1/-608", 12:
"15/2/-608"}, {1: "17/3/-608", 2: "16/4/-608", 3: "15/5/-608", 4:
"14/6/-608", 5: "14/7/-608", 6: "12/8/-608", 7: "10/9/-608", 8:
"10/10/-608", 9: "8/11/-608", 10: "8/12/-608", 11: "6/1/-607", 12:
"5/2/-607"}, {1: "6/3/-607", 2: "5/4/-607", 3: "4/5/-607", 4:
"3/6/-607", 5: "3/7/-607", 6: "1/8/-607", b6: "31/8/-607", 7:
"29/9/-607", 8: "29/10/-607", 9: "27/11/-607", 10: "27/12/-607", 11:
"25/1/-606", 12: "24/2/-606"}, {1: "25/3/-606", 2: "24/4/-606", 3:
"23/5/-606", 4: "22/6/-606", 5: "21/7/-606", 6: "20/8/-606", 7:
"19/9/-606", 8: "18/10/-606", 9: "17/11/-606", 10: "17/12/-606", 11:
"15/1/-605", 12: "13/2/-605", b12: "14/3/-605"}, {1: "12/4/-605", 2:
"11/5/-605", 3: "10/6/-605", 4: "9/7/-605", 5: "8/8/-605", 6:
"7/9/-605", 7: "7/10/-605", 8: "5/11/-605", 9: "5/12/-605", 10:
"4/1/-604", 11: "2/2/-604", 12: "3/3/-604"} ],
Nebuchadnezzar: [ {1: "12/4/-605", 2: "11/5/-605", 3: "10/6/-605", 4:
"9/7/-605", 5: "8/8/-605", 6: "7/9/-605", 7: "7/10/-605", 8:
"5/11/-605", 9: "5/12/-605", 10: "4/1/-604", 11: "2/2/-604", 12:
"3/3/-604"}, {1: "2/4/-604", 2: "1/5/-604", 3: "30/5/-604", 4:
"29/6/-604", 5: "28/7/-604", 6: "27/8/-604", 7: "26/9/-604", 8:
"25/10/-604", 9: "24/11/-604", 10: "24/12/-604", 11: "23/1/-603", 12:
"21/2/-603"}, {1: "22/3/-603", 2: "21/4/-603", 3: "20/5/-603", 4:
"18/6/-603", 5: "17/7/-603", 6: "16/8/-603", b6: "15/9/-603", 7:
"15/10/-603", 8: "13/11/-603", 9: "13/12/-603", 10: "12/1/-602", 11:
"10/2/-602", 12: "12/3/-602"}, {1: "10/4/-602", 2: "10/5/-602", 3:
"8/6/-602", 4: "7/7/-602", 5: "6/8/-602", 6: "4/9/-602", 7:
"4/10/-602", 8: "3/11/-602", 9: "2/12/-602", 10: "1/1/-601", 11:
"30/1/-601", 12: "29/2/-601"}, {1: "30/3/-601", 2: "28/4/-601", 3:
"28/5/-601", 4: "26/6/-601", 5: "25/7/-601", 6: "24/8/-601", 7:
"22/9/-601", 8: "22/10/-601", 9: "21/11/-601", 10: "20/12/-601", 11:
"19/1/-600", 12: "17/2/-600"}, {1: "19/3/-600", 2: "17/4/-600", 3:
"17/5/-600", 4: "15/6/-600", 5: "15/7/-600", 6: "13/8/-600", b6:
"12/9/-600", 7: "10/10/-600", 8: "9/11/-600", 9: "9/12/-600", 10:
"8/1/-599", 11: "6/2/-599", 12: "7/3/-599"}, {1: "6/4/-599", 2:
"6/5/-599", 3: "5/6/-599", 4: "4/7/-599", 5: "3/8/-599", 6: "2/9/-599",
7: "1/10/-599", 8: "31/10/-599", 9: "29/11/-599", 10: "28/12/-599", 11:
"27/1/-598", 12: "25/2/-598"}, {1: "27/3/-598", 2: "25/4/-598", 3:
"25/5/-598", 4: "23/6/-598", 5: "23/7/-598", 6: "22/8/-598", b6:
"21/9/-598", 7: "20/10/-598", 8: "19/11/-598", 9: "18/12/-598", 10:
"16/1/-597", 11: "15/2/-597", 12: "15/3/-597"}, {1: "13/4/-597", 2:
"13/5/-597", 3: "11/6/-597", 4: "11/7/-597", 5: "10/8/-597", 6:
"9/9/-597", 7: "9/10/-597", 8: "7/11/-597", 9: "6/12/-597", 10:
"5/1/-596", 11: "3/2/-596", 12: "5/3/-596"}, {1: "3/4/-596", 2:
"2/5/-596", 3: "1/6/-596", 4: "30/6/-596", 5: "30/7/-596", 6:
"29/8/-596", b6: "28/9/-596", 7: "28/10/-596", 8: "26/11/-596", 9:
"25/12/-596", 10: "24/1/-595", 11: "22/2/-595", 12: "24/3/-595"}, {1:
"22/4/-595", 2: "21/5/-595", 3: "20/6/-595", 4: "19/7/-595", 5:
"18/8/-595", 6: "17/9/-595", 7: "16/10/-595", 8: "15/11/-595", 9:
"15/12/-595", 10: "13/1/-594", 11: "12/2/-594", 12: "13/3/-594"}, {1:
"12/4/-594", 2: "11/5/-594", 3: "9/6/-594", 4: "9/7/-594", 5:
"7/8/-594", 6: "6/9/-594", 7: "6/10/-594", 8: "4/11/-594", 9:
"4/12/-594", 10: "2/1/-593", 11: "1/2/-593", 12: "2/3/-593", b12:
"31/3/-593"}, {1: "30/4/-593", 2: "29/5/-593", 3: "27/6/-593", 4:
"27/7/-593", 5: "25/8/-593", 6: "24/9/-593", 7: "23/10/-593", 8:
"22/11/-593", 9: "21/12/-593", 10: "20/1/-592", 11: "19/2/-592", 12:
"21/3/-592"}, {1: "19/4/-592", 2: "19/5/-592", 3: "17/6/-592", 4:
"17/7/-592", 5: "15/8/-592", 6: "13/9/-592", 7: "13/10/-592", 8:
"11/11/-592", 9: "10/12/-592", 10: "9/1/-591", 11: "8/2/-591", 12:
"10/3/-591"}, {1: "8/4/-591", 2: "8/5/-591", 3: "7/6/-591", 4:
"6/7/-591", 5: "5/8/-591", 6: "3/9/-591", 7: "2/10/-591", 8:
"1/11/-591", 9: "30/11/-591", 10: "29/12/-591", 11: "28/1/-590", 12:
"27/2/-590", b12: "28/3/-590"}, {1: "27/4/-590", 2: "27/5/-590", 3:
"25/6/-590", 4: "25/7/-590", 5: "23/8/-590", 6: "22/9/-590", 7:
"21/10/-590", 8: "20/11/-590", 9: "19/12/-590", 10: "18/1/-589", 11:
"16/2/-589", 12: "16/3/-589"}, {1: "15/4/-589", 2: "15/5/-589", 3:
"13/6/-589", 4: "13/7/-589", 5: "11/8/-589", 6: "10/9/-589", 7:
"10/10/-589", 8: "8/11/-589", 9: "8/12/-589", 10: "6/1/-588", 11:
"5/2/-588", 12: "6/3/-588"}, {1: "4/4/-588", 2: "4/5/-588", 3:
"2/6/-588", 4: "2/7/-588", 5: "31/7/-588", 6: "30/8/-588", 7:
"29/9/-588", 8: "29/10/-588", 9: "27/11/-588", 10: "27/12/-588", 11:
"25/1/-587", 12: "24/2/-587", b12: "25/3/-587"}, {1: "23/4/-587", 2:
"23/5/-587", 3: "21/6/-587", 4: "21/7/-587", 5: "19/8/-587", 6:
"18/9/-587", 7: "18/10/-587", 8: "17/11/-587", 9: "16/12/-587", 10:
"15/1/-586", 11: "13/2/-586", 12: "15/3/-586"}, {1: "13/4/-586", 2:
"12/5/-586", 3: "11/6/-586", 4: "10/7/-586", 5: "8/8/-586", 6:
"7/9/-586", 7: "7/10/-586", 8: "6/11/-586", 9: "6/12/-586", 10:
"4/1/-585", 11: "3/2/-585", 12: "3/3/-585"}, {1: "2/4/-585", 2:
"1/5/-585", 3: "30/5/-585", 4: "29/6/-585", 5: "28/7/-585", 6:
"26/8/-585", 7: "25/9/-585", 8: "25/10/-585", 9: "24/11/-585", 10:
"23/12/-585", 11: "22/1/-584", 12: "21/2/-584"}, {1: "22/3/-584", 2:
"21/4/-584", 3: "20/5/-584", 4: "18/6/-584", 5: "18/7/-584", 6:
"16/8/-584", b6: "14/9/-584", 7: "14/10/-584", 8: "13/11/-584", 9:
"13/12/-584", 10: "11/1/-583", 11: "10/2/-583", 12: "11/3/-583"}, {1:
"10/4/-583", 2: "9/5/-583", 3: "8/6/-583", 4: "7/7/-583", 5:
"6/8/-583", 6: "4/9/-583", 7: "4/10/-583", 8: "2/11/-583", 9:
"2/12/-583", 10: "31/12/-583", 11: "30/1/-582", 12: "28/2/-582"}, {1:
"30/3/-582", 2: "29/4/-582", 3: "28/5/-582", 4: "27/6/-582", 5:
"26/7/-582", 6: "25/8/-582", 7: "23/9/-582", 8: "23/10/-582", 9:
"21/11/-582", 10: "21/12/-582", 11: "19/1/-581", 12: "18/2/-581", b12:
"18/3/-581"}, {1: "17/4/-581", 2: "16/5/-581", 3: "15/6/-581", 4:
"15/7/-581", 5: "13/8/-581", 6: "12/9/-581", 7: "12/10/-581", 8:
"10/11/-581", 9: "9/12/-581", 10: "8/1/-580", 11: "6/2/-580", 12:
"7/3/-580"}, {1: "6/4/-580", 2: "5/5/-580", 3: "4/6/-580", 4:
"4/7/-580", 5: "3/8/-580", 6: "1/9/-580", 7: "1/10/-580", 8:
"31/10/-580", 9: "29/11/-580", 10: "28/12/-580", 11: "27/1/-579", 12:
"25/2/-579"}, {1: "26/3/-579", 2: "25/4/-579", 3: "24/5/-579", 4:
"23/6/-579", 5: "23/7/-579", 6: "22/8/-579", 7: "20/9/-579", 8:
"20/10/-579", 9: "19/11/-579", 10: "18/12/-579", 11: "16/1/-578", 12:
"15/2/-578", b12: "16/3/-578"}, {1: "14/4/-578", 2: "14/5/-578", 3:
"12/6/-578", 4: "12/7/-578", 5: "10/8/-578", 6: "9/9/-578", 7:
"9/10/-578", 8: "8/11/-578", 9: "7/12/-578", 10: "6/1/-577", 11:
"4/2/-577", 12: "5/3/-577"}, {1: "3/4/-577", 2: "2/5/-577", 3:
"1/6/-577", 4: "30/6/-577", 5: "30/7/-577", 6: "28/8/-577", 7:
"27/9/-577", 8: "27/10/-577", 9: "25/11/-577", 10: "25/12/-577", 11:
"24/1/-576", 12: "22/2/-576", b12: "24/3/-576"}, {1: "22/4/-576", 2:
"21/5/-576", 3: "20/6/-576", 4: "19/7/-576", 5: "18/8/-576", 6:
"16/9/-576", 7: "16/10/-576", 8: "14/11/-576", 9: "14/12/-576", 10:
"13/1/-575", 11: "11/2/-575", 12: "13/3/-575"}, {1: "12/4/-575", 2:
"11/5/-575", 3: "9/6/-575", 4: "9/7/-575", 5: "7/8/-575", 6:
"6/9/-575", 7: "5/10/-575", 8: "4/11/-575", 9: "3/12/-575", 10:
"2/1/-574", 11: "31/1/-574", 12: "2/3/-574"}, {1: "1/4/-574", 2:
"30/4/-574", 3: "30/5/-574", 4: "28/6/-574", 5: "28/7/-574", 6:
"26/8/-574", b6: "25/9/-574", 7: "24/10/-574", 8: "22/11/-574", 9:
"22/12/-574", 10: "20/1/-573", 11: "19/2/-573", 12: "20/3/-573"}, {1:
"19/4/-573", 2: "18/5/-573", 3: "17/6/-573", 4: "16/7/-573", 5:
"15/8/-573", 6: "13/9/-573", 7: "13/10/-573", 8: "11/11/-573", 9:
"10/12/-573", 10: "9/1/-572", 11: "7/2/-572", 12: "9/3/-572"}, {1:
"8/4/-572", 2: "7/5/-572", 3: "6/6/-572", 4: "6/7/-572", 5: "4/8/-572",
6: "3/9/-572", 7: "2/10/-572", 8: "1/11/-572", 9: "30/11/-572", 10:
"29/12/-572", 11: "28/1/-571", 12: "26/2/-571", b12: "28/3/-571"}, {1:
"26/4/-571", 2: "26/5/-571", 3: "25/6/-571", 4: "24/7/-571", 5:
"23/8/-571", 6: "22/9/-571", 7: "21/10/-571", 8: "20/11/-571", 9:
"19/12/-571", 10: "18/1/-570", 11: "16/2/-570", 12: "17/3/-570"}, {1:
"16/4/-570", 2: "15/5/-570", 3: "14/6/-570", 4: "13/7/-570", 5:
"12/8/-570", 6: "10/9/-570", 7: "10/10/-570", 8: "9/11/-570", 9:
"9/12/-570", 10: "7/1/-569", 11: "6/2/-569", 12: "6/3/-569"}, {1:
"4/4/-569", 2: "4/5/-569", 3: "2/6/-569", 4: "1/7/-569", 5:
"31/7/-569", 6: "30/8/-569", 7: "28/9/-569", 8: "28/10/-569", 9:
"27/11/-569", 10: "27/12/-569", 11: "25/1/-568", 12: "24/2/-568", b12:
"25/3/-568"}, {1: "23/4/-568", 2: "23/5/-568", 3: "21/6/-568", 4:
"20/7/-568", 5: "19/8/-568", 6: "17/9/-568", 7: "17/10/-568", 8:
"16/11/-568", 9: "16/12/-568", 10: "15/1/-567", 11: "13/2/-567", 12:
"15/3/-567"}, {1: "13/4/-567", 2: "12/5/-567", 3: "11/6/-567", 4:
"10/7/-567", 5: "8/8/-567", 6: "7/9/-567", 7: "6/10/-567", 8:
"5/11/-567", 9: "5/12/-567", 10: "4/1/-566", 11: "2/2/-566", 12:
"4/3/-566"}, {1: "2/4/-566", 2: "2/5/-566", 3: "31/5/-566", 4:
"29/6/-566", 5: "29/7/-566", 6: "27/8/-566", 7: "26/9/-566", 8:
"25/10/-566", 9: "24/11/-566", 10: "24/12/-566", 11: "22/1/-565", 12:
"21/2/-565"}, {1: "22/3/-565", 2: "20/4/-565", 3: "20/5/-565", 4:
"18/6/-565", 5: "17/7/-565", 6: "16/8/-565", 7: "14/9/-565", 8:
"14/10/-565", 9: "13/11/-565", 10: "12/12/-565", 11: "11/1/-564", 12:
"9/2/-564"}, {1: "11/3/-564", 2: "9/4/-564", 3: "9/5/-564", 4:
"7/6/-564", 5: "7/7/-564", 6: "5/8/-564", b6: "4/9/-564", 7:
"4/10/-564", 8: "2/11/-564", 9: "2/12/-564", 10: "31/12/-564", 11:
"29/1/-563", 12: "28/2/-563"}, {1: "29/3/-563", 2: "28/4/-563", 3:
"28/5/-563", 4: "26/6/-563", 5: "26/7/-563", 6: "25/8/-563", 7:
"23/9/-563", 8: "23/10/-563", 9: "21/11/-563", 10: "21/12/-563", 11:
"19/1/-562", 12: "17/2/-562", b12: "19/3/-562"}, {1: "17/4/-562", 2:
"17/5/-562", 3: "15/6/-562", 4: "15/7/-562", 5: "14/8/-562", 6:
"13/9/-562"} ],
EvilMerodach: [ {7: "13/10/-562", 8: "11/11/-562", 9: "10/12/-562", 10:
"9/1/-561", 11: "7/2/-561", 12: "7/3/-561"}, {1: "6/4/-561", 2:
"5/5/-561", 3: "3/6/-561", 4: "3/7/-561", 5: "2/8/-561", 6: "1/9/-561",
7: "1/10/-561", 8: "30/10/-561", 9: "29/11/-561", 10: "28/12/-561", 11:
"27/1/-560", 12: "25/2/-560"}, {1: "26/3/-560", 2: "24/4/-560", 3:
"24/5/-560", 4: "22/6/-560", 5: "22/7/-560", 6: "21/8/-560", 7:
"20/9/-560", 8: "20/10/-560", 9: "18/11/-560", 10: "18/12/-560", 11:
"16/1/-559", 12: "15/2/-559", b12: "16/3/-559"} ],
Neriglissar: [ {1: "26/3/-560", 2: "24/4/-560", 3: "24/5/-560", 4:
"22/6/-560", 5: "22/7/-560", 6: "21/8/-560", 7: "20/9/-560", 8:
"20/10/-560", 9: "18/11/-560", 10: "18/12/-560", 11: "16/1/-559", 12:
"15/2/-559", b12: "16/3/-559"}, {1: "14/4/-559", 2: "14/5/-559", 3:
"12/6/-559", 4: "11/7/-559", 5: "10/8/-559", 6: "9/9/-559", 7:
"9/10/-559", 8: "7/11/-559", 9: "7/12/-559", 10: "5/1/-558", 11:
"4/2/-558", 12: "5/3/-558"}, {1: "4/4/-558", 2: "3/5/-558", 3:
"2/6/-558", 4: "1/7/-558", 5: "31/7/-558", 6: "29/8/-558", 7:
"28/9/-558", 8: "27/10/-558", 9: "26/11/-558", 10: "25/12/-558", 11:
"24/1/-557", 12: "23/2/-557"}, {1: "23/3/-557", 2: "22/4/-557", 3:
"21/5/-557", 4: "20/6/-557", 5: "19/7/-557", 6: "18/8/-557", 7:
"16/9/-557", 8: "15/10/-557", 9: "14/11/-557", 10: "13/12/-557", 11:
"12/1/-556", 12: "11/2/-556", b12: "12/3/-556"}, {1: "11/4/-556", 2:
"11/5/-556", 3: "9/6/-556", 4: "9/7/-556", 5: "7/8/-556", 6:
"6/9/-556", 7: "5/10/-556", 8: "3/11/-556", 9: "3/12/-556", 10:
"1/1/-555", 11: "30/1/-555", 12: "1/3/-555"} ],
Nabonidus: [ {1: "11/4/-556", 2: "11/5/-556", 3: "9/6/-556", 4:
"9/7/-556", 5: "7/8/-556", 6: "6/9/-556", 7: "5/10/-556", 8:
"3/11/-556", 9: "3/12/-556", 10: "1/1/-555", 11: "30/1/-555", 12:
"1/3/-555"}, {1: "31/3/-555", 2: "30/4/-555", 3: "30/5/-555", 4:
"28/6/-555", 5: "28/7/-555", 6: "26/8/-555", 7: "25/9/-555", 8:
"24/10/-555", 9: "22/11/-555", 10: "22/12/-555", 11: "20/1/-554", 12:
"19/2/-554", b12: "20/3/-554"}, {1: "19/4/-554", 2: "19/5/-554", 3:
"17/6/-554", 4: "17/7/-554", 5: "15/8/-554", 6: "14/9/-554", 7:
"14/10/-554", 8: "12/11/-554", 9: "11/12/-554", 10: "10/1/-553", 11:
"8/2/-553", 12: "9/3/-553"}, {1: "7/4/-553", 2: "7/5/-553", 3:
"5/6/-553", 4: "5/7/-553", 5: "3/8/-553", 6: "2/9/-553", 7:
"2/10/-553", 8: "31/10/-553", 9: "30/11/-553", 10: "29/12/-553", 11:
"28/1/-552", 12: "26/2/-552", b12: "28/3/-552"}, {1: "26/4/-552", 2:
"25/5/-552", 3: "24/6/-552", 4: "23/7/-552", 5: "22/8/-552", 6:
"21/9/-552", 7: "21/10/-552", 8: "19/11/-552", 9: "19/12/-552", 10:
"18/1/-551", 11: "16/2/-551", 12: "17/3/-551"}, {1: "16/4/-551", 2:
"15/5/-551", 3: "13/6/-551", 4: "13/7/-551", 5: "11/8/-551", 6:
"10/9/-551", 7: "10/10/-551", 8: "8/11/-551", 9: "8/12/-551", 10:
"7/1/-550", 11: "6/2/-550", 12: "7/3/-550"}, {1: "5/4/-550", 2:
"5/5/-550", 3: "3/6/-550", 4: "2/7/-550", 5: "1/8/-550", 6:
"30/8/-550", 7: "29/9/-550", 8: "29/10/-550", 9: "27/11/-550", 10:
"27/12/-550", 11: "26/1/-549", 12: "24/2/-549", b12: "25/3/-549"}, {1:
"23/4/-549", 2: "23/5/-549", 3: "21/6/-549", 4: "20/7/-549", 5:
"19/8/-549", 6: "17/9/-549", 7: "17/10/-549", 8: "16/11/-549", 9:
"15/12/-549", 10: "14/1/-548", 11: "13/2/-548", 12: "14/3/-548"}, {1:
"13/4/-548", 2: "12/5/-548", 3: "11/6/-548", 4: "10/7/-548", 5:
"8/8/-548", 6: "7/9/-548", 7: "6/10/-548", 8: "5/11/-548", 9:
"5/12/-548", 10: "3/1/-547", 11: "2/2/-547", 12: "3/3/-547"}, {1:
"2/4/-547", 2: "2/5/-547", 3: "31/5/-547", 4: "29/6/-547", 5:
"29/7/-547", 6: "27/8/-547", 7: "26/9/-547", 8: "25/10/-547", 9:
"24/11/-547", 10: "23/12/-547", 11: "22/1/-546", 12: "20/2/-546"}, {1:
"22/3/-546", 2: "21/4/-546", 3: "20/5/-546", 4: "19/6/-546", 5:
"18/7/-546", 6: "17/8/-546", b6: "15/9/-546", 7: "15/10/-546", 8:
"14/11/-546", 9: "13/12/-546", 10: "11/1/-545", 11: "10/2/-545", 12:
"10/3/-545"}, {1: "9/4/-545", 2: "8/5/-545", 3: "7/6/-545", 4:
"6/7/-545", 5: "5/8/-545", 6: "4/9/-545", 7: "3/10/-545", 8:
"2/11/-545", 9: "2/12/-545", 10: "31/12/-545", 11: "29/1/-544", 12:
"28/2/-544"}, {1: "29/3/-544", 2: "27/4/-544", 3: "27/5/-544", 4:
"25/6/-544", 5: "25/7/-544", 6: "24/8/-544", 7: "23/9/-544", 8:
"23/10/-544", 9: "21/11/-544", 10: "21/12/-544", 11: "19/1/-543", 12:
"17/2/-543", b12: "19/3/-543"}, {1: "17/4/-543", 2: "16/5/-543", 3:
"15/6/-543", 4: "14/7/-543", 5: "13/8/-543", 6: "12/9/-543", 7:
"12/10/-543", 8: "11/11/-543", 9: "10/12/-543", 10: "9/1/-542", 11:
"7/2/-542", 12: "8/3/-542"}, {1: "6/4/-542", 2: "6/5/-542", 3:
"4/6/-542", 4: "4/7/-542", 5: "2/8/-542", 6: "1/9/-542", 7:
"1/10/-542", 8: "30/10/-542", 9: "29/11/-542", 10: "29/12/-542", 11:
"27/1/-541", 12: "26/2/-541"}, {1: "26/3/-541", 2: "25/4/-541", 3:
"24/5/-541", 4: "22/6/-541", 5: "22/7/-541", 6: "20/8/-541", 7:
"19/9/-541", 8: "18/10/-541", 9: "17/11/-541", 10: "17/12/-541", 11:
"16/1/-540", 12: "14/2/-540", b12: "16/3/-540"}, {1: "14/4/-540", 2:
"14/5/-540", 3: "12/6/-540", 4: "11/7/-540", 5: "10/8/-540", 6:
"8/9/-540", 7: "8/10/-540", 8: "7/11/-540", 9: "6/12/-540", 10:
"5/1/-539", 11: "3/2/-539", 12: "5/3/-539"}, {1: "4/4/-539", 2:
"3/5/-539", 3: "2/6/-539", 4: "1/7/-539", 5: "31/7/-539", 6:
"29/8/-539", 7: "27/9/-539", 8: "27/10/-539", 9: "25/11/-539", 10:
"24/12/-539", 11: "23/1/-538", 12: "22/2/-538"} ],
Cyrus: [ {1: "4/4/-539", 2: "3/5/-539", 3: "2/6/-539", 4: "1/7/-539",
5: "31/7/-539", 6: "29/8/-539", 7: "27/9/-539", 8: "27/10/-539", 9:
"25/11/-539", 10: "24/12/-539", 11: "23/1/-538", 12: "22/2/-538"}, {1:
"24/3/-538", 2: "22/4/-538", 3: "22/5/-538", 4: "20/6/-538", 5:
"20/7/-538", 6: "19/8/-538", 7: "17/9/-538", 7: "16/10/-538", 8:
"15/11/-538", 9: "14/12/-538", 10: "13/1/-537", 11: "11/2/-537"}, {1:
"12/3/-537", 2: "10/4/-537", 3: "10/5/-537", 4: "9/6/-537", 5:
"8/7/-537", 6: "7/8/-537", b6: "6/9/-537", 7: "5/10/-537", 8:
"3/11/-537", 9: "3/12/-537", 10: "1/1/-536", 11: "30/1/-536", 12:
"1/3/-536"}, {1: "31/3/-536", 2: "29/4/-536", 3: "29/5/-536", 4:
"28/6/-536", 5: "27/7/-536", 6: "26/8/-536", 7: "25/9/-536", 8:
"24/10/-536", 9: "22/11/-536", 10: "22/12/-536", 11: "20/1/-535", 12:
"19/2/-535", b12: "20/3/-535"}, {1: "18/4/-535", 2: "18/5/-535", 3:
"17/6/-535", 4: "16/7/-535", 5: "15/8/-535", 6: "14/9/-535", 7:
"13/10/-535", 8: "12/11/-535", 9: "11/12/-535", 10: "9/1/-534", 11:
"8/2/-534", 12: "9/3/-534"}, {1: "8/4/-534", 2: "5/5/-534", 3:
"6/6/-534", 4: "6/7/-534", 5: "4/8/-534", 6: "3/9/-534", 7:
"2/10/-534", 8: "1/11/-534", 9: "1/12/-534", 10: "30/12/-534", 11:
"29/1/-533", 12: "27/2/-533"}, {1: "28/3/-533", 2: "26/4/-533", 3:
"25/5/-533", 4: "24/6/-533", 5: "24/7/-533", 6: "22/8/-533", 7:
"20/9/-533", 8: "20/10/-533", 9: "19/11/-533", 10: "19/12/-533", 11:
"17/1/-532", 12: "16/2/-532", b12: "17/3/-532"}, {1: "16/4/-532", 2:
"15/5/-532", 3: "13/6/-532", 4: "13/7/-532", 5: "11/8/-532", 6:
"9/9/-532", 7: "9/10/-532", 8: "8/11/-532", 9: "8/12/-532", 10:
"6/1/-531", 11: "5/2/-531", 12: "7/3/-531"}, {1: "5/4/-531", 2:
"5/5/-531", 3: "3/6/-531", 4: "2/7/-531", 5: "31/7/-531", 6:
"30/8/-531", 7: "28/9/-531", 8: "28/10/-531", 9: "27/11/-531", 10:
"27/12/-531", 11: "25/1/-530", 12: "23/2/-530"}, {1: "26/3/-530", 2:
"24/4/-530", 3: "24/5/-530", 4: "22/6/-530", 5: "21/7/-530", 6:
"20/8/-530", b6: "18/9/-530", 7: "18/10/-530", 8: "16/11/-530", 9:
"16/12/-530", 10: "14/1/-529", 11: "13/2/-529", 12: "14/3/-529"} ],
Cambyses: [ {1: "26/3/-530", 2: "24/4/-530", 3: "24/5/-530", 4:
"22/6/-530", 5: "21/7/-530", 6: "20/8/-530", b6: "18/9/-530", 7:
"18/10/-530", 8: "16/11/-530", 9: "16/12/-530", 10: "14/1/-529", 11:
"13/2/-529", 12: "14/3/-529"}, {1: "12/4/-529", 2: "12/5/-529", 3:
"10/6/-529", 4: "10/7/-529", 5: "8/8/-529", 6: "7/9/-529", 7:
"6/10/-529", 8: "5/11/-529", 9: "4/12/-529", 10: "3/1/-528", 11:
"1/2/-528", 12: "3/3/-528"}, {1: "1/4/-528", 2: "1/5/-528", 3:
"30/5/-528", 4: "29/6/-528", 5: "29/7/-528", 6: "27/8/-528", 7:
"26/9/-528", 8: "26/10/-528", 9: "24/11/-528", 10: "23/12/-528", 11:
"22/1/-527", 12: "20/2/-527"}, {1: "21/3/-527", 2: "20/4/-527", 3:
"19/5/-527", 4: "18/6/-527", 5: "18/7/-527", 6: "16/8/-527", b6:
"15/9/-527", 7: "15/10/-527", 8: "14/11/-527", 9: "13/12/-527", 10:
"11/1/-526", 11: "10/2/-526", 12: "11/3/-526"}, {1: "9/4/-526", 2:
"9/5/-526", 3: "7/6/-526", 4: "7/7/-526", 5: "6/8/-526", 6: "5/9/-526",
7: "5/10/-526", 8: "3/11/-526", 9: "2/12/-526", 10: "1/1/-525", 11:
"30/1/-525", 12: "29/2/-525"}, {1: "29/3/-525", 2: "27/4/-525", 3:
"26/5/-525", 4: "25/6/-525", 5: "25/7/-525", 6: "24/8/-525", 7:
"23/9/-525", 8: "22/10/-525", 9: "21/11/-525", 10: "20/12/-525", 11:
"19/1/-524", 12: "17/2/-524", b12: "19/3/-524"}, {1: "17/4/-524", 2:
"16/5/-524", 3: "14/6/-524", 4: "14/7/-524", 5: "13/8/-524", 6:
"12/9/-524", 7: "11/10/-524", 8: "10/11/-524", 9: "10/12/-524", 10:
"8/1/-523", 11: "7/2/-523", 12: "8/3/-523"}, {1: "7/4/-523", 2:
"6/5/-523", 3: "4/6/-523", 4: "4/7/-523", 5: "2/8/-523", 6: "1/9/-523",
7: "1/10/-523", 8: "30/10/-523", 9: "29/11/-523", 10: "28/12/-523", 11:
"27/1/-522", 12: "26/2/-522"}, {1: "27/3/-522", 2: "25/4/-522", 3:
"25/5/-522", 4: "23/6/-522", 5: "23/7/-522", 6: "21/8/-522", 7:
"20/9/-522", 8: "19/10/-522", 9: "18/11/-522", 10: "17/12/-522", 11:
"16/1/-521", 12: "15/2/-521", b12: "15/3/-521"} ],
Bardiya: [ {1: "27/3/-522", 2: "25/4/-522", 3: "25/5/-522", 4:
"23/6/-522", 5: "23/7/-522", 6: "21/8/-522", 7: "20/9/-522", 8:
"19/10/-522", 9: "18/11/-522", 10: "17/12/-522", 11: "16/1/-521", 12:
"15/2/-521", b12: "15/3/-521"} ],
NebuchadnezzarIII: [ {1: "27/3/-522", 2: "25/4/-522", 3: "25/5/-522",
4: "23/6/-522", 5: "23/7/-522", 6: "21/8/-522", 7: "20/9/-522", 8:
"19/10/-522", 9: "18/11/-522", 10: "17/12/-522", 11: "16/1/-521", 12:
"15/2/-521", b12: "15/3/-521"} ],
Darius: [ {1: "27/3/-522", 2: "25/4/-522", 3: "25/5/-522", 4:
"23/6/-522", 5: "23/7/-522", 6: "21/8/-522", 7: "20/9/-522", 8:
"19/10/-522", 9: "18/11/-522", 10: "17/12/-522", 11: "16/1/-521", 12:
"15/2/-521", b12: "15/3/-521"}, {1: "14/4/-521", 2: "13/5/-521", 3:
"12/6/-521", 4: "11/7/-521", 5: "10/8/-521", 6: "8/9/-521", 7:
"8/10/-521", 8: "6/11/-521", 9: "6/12/-521", 10: "4/1/-520", 11:
"3/2/-520", 12: "4/3/-520"}, {1: "3/4/-520", 2: "3/5/-520", 3:
"1/6/-520", 4: "1/7/-520", 5: "31/7/-520", 6: "29/8/-520", 7:
"27/9/-520", 8: "27/10/-520", 9: "25/11/-520", 10: "24/12/-520", 11:
"23/1/-519", 12: "21/2/-519"}, {1: "23/3/-519", 2: "22/4/-519", 3:
"21/5/-519", 4: "20/6/-519", 5: "20/7/-519", 6: "19/8/-519", b6:
"17/9/-519", 7: "16/10/-519", 8: "15/11/-519", 9: "14/12/-519", 10:
"12/1/-518", 11: "11/2/-518", 12: "12/3/-518"}, {1: "11/4/-518", 2:
"10/5/-518", 3: "9/6/-518", 4: "9/7/-518", 5: "8/8/-518", 6:
"6/9/-518", 7: "6/10/-518", 8: "4/11/-518", 9: "4/12/-518", 10:
"2/1/-517", 11: "31/1/-517", 12: "1/3/-517"}, {1: "30/3/-517", 2:
"29/4/-517", 3: "28/5/-517", 4: "27/6/-517", 5: "27/7/-517", 6:
"25/8/-517", 7: "24/9/-517", 8: "24/10/-517", 9: "22/11/-517", 10:
"22/12/-517", 11: "20/1/-516", 12: "19/2/-516", b12: "20/3/-516"}, {1:
"18/4/-516", 2: "18/5/-516", 3: "16/6/-516", 4: "16/7/-516", 5:
"14/8/-516", 6: "13/9/-516", 7: "13/10/-516", 8: "11/11/-516", 9:
"11/12/-516", 10: "10/1/-515", 11: "8/2/-515", 12: "10/3/-515"}, {1:
"8/4/-515", 2: "7/5/-515", 3: "6/6/-515", 4: "5/7/-515", 5: "3/8/-515",
6: "2/9/-515", 7: "2/10/-515", 8: "1/11/-515", 9: "30/11/-515", 10:
"30/12/-515", 11: "29/1/-514", 12: "27/2/-514"}, {1: "29/3/-514", 2:
"27/4/-514", 3: "26/5/-514", 4: "25/6/-514", 5: "24/7/-514", 6:
"22/8/-514", 7: "21/9/-514", 8: "20/10/-514", 9: "19/11/-514", 10:
"19/12/-514", 11: "18/1/-513", 12: "16/2/-513", b12: "17/3/-513"}, {1:
"16/4/-513", 2: "15/5/-513", 3: "13/6/-513", 4: "13/7/-513", 5:
"11/8/-513", 6: "10/9/-513", 7: "9/10/-513", 8: "7/11/-513", 9:
"7/12/-513", 10: "6/1/-512", 11: "5/2/-512", 12: "6/3/-512"}, {1:
"5/4/-512", 2: "4/5/-512", 3: "3/6/-512", 4: "2/7/-512", 5:
"31/7/-512", 6: "30/8/-512", 7: "29/9/-512", 8: "28/10/-512", 9:
"28/11/-512", 10: "27/12/-512", 11: "25/1/-511", 12: "23/2/-511"}, {1:
"25/3/-511", 2: "24/4/-511", 3: "24/5/-511", 4: "22/6/-511", 5:
"21/7/-511", 6: "20/8/-511", b6: "19/9/-511", 7: "18/10/-511", 8:
"17/11/-511", 9: "16/12/-511", 10: "14/1/-510", 11: "13/2/-510", 12:
"15/3/-510"}, {1: "13/4/-510", 2: "12/5/-510", 3: "11/6/-510", 4:
"10/7/-510", 5: "9/8/-510", 6: "8/9/-510", 7: "7/10/-510", 8:
"6/11/-510", 9: "5/12/-510", 10: "4/1/-509", 11: "2/2/-509", 12:
"2/3/-509"}, {1: "1/4/-509", 2: "30/4/-509", 3: "30/5/-509", 4:
"28/6/-509", 5: "28/7/-509", 6: "27/8/-509", 7: "26/9/-509", 8:
"25/10/-509", 9: "24/11/-509", 10: "23/12/-508", 11: "22/1/-508", 12:
"20/2/-508", b12: "21/3/-508"}, {1: "20/4/-508", 2: "19/5/-508", 3:
"17/6/-508", 4: "17/7/-508", 5: "16/8/-508", 6: "15/9/-508", 7:
"15/10/-508", 8: "14/11/-508", 9: "13/12/-508", 10: "11/1/-507", 11:
"10/2/-507", 12: "11/3/-507"}, {1: "9/4/-507", 2: "8/5/-507", 3:
"7/6/-507", 4: "6/7/-507", 5: "5/8/-507", 6: "4/9/-507", 7:
"4/10/-507", 8: "3/11/-507", 9: "2/12/-507", 10: "1/1/-506", 11:
"30/1/-506", 12: "1/3/-506"}, {1: "30/3/-506", 2: "28/4/-506", 3:
"27/5/-506", 4: "26/6/-506", 5: "25/7/-506", 6: "24/8/-506", 7:
"23/9/-506", 8: "23/10/-506", 9: "21/11/-506", 10: "21/12/-506", 11:
"20/1/-505", 12: "18/2/-505", b12: "18/3/-505"}, {1: "17/4/-505", 2:
"16/5/-505", 3: "14/6/-505", 4: "14/7/-505", 5: "12/8/-505", 6:
"11/9/-505", 7: "11/10/-505", 8: "9/11/-505", 9: "9/12/-505", 10:
"8/1/-504", 11: "6/2/-504", 12: "8/3/-504"}, {1: "6/4/-504", 2:
"6/5/-504", 3: "4/6/-504", 4: "4/7/-504", 5: "2/8/-504", 6: "1/9/-504",
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"25/5/-503", 4: "23/6/-503", 5: "23/7/-503", 6: "21/8/-503", b6:
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"18/8/-500", 7: "17/9/-500", 8: "16/10/-500", 9: "15/11/-500", 10:
"14/12/-500", 11: "12/1/-499", 12: "11/2/-499", b12: "12/3/-499"}, {1:
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"7/8/-499", 6: "6/9/-499", 7: "5/10/-499", 8: "4/11/-499", 9:
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"27/7/-498", 6: "26/8/-498", 7: "24/9/-498", 8: "24/10/-498", 9:
"23/11/-498", 10: "22/12/-498", 11: "21/1/-497", 12: "20/2/-497", b12:
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"15/7/-497", 5: "14/8/-497", 6: "12/9/-497", 7: "12/10/-497", 8:
"11/11/-497", 9: "10/12/-497", 10: "9/1/-496", 11: "8/2/-496", 12:
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"22/5/-492", 3: "21/6/-492", 4: "21/7/-492", 5: "19/8/-492", 6:
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NebuchadnezzarIV: [ {1: "14/4/-521", 2: "13/5/-521", 3: "12/6/-521", 4:
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"23/8/-373", 7: "22/9/-373", 8: "21/10/-373", 9: "20/11/-373", 10:
"20/12/-373", 11: "18/1/-372", 12: "17/2/-372", b12: "18/3/-372"}, {1:
"17/4/-372", 2: "16/5/-372", 3: "14/6/-372", 4: "14/7/-372", 5:
"12/8/-372", 6: "11/9/-372", 7: "11/10/-372", 8: "9/11/-372", 9:
"9/12/-372", 10: "7/1/-371", 11: "6/2/-371", 12: "8/3/-371"}, {1:
"6/4/-371", 2: "6/5/-371", 3: "4/6/-371", 4: "4/7/-371", 5: "2/8/-371",
6: "1/9/-371", 7: "30/9/-371", 8: "29/10/-371", 9: "28/11/-371", 10:
"27/12/-371", 11: "26/1/-370", 12: "25/2/-370"}, {1: "26/3/-370", 2:
"25/4/-370", 3: "25/5/-370", 4: "23/6/-370", 5: "23/7/-370", 6:
"21/8/-370", b6: "20/9/-370", 7: "19/10/-370", 8: "17/11/-370", 9:
"17/12/-370", 10: "15/1/-369", 11: "14/2/-369", 12: "14/3/-369"}, {1:
"13/4/-369", 2: "13/5/-369", 3: "11/6/-369", 4: "11/7/-369", 5:
"9/8/-369", 6: "8/9/-369", 7: "7/10/-369", 8: "6/11/-369", 9:
"5/12/-369", 10: "4/1/-368", 11: "2/2/-368", 12: "4/3/-368"}, {1:
"2/4/-368", 2: "2/5/-368", 3: "31/5/-368", 4: "30/6/-368", 5:
"30/7/-368", 6: "29/8/-368", 7: "27/9/-368", 8: "26/10/-368", 9:
"25/11/-368", 10: "24/12/-368", 11: "23/1/-367", 12: "21/2/-367", b12:
"22/3/-367"}, {1: "21/4/-367", 2: "21/5/-367", 3: "19/6/-367", 4:
"19/7/-367", 5: "18/8/-367", 6: "16/9/-367", 7: "16/10/-367", 8:
"14/11/-367", 9: "14/12/-367", 10: "12/1/-366", 11: "11/2/-366", 12:
"12/3/-366"}, {1: "10/4/-366", 2: "10/5/-366", 3: "8/6/-366", 4:
"8/7/-366", 5: "7/8/-366", 6: "5/9/-366", 7: "5/10/-366", 8:
"4/11/-366", 9: "3/12/-366", 10: "2/1/-365", 11: "31/1/-365", 12:
"1/3/-365"}, {1: "30/3/-365", 2: "28/4/-365", 3: "28/5/-365", 4:
"26/6/-365", 5: "26/7/-365", 6: "24/8/-365", 7: "23/9/-365", 8:
"23/10/-365", 9: "21/11/-365", 10: "21/12/-365", 11: "20/1/-364", 12:
"18/2/-364", b12: "20/3/-364"}, {1: "18/4/-364", 2: "17/5/-364", 3:
"16/6/-364", 4: "15/7/-364", 5: "13/8/-364", 6: "12/9/-364", 7:
"12/10/-364", 8: "10/11/-364", 9: "10/12/-364", 10: "9/1/-363", 11:
"8/2/-363", 12: "9/3/-363"}, {1: "8/4/-363", 2: "7/5/-363", 3:
"5/6/-363", 4: "5/7/-363", 5: "3/8/-363", 6: "1/9/-363", 7:
"1/10/-363", 8: "31/10/-363", 9: "29/11/-363", 10: "29/12/-363", 11:
"28/1/-362", 12: "27/2/-362"}, {1: "28/3/-362", 2: "27/4/-362", 3:
"26/5/-362", 4: "24/6/-362", 5: "24/7/-362", 6: "22/8/-362", 7:
"21/9/-362", 8: "20/10/-362", 9: "19/11/-362", 10: "18/12/-362", 11:
"17/1/-361", 12: "16/2/-361", b12: "16/3/-361"}, {1: "15/4/-361", 2:
"14/5/-361", 3: "13/6/-361", 4: "12/7/-361", 5: "11/8/-361", 6:
"9/9/-361", 7: "9/10/-361", 8: "7/11/-361", 9: "7/12/-361", 10:
"5/1/-360", 11: "4/2/-360", 12: "5/3/-360"}, {1: "4/4/-360", 2:
"3/5/-360", 3: "2/6/-360", 4: "2/7/-360", 5: "31/7/-360", 6:
"30/8/-360", 7: "28/9/-360", 8: "28/10/-360", 9: "26/11/-360", 10:
"26/12/-360", 11: "24/1/-359", 12: "23/2/-359", b12: "24/3/-359"}, {1:
"23/4/-359", 2: "22/5/-359", 3: "21/6/-359", 4: "20/7/-359", 5:
"19/8/-359", 6: "18/9/-359", 7: "18/10/-359", 8: "16/11/-359", 9:
"16/12/-359", 10: "14/1/-358", 11: "12/2/-358"}, {12: "13/3/-358"} ],
ArtaxerxesIII: [ {1: "23/4/-359", 2: "22/5/-359", 3: "21/6/-359", 4:
"20/7/-359", 5: "19/8/-359", 6: "18/9/-359", 7: "18/10/-359", 8:
"16/11/-359", 9: "16/12/-359", 10: "14/1/-358", 11: "12/2/-358", 12:
"13/3/-358"}, {1: "12/4/-358", 2: "11/5/-358", 3: "10/6/-358", 4:
"9/7/-358", 5: "8/8/-358", 6: "7/9/-358", 7: "7/10/-358", 8:
"6/11/-358", 9: "5/12/-358", 10: "3/1/-357", 11: "2/2/-357", 12:
"2/3/-357"}, {1: "31/3/-357", 2: "30/4/-357", 3: "29/5/-357", 4:
"28/6/-357", 5: "27/7/-357", 6: "26/8/-357", 7: "25/9/-357", 8:
"25/10/-357", 9: "24/11/-357", 10: "23/12/-357", 11: "21/1/-356", 12:
"20/2/-356", b12: "21/3/-356"}, {1: "19/4/-356", 2: "19/5/-356", 3:
"17/6/-356", 4: "17/7/-356", 5: "15/8/-356", 6: "14/9/-356", 7:
"14/10/-356", 8: "13/11/-356", 9: "12/12/-356", 10: "11/1/-355", 11:
"9/2/-355", 12: "11/3/-355"}, {1: "9/4/-355", 2: "8/5/-355", 3:
"7/6/-355", 4: "6/7/-355", 5: "5/8/-355", 6: "3/9/-355", 7:
"3/10/-355", 8: "2/11/-355", 9: "1/12/-355", 10: "31/12/-355", 11:
"29/1/-354", 12: "28/2/-354"}, {1: "30/3/-354", 2: "28/4/-354", 3:
"27/5/-354", 4: "26/6/-354", 5: "25/7/-354", 6: "24/8/-354", 7:
"22/9/-354", 8: "22/10/-354", 9: "20/11/-354", 10: "20/12/-354", 11:
"18/1/-353", 12: "17/2/-353", b12: "18/3/-353"}, {1: "16/4/-353", 2:
"16/5/-353", 3: "15/6/-353", 4: "14/7/-353", 5: "12/8/-353", 6:
"11/9/-353", 7: "10/10/-353", 8: "9/11/-353", 9: "8/12/-353", 10:
"7/1/-352", 11: "5/2/-352", 12: "7/3/-352"}, {1: "6/4/-352", 2:
"5/5/-352", 3: "4/6/-352", 4: "4/7/-352", 5: "2/8/-352", 6: "1/9/-352",
7: "30/9/-352", 8: "29/10/-352", 9: "27/11/-352", 10: "27/12/-352", 11:
"25/1/-351", 12: "24/2/-351"}, {1: "26/3/-351", 2: "24/4/-351", 3:
"24/5/-351", 4: "23/6/-351", 5: "23/7/-351", 6: "21/8/-351", b6:
"20/9/-351", 7: "19/10/-351", 8: "17/11/-351", 9: "16/12/-351", 10:
"15/1/-350", 11: "13/2/-350", 12: "15/3/-350"}, {1: "13/4/-350", 2:
"13/5/-350", 3: "12/6/-350", 4: "12/7/-350", 5: "10/8/-350", 6:
"9/9/-350", 7: "8/10/-350", 8: "7/11/-350", 9: "6/12/-350", 10:
"5/1/-349", 11: "3/2/-349", 12: "3/3/-349"}, {1: "2/4/-349", 2:
"1/5/-349", 3: "31/5/-349", 4: "30/6/-349", 5: "29/7/-349", 6:
"28/8/-349", 7: "27/9/-349", 8: "26/10/-349", 9: "25/11/-349", 10:
"24/12/-349", 11: "23/1/-348", 12: "21/2/-348", b12: "22/3/-348"}, {1:
"21/4/-348", 2: "20/5/-348", 3: "19/6/-348", 4: "18/7/-348", 5:
"17/8/-348", 6: "16/9/-348", 7: "15/10/-348", 8: "14/11/-348", 9:
"14/12/-348", 10: "12/1/-347", 11: "11/2/-347", 12: "12/3/-347"}, {1:
"10/4/-347", 2: "10/5/-347", 3: "8/6/-347", 4: "8/7/-347", 5:
"6/8/-347", 6: "5/9/-347", 7: "4/10/-347", 8: "3/11/-347", 9:
"3/12/-347", 10: "2/1/-346", 11: "31/1/-346", 12: "2/3/-346"}, {1:
"31/3/-346", 2: "29/4/-346", 3: "29/5/-346", 4: "27/6/-346", 5:
"26/7/-346", 6: "25/8/-346", 7: "23/9/-346", 8: "23/10/-346", 9:
"22/11/-346", 10: "22/12/-346", 11: "20/1/-345", 12: "19/2/-345", b12:
"20/3/-345"}, {1: "18/4/-345", 2: "17/5/-345", 3: "16/6/-345", 4:
"15/7/-345", 5: "13/8/-345", 6: "12/9/-345", 7: "11/10/-345", 8:
"10/11/-345", 9: "10/12/-345", 10: "8/1/-344", 11: "7/2/-344", 12:
"9/3/-344"}, {1: "7/4/-344", 2: "7/5/-344", 3: "5/6/-344", 4:
"5/7/-344", 5: "3/8/-344", 6: "1/9/-344", 7: "1/10/-344", 8:
"30/10/-344", 9: "29/11/-344", 10: "29/12/-344", 11: "27/1/-343", 12:
"26/2/-343"}, {1: "27/3/-343", 2: "26/4/-343", 3: "26/5/-343", 4:
"24/6/-343", 5: "24/7/-343", 6: "22/8/-343", 7: "21/9/-343", 8:
"20/10/-343", 9: "19/11/-343", 10: "18/12/-343", 11: "17/1/-342", 12:
"15/2/-342", b12: "17/3/-342"}, {1: "15/4/-342", 2: "15/5/-342", 3:
"13/6/-342", 4: "13/7/-342", 5: "12/8/-342", 6: "10/9/-342", 7:
"10/10/-342", 8: "8/11/-342", 9: "8/12/-342", 10: "6/1/-341", 11:
"4/2/-341", 12: "5/3/-341"}, {1: "3/4/-341", 2: "3/5/-341", 3:
"1/6/-341", 4: "1/7/-341", 5: "31/7/-341", 6: "30/8/-341", 7:
"28/9/-341", 8: "28/10/-341", 9: "27/11/-341", 10: "27/12/-341", 11:
"24/1/-340", 12: "22/2/-340", b12: "24/3/-340"}, {1: "22/4/-340", 2:
"22/5/-340", 3: "20/6/-340", 4: "20/7/-340", 5: "19/8/-340", 6:
"18/9/-340", 7: "17/10/-340", 8: "16/11/-340", 9: "15/12/-340", 10:
"14/1/-339", 11: "12/2/-339", 12: "13/3/-339"}, {1: "12/4/-339", 2:
"11/5/-339", 3: "9/6/-339", 4: "9/7/-339", 5: "8/8/-339", 6:
"7/9/-339", 7: "7/10/-339", 8: "5/11/-339", 9: "5/12/-339", 10:
"3/1/-338", 11: "2/2/-338", 12: "3/3/-338"}, {1: "1/4/-338", 2:
"1/5/-338", 3: "30/5/-338", 4: "28/6/-338", 5: "28/7/-338", 6:
"27/8/-338", 7: "26/9/-338", 8: "25/10/-338", 9: "24/11/-338", 10:
"24/12/-338", 11: "22/1/-337", 12: "21/2/-337", b12: "21/3/-337"} ],
Arses: [ {1: "19/4/-337", 2: "19/5/-337", 3: "17/6/-337", 4:
"16/7/-337", 5: "15/8/-337", 6: "14/9/-337", 7: "13/10/-337", 8:
"12/11/-337", 9: "12/12/-337", 10: "10/1/-336", 11: "9/2/-336", 12:
"10/3/-336"}, {1: "9/4/-336", 2: "8/5/-336", 3: "7/6/-336", 4:
"6/7/-336", 5: "5/8/-336", 6: "3/9/-336", 7: "3/10/-336", 8:
"1/11/-336", 9: "1/12/-336", 10: "30/12/-336", 11: "29/1/-335", 12:
"28/2/-335"} ],
DariusIII: [ {1: "9/4/-336", 2: "8/5/-336", 3: "7/6/-336", 4:
"6/7/-336", 5: "5/8/-336", 6: "3/9/-336", 7: "3/10/-336", 8:
"1/11/-336", 9: "1/12/-336", 10: "30/12/-336", 11: "29/1/-335", 12:
"28/2/-335", b12: "18/3/-334"}, {1: "17/4/-334", 2: "17/5/-334", 3:
"15/6/-334", 4: "15/7/-334", 5: "13/8/-334", 6: "12/9/-334", 7:
"11/10/-334", 8: "9/11/-334", 9: "9/12/-334", 10: "7/1/-333", 11:
"6/2/-333", 12: "6/3/-333"}, {1: "5/4/-333", 2: "5/5/-333", 3:
"3/6/-333", 4: "3/7/-333", 5: "2/8/-333", 6: "31/8/-333", 7:
"30/9/-333", 8: "29/10/-333", 9: "27/11/-333", 10: "27/12/-333", 11:
"25/1/-332", 12: "24/2/-332"}, {1: "25/3/-332", 2: "24/4/-332", 3:
"23/5/-332", 4: "22/6/-332", 5: "22/7/-332", 6: "21/8/-332", b6:
"19/9/-332", 7: "19/10/-332", 8: "17/11/-332", 9: "16/12/-332", 10:
"15/1/-331", 11: "13/2/-331", 12: "15/3/-331"}, {1: "13/4/-331", 2:
"13/5/-331", 3: "11/6/-331", 4: "11/7/-331", 5: "10/8/-331", 6:
"8/9/-331", 7: "8/10/-331", 8: "6/11/-331", 9: "6/12/-331", 10:
"5/1/-330", 11: "3/2/-330", 12: "4/3/-330"} ] };
// End of the "main" function.
}
function date_update_years() {
var king = date_king.value;
var year = document.getElementById("date_year");
var month = document.getElementById("date_month");
var day = document.getElementById("date_day");
year.options.length = 0;
month.options.length = 0;
day.options.length = 0;
if (king != "null") {
for (var i = 0; i < calendar[king].length; i++) {
year.options[year.options.length] = new Option(i);
}
date_update_months();
} else {
display_result("", "date_result");
}
}
function compare_months(month1, month2) {
var month_order = {1: 1, 2: 2, 3: 3, 4: 4, 5: 5, 6: 6, b6: 7, 7:
8, 8: 9, 9: 10, 10: 11, 11: 12, 12: 13, b12: 14};
return month_order[month1] < month_order[month2] ? -1 :
month_order[month1] > month_order[month2] ? 1 :
0;
}
function date_update_months() {
var king = date_king.value;
var year = date_year.value;
var month = document.getElementById("date_month");
var months_list = Object.keys(calendar[king][year]).sort(compare_months);
month.options.length = 0;
if (king != "null") {
for (var i = 0; i < months_list.length; i++) {
var month_name = months_list[i] == "b6" ? "6b" :
months_list[i] == "b12" ? "12b"
: months_list[i];
month.options[month.options.length] =
new Option(month_name, months_list[i]);
}
date_update_days();
}
}
function nb_days_in_a_month (king, year, month) {
var last_king = kings_order[kings_order.length - 1];
var last_year = calendar[king].length - 1;
var months_list = Object.keys(calendar[king][year]).sort(compare_months);
var last_month = months_list[months_list.length - 1];
var max_nb_days = 40; // This value is arbitrarily chosen.
var first_day = new Date();
var dateParts = calendar[king][year][month].split("/");
first_day.setYear(dateParts[2]);
first_day.setMonth(dateParts[1] - 1);
first_day.setDate(dateParts[0]);
first_day.setHours(0,0,0,0);
var next_month;
if (calendar[king][year]["b" + month]) {
next_month = calendar[king][year]["b" + month];
} else if (month == "b6" && calendar[king][year]["7"]) {
next_month = calendar[king][year]["7"];
} else if (calendar[king][year][(parseInt(month) + 1).toString()]) {
next_month = calendar[king][year][(parseInt(month) + 1).toString()];
} else if (calendar[king][parseInt(year) + 1]) {
next_month = calendar[king][parseInt(year) + 1][1];
} else {
return max_nb_days;
}
var next_day = new Date();
dateParts = next_month.split("/");
next_day.setYear(dateParts[2]);
next_day.setMonth(dateParts[1] - 1);
next_day.setDate(dateParts[0]);
next_day.setHours(0,0,0,0);
return Math.round((next_day - first_day)/(1000*60*60*24));
}
function date_update_days() {
var king = date_king.value;
var year = date_year.value;
var month = date_month.value;
var days_per_month = nb_days_in_a_month(king, year, month);
var day = document.getElementById("date_day");
day.options.length = 0;
if (king != "null") {
for (var i = 1; i <= days_per_month; i++) {
day.options[day.options.length] = new Option(i);
}
date_display_result();
}
}
function date_update_days_old() {
var king = date_king.value;
var year = date_year.value;
var month = date_month.value;
var days_per_month = 30;
var day = document.getElementById("date_day");
day.options.length = 0;
if (king != "null") {
for (var i = 1; i <= days_per_month; i++) {
day.options[day.options.length] = new Option(i);
}
date_display_result();
}
}
function date_display_result() {
var king = date_king.value;
var year = date_year.value;
var month = date_month.value;
var day = date_day.value;
if (king == "null") {
display_result("", "date_result");
} else {
var months = ["January", "February", "March", "April", "May", "June", "July",
"August", "September", "October", "November", "December"];
var dateParts = calendar[king][year][month].split("/");
var first_day = new Date();
first_day.setYear(dateParts[2]);
first_day.setMonth(dateParts[1] - 1);
first_day.setDate(dateParts[0]);
var current_day =
new Date(first_day.setTime(first_day.getTime() + (day - 1)
* (1000 * 60 * 60 * 24)));
var date_format = current_day.getUTCDate() + " "
+ months[current_day.getMonth()] + " "
+ current_day.getFullYear();
display_result(date_format, "date_result");
}
}
////////////////////////////////////////////////////////////////
// Display or hide Introduction
////////////////////////////////////////////////////////////////
// The Introduction gives somes explanation about Mesopotamian
// mathematics. It must be hidden for people using MesoCalc
// everyday (otherwise they will have to go down and down and down
// before seing the calculator). But it is useful for people who
// know nothing about Mesopotamian mathematics. So people can chose
// whether they display it or not.
function display_intro() {
document.getElementById('deplie').style.display = 'block';
document.getElementById('replie').style.display = 'none';
}
function hide_intro() {
document.getElementById('deplie').style.display = 'none';
document.getElementById('replie').style.display = 'block';
}
////////////////////////////////////////////////////////////////
// General arithmetics (base-independant)
////////////////////////////////////////////////////////////////
// This function adds numbers.
function addition_general(nb1, nb2, base) {
// This algorithm is fully general:
// 1. It does not suffer from JavaScript's limitations: sexas can be
// as big as their string can be, even if their decimal
// expression is higher than what JavaScript can accept as a
// number. The only limitation is the length of a string in
// JavaScript, which is 2^31 characters. So, please, do not use
// numbers greater than 10^(2^31), i.e. containing more than two
// billions digits.
// 2. It does not depend on a particular base. It may be 10, or 60,
// or whatever you want.
// Note: addition is always absolute, never floating.
// This is the separator when we note a number. For
// example, when we note 1729 in decimal notation,
// the separator is "". When we write 28.49 in
// sexagesimal notation, the separator is ".". The
// criterium is, of course, to know whether the base
// is less or greater than 10.
var separator = base <= 10 ? "" : ".";
// Take both operands as arrays.
if (!nb1) nb1 = "0";
if (!nb2) nb2 = "0";
var array_nb1 = nb1.split(separator).reverse();
var array_nb2 = nb2.split(separator).reverse();
var array_result = new Array(); // The result array.
var carry = 0;
// Addition of the two sexas, digit by digit: array_result[i] =
// array_nb1[i] + array_nb2[i].
for (var i = 0; i < Math.max(array_nb1.length, array_nb2.length); i++) {
array_result[i] = carry + (array_nb1[i] ? parseInt(array_nb1[i]) : 0)
+ (array_nb2[i] ? parseInt(array_nb2[i]) : 0);
// How to handle the carry.
carry = 0;
if (array_result[i] >= base) {
carry = 1;
array_result[i] -= base;
}
}
if (carry == 1)
array_result[array_result.length] = 1;
// We reverse the result array, so that it appears as a true sexa.
var result = array_result.reverse().join(separator);
return result;
}
function subtraction_general(nb1, nb2, base) {
// This algorithm is fully general:
// 1. It does not suffer from JavaScript's limitations: sexas can be
// as big as their string can be, even if their decimal
// expression is higher than what JavaScript can accept as a
// number. The only limitation is the length of a string in
// JavaScript, which is 2^31 characters. So, please, do not use
// numbers greater than 10^(2^31), i.e. containing more than two
// billions digits.
// 2. It does not depend on a particular base. It may be 10, or 60,
// or whatever you want.
// Note: addition is always absolute, never floating.
// This is the separator when we note a number. For
// example, when we note 1729 in decimal notation,
// the separator is "". When we write 28.49 in
// sexagesimal notation, the separator is ".". The
// criterium is, of course, to know whether the base
// is less or greater than 10.
var separator = base <= 10 ? "" : ".";
if (!nb1) nb1 = "0";
if (!nb2) nb2 = "0";
var array_nb1 = nb1.split(separator).reverse();
var array_nb2 = nb2.split(separator).reverse();
var array_result = new Array(); // The result as an array.
var carry = 0;
// Subtraction of the two sexas, digit by digit: array_result[i] =
// array_nb1[i] - array_nb2[i].
for (var i = 0; i < Math.max(array_nb1.length, array_nb2.length); i++) {
array_result[i] = - carry + (array_nb1[i] ? parseInt(array_nb1[i]) : 0)
- (array_nb2[i] ? parseInt(array_nb2[i]) : 0);
// How to handle the carry.
carry = 0;
if (array_result[i] < 0) {
carry = 1;
array_result[i] += parseInt(base);
}
}
// For negative numbers.
if (carry == 1)
array_result[array_result.length] = 0;
// We reverse the result array, so that it appears as a true sexa.
var result = array_result.reverse().join(separator);
// Remove all useless ".0"s in the tail of the reversed list.
var head = new RegExp("^(0\\\.)+", "g");
// If there is such a tail, then it is replaced by nothing.
if (head.test(result))
result = result.replace(head, "");
return result;
}
// This function multiplies numbers.
function multiplication_general(nb1, nb2, base) {
// This function is fully general:
//
// 1. It does not depend on JavaScript's limitation of 2^53.
//
// 2. It does not depend on any particular base. It can be 10 or 60,
// or whatever you want.
// This algorithm used here is the same as the one taught in French
// schools. For instance (in base 60):
//
// 1.57.01 (with indices i for the multiplicand)
// x 1.03 (with indices j for the multiplier)
// ------------ (here we get a bidimensional array for addition:)
// 5.51.03 (we multiplied 1.57.01 by 3)
// + 1.57.01.00 (we multiplied 1.57.01 by 1, and shifted it to the left)
// ------------
// 2.02.52.03 (we add the results)
//
// To do that, at some point, we need to fill a matrix like:
// ( 3 51 5 * ...) (with j lines)
// ( * 1 57 1 ...) (places marked by * will count as 0 during addition)
// ( * * ... )
// ( * * * ... )
//
// To make things easier, the number 1.3 is represented as 3.1 (this
// is why we use reverse() a lot).
//
// Why use this algorithm, instead of JavaScript's decimal
// multiplication? Because it is limited to 2^53. With our
// algorithm, there is no use of big numbers. Instead, we consider
// numbers as mere strings of digits. Now, the limitation is
// something like 10^(2^35).
// We define the separator, which is "" in base 10
// (for example in "1729"), and "." in other bases
// (such as "28.49" in base 60).
var separator = base <= 10 ? "" : ".";
var multiplicand = nb1.split(separator).reverse(); // The
// multiplicand, seen as a reversed array.
var multiplier = nb2.split(separator).reverse(); // The multiplier,
// seen as a reversed array as well.
var i = 0; // Indices for the multiplicand.
var j = 0; // Indices for the multiplier.
var carry = 0; // The carry.
// Create the bidimensional array (the matrix) for addition.
var addition = new Array();
for (j = 0; j < multiplier.length; j++)
addition[j] = new Array();
// Perform the multiplications.
for (var j = 0; j < multiplier.length; j++) { // For each digit of the
// multiplier.
for (i = 0; i < multiplicand.length; i++) { // For each digit of
// the multiplicand.
// Multiply the i-th digit of the multiplicand by the j-th
// digit of the multiplier, and store the result in the cell
// (j, j+i).
addition[j][j+i] =
String(parseInt(multiplicand[i]) * parseInt(multiplier[j])
+ carry); // In base 60, this will never be more
// than 59*59+1 (hence, it is always
// less than 2^53).
carry = 0; // Reset the carry after using it.
// Avoid false "sexagesimal" digits like 127 in base 60:
// remove 2*60 and put 2 in the carry.
while (parseInt(addition[j][j+i]) >= base) {
addition[j][j+i] = String(parseInt(addition[j][j+i]) - base);
carry += 1;
}
}
if (carry != 0) { // For the last carry of the line, if any.
addition[j][j+i] = String(carry);
}
carry = 0; // Reset carry before going to the next line of the matrix.
}
// Fill the matrix with zeros under the diagonal, as follows:
//
// ( ... . . . )
// ( ... . . 0 )
// ( ... . 0 0 )
// ( ... 0 0 0 )
for (var j = 0; j < multiplier.length; j++)
for (var i = 0; i < j; i++)
addition[j][i] = "0";
// Perform the additions.
var result = "0";
// Add the lines of the matrix, one by one. No number in this
// computation will be greater than "base x 2 - 1".
for (var j = 0; j < multiplier.length; j++) {
result = addition_general(result,
addition[j].reverse().join(separator),
base);
}
var head = new RegExp("^(0" + separator + ")+", "g"); // To remove
// useless 0s as in "00412".
result = result.replace(head, "");
result = result == "" ? "0" : result;
// This is it!
return result;
}
// This function divides numbers, and returns a hash table containing
// both result["quotient"] and result["remainder"].
function division_general(dividend, divisor, base) {
// TODO: this function only works in decimal numbers. It should be
// debugged in order to work with sexagesimal arithmetics. Until
// then, I use a (harmless) trick in division_sexa().
var separator = base <= 10 ? "" : ".";
var big_dividend = new String(dividend); // The decimal number to convert.
var small_dividend = new String(""); // The small parts (between 0
// and 599) which will effectively be divided. So we are sure we
// will never reach 2^53.
var quotient = new String(""); // Quotient of the current
// division by 60.
var remainder = "0"; // The remainder.
var head = new RegExp("^(0" + separator + ")+", "g"); // To remove
// useless 0s as in "00412".
var result = new Object();
do { // Take small parts of the dividend to perform little
// divisions from left to right.
// We feed the "small dividend" by removing the first digits
// of the "big dividend".
small_dividend = small_dividend.replace(head, "")
+ big_dividend.substr(0, 1);
big_dividend = big_dividend.substr(1, big_dividend.length);
// Update the quotient and the remainder.
if (parseInt(small_dividend) < parseInt(divisor)) {
quotient = quotient + "0";
remainder = small_dividend;
} else {
// Remember: "small_dividend" is really small! (less than
// base^2). So the following operations are harmless up to
// the base 2^26...
quotient =
quotient
+ Math.floor(parseInt(small_dividend) / parseInt(divisor));
remainder = String(parseInt(small_dividend) % parseInt(divisor));
small_dividend = remainder;
}
} while (big_dividend.length != 0);
quotient = quotient.replace(head, ""); // Remove the "0"s at head.
// The result is a hash table, containing both result["quotient"]
// and result["remainder"].
result["quotient"] = quotient;
result["remainder"] = String(remainder);
return result;
}
// Compute powers in any base.
function power_general(nb, power_nb, base) {
// This is a quick algorithm for powers.
//
// The idea is the following. Say we want to compute 2^13. Instead
// of computing 2*2*2*2*2*2*2*2*2*2*2*2*2, we compute 2*2 = 4
// (= 2^2), 4*4 = 16 (= 2^4) and 16*16 = 256 (= 2^8). We finally
// compute 256*16*2 = 8192.
//
// How to do that? Take your power, here 13. Write it in binary
// notation: you get 1101, which is composed of four binary digits.
// We will then need four powers: 2, 2*2, 4*4, 16*16. Take the
// powers which are representend by 1 in the binary number: 16, 4,
// 2. Multiply them and you get the result.
//
// The complexity should be something like n.log(n) instead of n.
// Trivial results.
var result = "1";
if (power_nb == "0" || nb == "1")
return result;
// The separator of digits depends on the base chosen.
var separator = base <= 10 ? "" : ".";
// Remove useless head of numbers, such as 00412.
var head = new RegExp("^(0" + separator + ")+", "g");
nb.replace(head, "");
// The binary expression of the power.
var power_binary = base_to_base(power_nb, base, 2).split("").reverse();
// The list of powers which we will need.
var powers = new Object();
powers[0] = "1";
powers[1] = nb;
// Compute all needed powers.
for (var i = 2; i <= power_binary.length; i++) {
powers[i] = multiplication_general(powers[i-1], powers[i-1], base);
}
// Multiply all needed powers.
for (var i = 0; i < power_binary.length; i++) {
if (power_binary[i] == "1") {
result = multiplication_general(result, powers[i+1], base);
}
}
// That's all, folks!
return result;
}
////////////////////////////////////////////////////////////////
// Base conversion
////////////////////////////////////////////////////////////////
// This function converts numbers from one base to another.
function base_to_base (number, from, to) {
var result = from == to ? number :
base10_to_base(base_to_base10(number, from), to);
return result;
}
function base_to_base10(number, from) {
var result = "0";
var puissance;
var to = 10;
// This is the separator between digits, which is "" until base 10
// (as in 1729), but "." for higher bases (as in 28.49).
var separator = from <= 10 ? "" : ".";
// The number is treated as a string of digits, not as a number
// (otherwise there would be the limitation at 2^53).
var array_number = number.split(separator);
// Let us take every digit of the number to convert.
for (var i = 0; i < array_number.length; i++) {
// We compute the power which corresponds to it. (The trick is
// that these powers themselves are considered as strings of
// digits, so that we never compute with big numbers such as
// 2^53).
puissance = "1";
for (var j = 1; j < array_number.length -i; j++) {
puissance =
multiplication_deci(puissance, from); // For
// example, we use the decimal multiplication to compute
// powers of 60.
}
// The number is decomposed into multiples of powers of the base (such
// as 1000+700+20+9), which we finally just have to add.
result = addition_general(result,
multiplication_deci(puissance,
array_number[i]),
to);
}
return result;
}
function base10_to_base(number, base) {
// The algorithm corresponds to the way pupils perform division in
// France. Why so? Because their algorithm does not depend on the
// length of the numbers: they just perform the division from left
// to right, whithout needing to know how big the number is. This
// way, we will not depend on JavaScript's number limitation at
// 2^53: the value of numbers is only limited by that of strings
// (which, contrary to 2^53, is far enough for Mesopotamian
// mathematics).
// Division is iterated. For example, let us convert 24721 into a sexa.
// 24721 is the "big dividend". We take 2, then 24, then 247, which is
// eventually a greater number than 60 (but less than 599, so far from
// 2^53), as "small dividend". We divide by 60. The quotient is 004, the
// remainder is 7; it becomes the "small dividend". Then we take 72 as
// "small dividend", and so on. At the end, we get 00412 as quotient. We
// remove the first zeros and we get 412. Now, 412 contains at least
// three digits, which means that it is greater than 60. So we do once
// again the same, until getting 006 as a quotient. Then we take the
// last quotient (here 6), followed by the reversed list of remainders
// (here 52 and 1), and we get the sexa which corresponds to 24721,
// i.e 6.52.1.
var big_dividend = new String(number); // The decimal number to convert.
var small_dividend = new String(""); // The small parts (between 0
// and 599) which will effectively be divided. So we are sure we
// will never reach 2^53.
var quotient = new String(""); // Quotient of the current division by 60.
var remainder = new Array(); // Array of successive remainders.
var i = 0; // Indices for the list of remainders.
var head = new RegExp("^0+", "g"); // To remove useless 0s as in "00412".
var separator = base <= 10 ? "" : ".";
do { // For each quotient which is greater than 60.
quotient = "";
small_dividend = "";
do { // Take small parts of the dividend to perform little
// divisions from left to right.
// We feed the "small dividend" by removing the first digits
// of the "big dividend".
small_dividend = small_dividend + big_dividend.substr(0,1);
big_dividend = big_dividend.substr(1,big_dividend.length);
// Update the quotient and the remainder.
if (parseInt(small_dividend) < base) {
quotient = quotient + "0";
remainder[i] = parseInt(small_dividend);
} else {
// Remember: "small_dividend" is really small! (less
// than 599). So the following operations are harmless.
quotient =
quotient + Math.floor(parseInt(small_dividend) / base);
remainder[i] = parseInt(small_dividend) % base;
small_dividend = remainder[i];
}
} while (big_dividend.length != 0 || parseInt(small_dividend) >= base);
i++; // Now we need to compute the next sexagesimal digit.
quotient = quotient.replace(head, ""); // Remove the "0"s at head.
big_dividend = quotient; // Recursive division.
} while (big_dividend.length > base.length
|| parseInt(big_dividend) >= base); // Because of the first
// condition (length >= 3), the second one (dividend >= 60) is only
// checked if the dividend is less than 99. Hence, there is no
// chance to compare 60 with 2^53. THIS WOULD NOT BE THE CASE IF
// THESE TWO CONDITIONS WERE PERMUTED!
// The result is the quotient (if not null) followed by the reversed
// list of remainders.
var result = (quotient != 0 ? quotient + separator : "")
+ remainder.reverse().join(separator);
// Return the number in absolute mode.
return result;
}
////////////////////////////////////////////////////////////////
// Sexagesimal numbers
////////////////////////////////////////////////////////////////
// This function takes a sexa as argument, and converts it into a deci.
function Sexa_vers_deci (sexa) {
// WARNING: it does not check if the argument really is a sexa. You
// must have checked it before calling this function.
var result = base_to_base(sexa, "60", "10");
return result;
}
// This function handles the conversion form from sexa to deci.
function sexa2deci(form) {
var sexa = form.input.value;
// Checks that the input really is a sexa and calls the conversion
// function.
var result = is_sexa(sexa) ? Sexa_vers_deci(sexa) : not_sexa;
// Display the result.
display_result(result, 'conversion-60-10');
}
// This function takes a sexa as argument, and returns it in floating
// mode (concretely, it just cuts the ".0"s at the end).
function floating(sexa) {
// The tail of an absolute number consists in a list of ".0"s (see
// e.g. the number 1.20.0.0). This is what we are going to cut in
// order to convert it into a floating number.
var tail = new RegExp("(\\\.0)+$", "g"); // "g" option to catch all ".0"s
// If the argument "sexa" has such a tail, then it is replaced by
// nothing.
if (tail.test(sexa))
sexa = sexa.replace(tail, "");
// Now we have a floating number.
return sexa;
}
// This function returns a floating or an absolute sexa, depending on
// the mode currently chosen by the user.
function floating_or_absolute(sexa) {
return (sexa_floating == true) ? floating(sexa) : sexa;
}
////////////////////////////////////////////////////////////////
// Decimal numbers
////////////////////////////////////////////////////////////////
// This function takes a deci as argument, and returns it as a sexa
// (floating or absolute, depending of the computing mode chosen by
// the user).
function Deci_to_sexa(number) {
// WARNING: Do not use this function in your code! Use instead one of
// these three functions:
//
// 1. Deci_to_sexa_floating_or_absolute,
// 2. Deci_to_sexa_absolute,
// 3. Deci_to_sexa_floating.
return base_to_base(String(number), "10", "60");
}
// This function takes a deci as argument, and returns it as a sexa (in
// absolute or floating mode, depending on what the user wants).
function Deci_to_sexa_floating_or_absolute(number) {
var result = floating_or_absolute(Deci_to_sexa(number));
return result;
}
// This function takes a deci as argument, and returns it as a sexa
// (always absolute, even in floating mode).
function Deci_to_sexa_absolute(number) {
var result = Deci_to_sexa(number);
return result;
}
// This function takes a deci as argument, and returns it as a sexa
// (always floating, even in absolute mode).
function Deci_to_sexa_floating(number) {
var result = floating(Deci_to_sexa(number));
return result;
}
// Conversion from deci to sexa.
function deci2sexa(form) {
var deci = form.input.value;
var result;
// Some easter eggs linked with the history of MesoCalc...
switch (deci) {
case "Christine": // Christine Proust
case "Cécile": // Cécile Michel
result = "d-nisaba zà-mí !";
break;
case "Karine": // Karine Chemla
result = "林力娜";
break;
case "Bob": // Robert Middeke-Conlin
result = "lu2-im-na4-na";
break;
case "Baptiste": // Baptiste Mélès
result = "梅乐思";
break;
default:
// The default behaviour is to convert the number if it is a deci.
result =
is_int(deci) ? Deci_to_sexa_floating_or_absolute(deci) : not_deci;
}
// Display the result.
display_result(result, 'conversion-10-60');
// Why these easter eggs? Let us say some words about MesoCalc's
// birth context.
//
// On 25-29 March 2013, the SAW group organized the conference
// "Cultures of computation and quantification in the ancient world"
// in Paris (Université Paris-Diderot). Baptiste Mélès had a talk
// about how to use concepts of computer science to describe the use
// of computing tools such as the Chinese abacus. Robert
// Middeke-Conlin's talk was "The Nazbalum in Old Babylonian
// Mesopotamia: A Concrete Number or Administrative Tool"; Baptiste
// Mélès had to prepare a commentary for this talk, but since he
// knew absolutely nothing about Mesopotamian mathematics, he had to
// read some books about it, such as Christine Proust's; he learned
// to compute in sexagesimal notation, and was exercising to perform
// sexagesimal multiplications and divisions on paper, but he wanted
// to check his computations. This is why we wrote the following
// e-mails to Christine Proust...
// Date: Sun, 10 Mar 2013 16:09:53 +0100
// From: Baptiste Mélès <baptiste.meles@gmail.com>
// To: "christine.proust" <christine.proust@wanadoo.fr>
// Subject: Re: Classiques des mathématiques mésopotamiennes
//
// Chère Christine,
//
// Merci beaucoup pour ces textes ! Je vais me régaler : c'est
// vraiment joli, le cunéiforme.
//
// Bon après-midi !
//
// Baptiste.
// Date: Sun, 10 Mar 2013 17:22:45 +0100
// From: "christine.proust" <christine.proust@wanadoo.fr>
// To: Baptiste Mélès <baptiste.meles@gmail.com>
// Subject: Re: Classiques des mathématiques mésopotamiennes
//
// Attention, c'est dangereux le cunéiforme, c'est tellement beau qu'on
// tombe facilement dedans!
// bonne lecture
// chr
// Date: Mon, 11 Mar 2013 18:41:46 +0100
// From: Baptiste Mélès <baptiste.meles@gmail.com>
// To: "christine.proust" <christine.proust@wanadoo.fr>
// Subject: Re: Classiques des mathématiques mésopotamiennes
//
// Chère Christine,
//
// > Attention, c'est dangereux le cunéiforme, c'est tellement beau
// > qu'on tombe facilement dedans!
//
// Tu as bien raison : je me demande même si je ne vais pas arracher
// quatre boules toutes les deux tringles de mon boulier pour
// pouvoir compter en base 60 dans la vie de tous les jours.
//
// À ce propos, connais-tu un logiciel magique pour vérifier
// facilement les calculs en base 60 ? Pour l'instant, je les fais
// sur papier ou sur boulier, avec la règle à calcul en guise de
// table d'inverses, mais je me demande si je ne vais pas faire un
// petit programme pour me simplifier la vie...
//
// Bonne semaine,
//
// Baptiste.
// Date: Mon, 11 Mar 2013 19:07:11 +0100
// From: Christine Proust <christine.proust@paris7.jussieu.fr>
// To: Baptiste Mélès <baptiste.meles@gmail.com>
// Subject: Re: Classiques des mathématiques mésopotamiennes
//
// Tu sauras tout sur le calcul sexagésimal avec des jetons lors de la
// séance du 12 juin.
// En attendant, j'ai bien évidemment programmé le calcul positionnel
// sexagésimal flottant, avec des opérations qui font:
// - la suppression des ordres de grandeurs
// - la multiplication
// - l'inversion des nombres réguliers
// - les racines carrées et cubiques (quand elles sont exactes)
// - les décompositions en facteur premiers
// - la liste des nombres réguliers étant donnés le premier chiffre et le
// nombre de positions sexagésimales
// - la conversion base 10 / base 60 et vice versa
// - des tables diverses
// etc
// Je l'ai fait avec Mathematica. Si tu es équipé, je t'envoie les
// fichiers tout de suite. Sinon, il faudra que tu l'installes.
// Date: Tue, 12 Mar 2013 08:15:38 +0100
// From: Baptiste Mélès <baptiste.meles@gmail.com>
// To: Christine Proust <christine.proust@paris7.jussieu.fr>
// Subject: Re: Classiques des mathématiques mésopotamiennes
//
// Chère Christine,
//
// Hélas, je n'ai pas Mathematica, mais j'aimerais bien jeter un
// coup d'œil à ton code source (dont la liste de fonctionnalités
// aurait fait saliver plus d'un scribe !), pour pouvoir l'adapter
// sur mes logiciels...
//
// Bonne journée et merci !
//
// Baptiste.
// Date: Tue, 12 Mar 2013 11:00:18 +0100
// From: Christine Proust <christine.proust@paris7.jussieu.fr>
// To: Baptiste Mélès <baptiste.meles@gmail.com>, pichaigneau
// <pichaigneau@laposte.net>
// Subject: Re: Classiques des mathématiques mésopotamiennes
//
// [-- Attachement #1 --]
// [-- Type : text/plain, Codage : 8bit, Taille : 1,8K --]
//
// Cher Baptiste, Je n'ai pas le code source car j'ai utilisé les
// fonctions prédéfinies de Mathematica. Tu trouveras ci-joint le
// fichier où j'ai écrit les lignes de programme (calculette noyau),
// et le fichier contenant uniquement la liste des fonctions que
// j'utilise au quotidien (calculette active). Je sépare les deux
// fichiers pour éviter d'introduire des bugs par mégarde dans mes
// lignes de programme. Je te mets aussi une notice avec quelques
// explications.
// Si tu arrives à transformer tout cela en utilisant un
// logiciel libre, tu auras fait une oeuvre d'intérêt général de
// grande importance. En effet, je ne pense pas que des fonctions
// aussi simples que celles dont on a besoin pour le calcul
// sexagésimal flottant nécessitent la grosse machinerie
// Mathematica, et j'aimerais bien rendre ma calculette babylonienne
// accessible à tous sur le web, ce que Mathematica ne permet pas à
// cause de ses droits de propriété.
// Je mets Pierre en copie de ce message car il est lui aussi intéressé
// par l'idée de la mise en service publique de ma calculette magique.
// bien à toi
// Christine
// Date: Tue, 12 Mar 2013 14:27:05 +0100
// From: Baptiste Mélès <baptiste.meles@gmail.com>
// To: Christine Proust <christine.proust@paris7.jussieu.fr>
// CC: pichaigneau <pichaigneau@laposte.net>
// Subject: Re: Classiques des mathématiques mésopotamiennes
//
// Chère Christine, cher Pierre,
//
// Parfait, cela m'amusera beaucoup !
//
// Je pense que je vais programmer ta calculatrice mésopotamienne en
// JavaScript, ce qui permettra de l'utiliser aussi facilement sur
// un ordinateur local — quel que soit son système d'exploitation —
// que sur Internet.
//
// (Voilà pour la raison officielle. La vraie raison est que je
// voulais apprendre le JavaScript depuis quelque temps et que c'est
// l'occasion rêvée.)
//
// Si tu n'as pas d'objection, je suis assez partisan de la licence
// GPL : n'importe qui pourra copier le fichier, le modifier, et
// redistribuer ses modifications — à condition, toutefois, que ce
// soit en offrant aux utilisateurs suivants les mêmes libertés.
//
// Dans mes rêves les plus fous, une première version serait prête
// pour le colloque SAW : je m'y mets tout de suite.
//
// À bientôt,
//
// Baptiste.
// Date: Tue, 12 Mar 2013 14:38:14 +0100
// From: Christine Proust <christine.proust@paris7.jussieu.fr>
// To: Baptiste Mélès <baptiste.meles@gmail.com>
// CC: pichaigneau <pichaigneau@laposte.net>
// Subject: Re: Classiques des mathématiques mésopotamiennes
//
// Géant! mille mercis.
// chr
// Date: Tue, 12 Mar 2013 16:42:57 +0100
// From: Christine Proust <christine.proust@paris7.jussieu.fr>
// To: pichaigneau@laposte.net
// CC: Baptiste Mélès <baptiste.meles@gmail.com>
// Subject: Re: Classiques des mathématiques mésopotamiennes
//
// Va pour GPL. J'ignore totalement de quoi il s'agit, mais
// renseignements pris auprès de Wikipedia, l'idée me paraît
// sympathique. chr
// Date: Tue, 12 Mar 2013 18:06:27 +0100
// From: Baptiste Mélès <baptiste.meles@gmail.com>
// To: Christine Proust <christine.proust@paris7.jussieu.fr>
// CC: pichaigneau@laposte.net
// Subject: Re: Classiques des mathématiques mésopotamiennes
//
// Chère Christine, cher Pierre,
//
// Pardon, j'ai été un peu laconique pour la licence... Voici donc
// un peu plus de détails sur l'idée générale qui a donné naissance
// à la GPL.
//
// Il existait, d'un côté, des logiciels propriétaires, c'est-à-dire
// dont le code source est secret, que l'utilisateur ne peut donc
// pas modifier, et encore moins copier ou redistribuer.
//
// D'un autre côté, il existait des licences libres « un peu trop
// libres » (comme la licence BSD), qui laissait à l'utilisateur
// toute liberté (copie, modification, redistribution)... y compris
// celle de piller un code source libre pour en faire un code
// propriétaire.
//
// La licence GPL, pour éviter cette dernière dérive, est munie de
// ce que l'on appelle une « clause virale » : on laisse toute
// liberté à l'utilisateur, à condition qu'il ne privatise pas le
// code, et qu'il fasse profiter les autres des libertés dont il a
// lui-même profité.
//
// Vous pourrez donc faire tout ce que vous voulez de mon programme
// si vous voulez le réutiliser ailleurs, sans avoir à solliciter
// mon autorisation. Enfin, une fois que je l'aurai écrit...
//
// Bonne soirée !
//
// Baptiste.
// Date: Wed, 13 Mar 2013 11:10:04 +0100
// From: Baptiste Mélès <baptiste.meles@gmail.com>
// To: Christine Proust <christine.proust@paris7.jussieu.fr>
// CC: pichaigneau@laposte.net
// Subject: Re: Classiques des mathématiques mésopotamiennes
//
// Chère Christine, cher Pierre,
//
// Et voici une première version de la calculatrice mésopotamienne !
// http://baptiste.meles.free.fr/site/mesocalc.html
//
// Elle pèse seulement 32 Ko, pour environ 300 lignes de code. Vous
// pouvez l'utiliser en ligne, ou copier le fichier HTML sur votre
// ordinateur local et l'utiliser hors connexion. L'interface est
// rudimentaire, mais on ne fera de toute façon jamais aussi beau
// qu'une tablette d'argile.
//
// Il me reste à implanter quelques fonctions de la liste de
// Christine :
//
// - inversion ;
// - quotient ;
// - règle de trois ;
// - table de multiplication ;
// - liste des nombres réguliers étant donnés le premier chiffre et le
// nombre de chiffres ;
// - décomposition en facteurs premiers ;
// - suite géométrique de premier terme, raison et nombre de termes donnés.
//
// Signalez-moi si vous détectez des bogues ou désirez de nouvelles
// fonctionnalités !
//
// Une question, par exemple : faut-il que je supprime par défaut
// les ordres de grandeur (en écrivant 30.0 x 3 = 1.30 au lieu de
// 1.30.0) ?
//
// N'hésitez pas à faire tester ce programme par vos amis
// mésopotamistes...
//
// À bientôt,
//
// Baptiste.
}
////////////////////////////////////////////////////////////////
// Additions
////////////////////////////////////////////////////////////////
// These are the algorithms for addition. They do not deal with HTML:
// that is pure JavaScript.
// Sexagesimal addition.
function addition_sexa(nb1, nb2) {
var base = 60;
// In case nb1 or nb2 be decimal, convert them into sexagesimal
// numbers.
nb1 = is_sexa(nb1) ? nb1 : Deci_to_sexa_absolute(nb1);
nb2 = is_sexa(nb2) ? nb2 : Deci_to_sexa_absolute(nb2);
var result = addition_general(nb1, nb2, base);
return result;
}
// Decimal addition.
function addition_deci(nb1, nb2) {
var base = 10;
var result = addition_general(nb1, nb2, base);
return result;
}
////////////////////////////////////////////////////////////////
// Addition forms
////////////////////////////////////////////////////////////////
// These are the algorithms for the addition forms. They do deal with
// HTML.
// This function initializes the addition formular.
function clear_addition(form) {
// Initialize the addition fields, to avoid side effects.
for (var i = 1; i <= nb_additions; i++) {
form["input" + i].value = "";
addenda[i] = 0;
}
nb_additions = 2;
// Display it (namely nothing!).
document.getElementById('nouv_addition').innerHTML = "";
document.getElementById('tableau_addition').innerHTML = "";
document.getElementById('addenda1').focus();
}
function addition(form) {
// addenda[] is an array, where addenda[1], addenda[2] etc. will be
// the operands (if they are undefined, they will be treated
// as 0). The sum will be stored in addenda[0].
addenda[0] = "0";
// If all input numbers are sexas, we add them.
for (var i = 1; i <= nb_additions; i++) {
var sexa = form["input" + i].value;
// Every empty field is treated as 0 in "sexa", but displayed as
// empty in "addenda[i]".
if (!sexa)
sexa = "0";
addenda[i] = form["input" + i].value;
addenda[0] = addition_sexa(addenda[0], sexa);
}
// This is a magic feature: each time you perform an addition, a new
// addition field is given. Thus you can perform n-ary additions
// very easily.
var contenu = "";
nb_additions++; // The number of addenda, first defined in main().
for (var i = 3; i <= nb_additions; i++) {
contenu = contenu
+ "+ <input type='text' "
+ " name='input" + i + "' "
+ " id='addenda" + i + "' "
+ ' value="' + ((addenda[i]) ? addenda[i] : "") + '" '
+ " onkeypress=\"if (event.keyCode == 13) addition(this.form)\" />";
}
// Display the result.
document.getElementById('nouv_addition').innerHTML = contenu;
// Display the result in a table.
var result = "<p><table class=\"center\">"
+ "<tr><th>Addition</th></tr>";
for (var i = 1; i < nb_additions; i++) {
result = addenda[i] ?
result + '<tr><td align="right"> '
+ addenda[i]
+ '</td></tr>'
: result;
}
result += '<tr><td></td></tr><tr><td align="right"><strong>= ' + addenda[0]
+ '</strong></td></tr>'
+ "</table></p>";
document.getElementById('tableau_addition').innerHTML = result;
// Give the focus to the new field.
document.getElementById("addenda" + nb_additions).focus();
}
////////////////////////////////////////////////////////////////
// Subtractions
////////////////////////////////////////////////////////////////
// These functions are pure JavaScript. They do not deal with HTML.
// This function performs the subtraction of sexas.
function subtraction_sexa(nb1, nb2) {
var base = "60";
// In case nb1 or nb2 be decimal, convert them into sexagesimal
// numbers.
nb1 = is_sexa(nb1) ? nb1 : Deci_to_sexa_absolute(nb1);
nb2 = is_sexa(nb2) ? nb2 : Deci_to_sexa_absolute(nb2);
var result = subtraction_general(nb1, nb2, base);
return result;
}
// This function performs the subtraction of decimal numbers.
function subtraction_deci(nb1, nb2) {
// This function is probably useless in this source code. It is just
// here for the sake of generality and symmetry :-)
var base = "10";
var result = subtraction_general(nb1, nb2, base);
return result;
}
////////////////////////////////////////////////////////////////
// Subtraction forms
////////////////////////////////////////////////////////////////
// These functions are related with the subtraction forms. They do deal
// with HTML.
// This function clears the subtraction form.
function clear_soustraction(form) {
// Initialize the subtraction fields.
for (var i = 1; i <= nb_soustractions; i++) {
form["input" + i].value = "";
subtrahenda[i] = 0;
}
nb_soustractions = 2; // Number of subtrahenda, defined in main().
// Display it (namely nothing).
document.getElementById('nouv_soustraction').innerHTML = "";
document.getElementById('tableau_soustraction').innerHTML = "";
document.getElementById('subtrahenda1').focus();
}
// This function handles the subtraction formular.
function soustraction(form) {
// If all numbers are sexas, subtract them.
for (var i = 1; i <= nb_soustractions; i++) {
var sexa = form["input" + i].value;
subtrahenda[i] = form["input" + i].value;
}
// subtrahenda[0] will contain the result; subtrahenda[1] is the
// first number, from which the following ones will be subtracted.
if (!subtrahenda[1])
subtrahenda[1] = "0";
subtrahenda[0] = subtrahenda[1];
// Perform the subtractions.
for (var i = 2; i <= nb_soustractions; i++) {
// If subtrahenda[i] is empty, it will be displayed as empty,
// but treated as 0.
var sexa = subtrahenda[i] ? subtrahenda[i] : "0";
if (less_equal_sexa(sexa, subtrahenda[0])) {
subtrahenda[0] = subtraction_sexa(subtrahenda[0], sexa);
} else {
// Abort if the result is negative.
subtrahenda[0] = negative;
break;
}
}
// A magic feature: each time a subtraction is performed, add a new
// subtraction field. So you can perform n-ary subtractions.
var contenu = "";
nb_soustractions++; // First defined in main().
for (var i = 3; i <= nb_soustractions; i++) {
contenu = contenu
+ "- <input type='text' "
+ " name='input" + i + "' "
+ " id='subtrahenda" + i + "' "
+ ' value="' + ((subtrahenda[i]) ? subtrahenda[i] : "") + '" '
+ " onkeypress=\"if (event.keyCode == 13) soustraction(this.form)\" />";
}
// Display the result.
document.getElementById('nouv_soustraction').innerHTML = contenu;
// Display the computation in a table.
var result = "<p><table class=\"center\">"
+ "<tr><th>Subtraction</th></tr>";
for (var i = 1; i < nb_soustractions; i++) {
result = subtrahenda[i] ?
result + '<tr><td align="right"> '
+ (subtrahenda[i] ? subtrahenda[i] : "0")
+ '</td></tr>'
: result;
}
result += '<tr><td></td></tr><tr><td align="right"><strong>= '
+ subtrahenda[0]
+ '</strong></td></tr>'
+ "</table></p>";
document.getElementById('tableau_soustraction').innerHTML = result;
// Give the focus to the new subtraction field.
document.getElementById("subtrahenda" + nb_soustractions).focus();
}
////////////////////////////////////////////////////////////////
// Multiplications
////////////////////////////////////////////////////////////////
// These functions are pure JavaScript. They do not deal with HTML.
// Decimal multiplication.
function multiplication_deci(nb1, nb2) {
var base = 10;
var result = multiplication_general(nb1, nb2, base);
return result;
}
// Absolute sexagesimal multiplication.
function multiplication_sexa_absolu(nb1, nb2) {
var base = 60;
// In case nb1 or nb2 be decimal, convert them into sexagesimal
// numbers.
nb1 = is_sexa(nb1) ? nb1 : Deci_to_sexa_absolute(nb1);
nb2 = is_sexa(nb2) ? nb2 : Deci_to_sexa_absolute(nb2);
var result = multiplication_general(nb1, nb2, base);
return result;
}
// Floating or absolute sexagesimal multiplication.
function multiplication_sexa(nb1, nb2) {
var base = 60;
// In case nb1 or nb2 be decimal, convert them into sexagesimal
// numbers.
nb1 = is_sexa(nb1) ? nb1 : Deci_to_sexa_absolute(nb1);
nb2 = is_sexa(nb2) ? nb2 : Deci_to_sexa_absolute(nb2);
var result = multiplication_sexa_absolu(nb1, nb2, base);
return floating_or_absolute(result);
}
////////////////////////////////////////////////////////////////
// Multiplication forms
////////////////////////////////////////////////////////////////
// These functions are related with the multiplication forms. They do
// deal with HTML.
function clear_multiplication(form) {
// This function clears the multiplication formular.
// Reset the multiplication fields.
for (var i = 1; i <= nb_multiplications; i++) {
form["input" + i].value = "";
multiplicanda[i] = "";
}
nb_multiplications = 2;
// Display it (namely nothing).
document.getElementById('nouv_multiplication').innerHTML = "";
document.getElementById('tableau_multiplication').innerHTML = "";
document.getElementById('multiplicanda1').focus();
}
function multiplication(form) {
// On rangera ici le produit.
multiplicanda[0] = "1";
// On fait la multiplication si tout est sexagésimal.
for (var i = 1; i <= nb_multiplications; i++) {
var sexa = form["input" + i].value;
multiplicanda[i] = form["input" + i].value;
multiplicanda[0] =
multiplication_sexa(multiplicanda[0],
multiplicanda[i] ? multiplicanda[i] : "1");
}
// Et on ajoute des boîtes de multiplication.
var contenu = "";
nb_multiplications++;
for (var i = 3; i <= nb_multiplications; i++) {
contenu = contenu
+ "× <input type='text' "
+ " name='input" + i + "' "
+ " id='multiplicanda" + i + "' "
+ ' value="' + ((multiplicanda[i]) ? multiplicanda[i] : "") + '" '
+ " onkeypress=\"if (event.keyCode == 13) multiplication(this.form)\" />";
}
document.getElementById('nouv_multiplication').innerHTML = contenu;
var result = "<p><table class=\"center\">"
+ "<tr><th>Multiplication</th></tr>";
for (var i = 1; i < nb_multiplications; i++) {
result = multiplicanda[i] ?
result + '<tr><td align="right"> '
+ multiplicanda[i]
+ '</td></tr>'
: result;
}
result += '<tr><td></td></tr><tr><td align="right"><strong>= '
+ multiplicanda[0]
+ '</strong></td></tr>'
+ "</table></p>";
document.getElementById('tableau_multiplication').innerHTML = result;
// Donner le focus au nouveau nombre.
document.getElementById("multiplicanda" + nb_multiplications).focus();
}
////////////////////////////////////////////////////////////////
// Divisions
////////////////////////////////////////////////////////////////
// Division for sexagesimal numbers. This function returns both
// result["quotient"] and result["remainder"].
function division_sexa(dividend, divisor) {
var result = new Object();
if (sexa_floating) {
result["quotient"] = multiplication_sexa(dividend, igi(divisor));
result["remainder"] = "0";
} else {
return division_sexa_absolute(dividend, divisor);
}
// The result is a hash table: it contains both result["quotient"]
// and result["remainder"].
return result;
}
// Division for sexagesimal numbers. This function returns both
// result["quotient"] and result["remainder"].
function division_sexa_absolute(dividend, divisor) {
var result = new Object();
var result_deci = // This is a trick, using a decimal computation. That
// is because my division_general algorithm is still
// not so general... Fortunately, this is harmless,
// because we do not use big numbers.
division_general(Sexa_vers_deci(dividend),
Sexa_vers_deci(divisor),
"10");
result["quotient"] = Deci_to_sexa_absolute(result_deci["quotient"]);
result["remainder"] = Deci_to_sexa_absolute(result_deci["remainder"]);
// The result is a hash table: it contains both result["quotient"]
// and result["remainder"].
return result;
}
// Division for decimal numbers. This function returns both
// result["quotient"] and result["remainder"].
function division_deci(dividend, divisor) {
var result = division_general(dividend, divisor, "10");
// The result is a hash table: it contains both result["quotient"]
// and result["remainder"].
return result;
}
// Floating quotient of a sexagesimal division.
function quotient_sexa(dividend, divisor) {
var result = multiplication_sexa(dividend, igi(divisor));
// This is like division_sexa, but we return directly
// result["quotient"].
return result;
}
// Absolute quotient of a sexagesimal division.
function quotient_sexa_absolute(dividend, divisor) {
var result = division_sexa_absolute(dividend, divisor)["quotient"];
// This is like division_sexa, but we return directly
// result["quotient"].
return result;
}
// Absolute quotient of a decimal division.
function quotient_deci(dividend, divisor) {
var result = division_general(dividend, divisor, "10")["quotient"];
// This is like division_deci, but we return directly
// result["quotient"].
return result;
}
// Remainder of a sexagesimal division (like the "%" in native
// JavaScript).
function remainder_sexa(dividend, divisor) {
var result =
Deci_to_sexa_absolute(division_general(Sexa_vers_deci(dividend),
Sexa_vers_deci(divisor),
"10")["remainder"]);
// This is like division_sexa, but we return directly
// result["remainder"].
return result;
}
// Remainder of a decimal division (like the "%" in native JavaScript).
function remainder_deci(dividend, divisor) {
var result = division_general(dividend, divisor, "10")["remainder"];
// This is like division_deci, but we return directly
// result["remainder"].
return result;
}
function prime_list_to_igi(prime_list) {
// Description of the "Lottery algorithm" to compute the reciprocal
// number.
//
// The idea is that we have a lottery grid, which is formatted like
// the following:
//
// (2 2 3 5)
// (2 2 3 5)
// (2 2 3 5)
// (2 2 3 5)
// (2 2 3 5)
// (2 2 3 5)
// ...
//
// Now, we take the regular number of which we are searching the
// reciprocal. We take the list of its prime factors: say 2, 2, 2,
// 2, 2, 2, 2, 3, 3, 5, 5, 5 for the number 40.0.0 (= 144000). We
// fill out the grid from top to bottom and we get:
//
// (X X X X)
// (X X X X)
// (X X 3 X)
// (X 2 3 5)
// (2 2 3 5)
// (2 2 3 5)
// ...
//
// How many lines do we need? Four. So, in the first four lines, we
// compute the product of all non-checked numbers, which is 2*3*3*5
// = 1.30.
//
// The demonstration is easy: the product of both numbers is a power
// of 60, for it is a power of the number encoded by each of these
// lines, which is 2*2*3*5 = 60.
//
// In abstract terms:
//
// Let nb2 (resp. nb3, nb5) be the number of 2's (resp. of 3's, of
// 5's) in the list of prime factors of a regular number. The
// reciprocal of this number is:
//
// 2^(2n-nb2) * 3^(n-nb3) * 5^(n - nb5).
//
// Now, let us comment on this algorithm line by line.
//
// We have to count the number of 2, 3 and 5 in the list of prime
// factors.
var nb2 = prime_list["nb2"];
var nb3 = prime_list["nb3"];
var nb5 = prime_list["nb5"];
var lines = 0; // The power of 60 which will be needed.
var result = "";
// How many lines do we need?
lines = Math.ceil(Math.max(Math.max(nb2/2, nb3), nb5));
// Compute the respective powers of 2, 3 and 5 of the reciprocal number.
var power2 = Deci_to_sexa_absolute(2*lines - nb2);
var power3 = Deci_to_sexa_absolute(lines - nb3);
var power5 = Deci_to_sexa_absolute(lines - nb5);
// Compute the reciprocal number (floating or absolute).
result = multiplication_sexa(power_sexa("2", power2),
multiplication_sexa(
power_sexa("3", power3),
power_sexa("5", power5)));
// Return the result.
return floating(result);
}
// This function computes the "igi" (reciprocal number) of a given
// number, which is such that there exists some "n" such that
// number*igi=60^n.
function igi(sexa) {
var result;
// Take the list of prime factors. If it is the one of a regular
// number, then use it to compute its reciprocal number.
if (prime_list = is_regular(sexa))
result = floating(prime_list_to_igi(prime_list));
else // Otherwise, the result is undefined.
result = nu;
// Return result.
return result;
}
// Simplification of sexagesimal fractions.
function simplif_fraction(numerator, denominator) {
// We try all numbers which are less than the minimum of the
// numerator and the denominator.
for (var i = "2";
less_equal_sexa(i,
min_sexa(String(numerator),
String(denominator)));
i = addition_sexa(i, "1")) {
// We divide both the numerator and the denominator by their
// common divisor, if any.
while (remainder_sexa(numerator, i) == "0"
&& remainder_sexa(denominator, i) == "0") {
numerator = quotient_sexa_absolute(numerator, i);
denominator = quotient_sexa_absolute(denominator, i);
}
}
// Now we send the result.
var result = Sexa_vers_deci(numerator) + "/" + Sexa_vers_deci(denominator);
// var result = numerator + "/" + denominator;
return result;
}
////////////////////////////////////////////////////////////////
// Division forms
////////////////////////////////////////////////////////////////
// These functions are related with the division forms. They do deal
// with HTML.
// This function initializes the addition formular.
function clear_quotient(form) {
form.reset();
document.getElementById('quotient').innerHTML = "";
document.getElementById('quotient_input1').focus();
}
function quotient(form) {
var dividend = form.input1.value;
var divisor = form.input2.value;
var result =
(is_sexa(dividend) && is_sexa(divisor)) ?
((is_regular(divisor)) ? floating(quotient_sexa(dividend, divisor))
: "Divisor is not regular.")
: not_sexas;
display_result(result, "quotient");
}
function regle_trois(form) {
// Reset the output.
form.output.value = "";
var ara1 = form.input2.value;
var ara2 = form.input3.value;
var divisor = form.input1.value;
if (!is_sexa(ara1) || !is_sexa(ara2) || !is_sexa(divisor))
return not_sexas;
else {
var deci1 = Sexa_vers_deci(ara1);
var deci2 = Sexa_vers_deci(ara2);
var deci3 = Sexa_vers_deci(divisor);
form.output.value = is_regular(divisor) ?
floating(quotient_sexa(multiplication_sexa(ara1, ara2), divisor))
: "First number is not regular.";
}
}
function inverse(form) {
var sexa = form.input.value;
var prime_list = new Array();
var result;
// Check if the number is sexagesimal.
if (is_sexa(sexa)) {
// We take the list of prime factors and then use it to compute
// the reciprocal number. Otherwise, we would have to compute
// two times the prime factors.
if (prime_list = is_regular(sexa))
result = prime_list_to_igi(prime_list);
else
result = nu;
} else
result = not_sexa;
// Display the result.
display_result(result, "igi");
}
////////////////////////////////////////////////////////////////
// Powers and roots
////////////////////////////////////////////////////////////////
// These functions are pure mathematics---sorry, I meant pure
// JavaScript. They do not deal with HTML.
// This function computes sexagesimal powers.
function power_sexa(nb, power_nb) {
var base = "60";
var result = power_general(nb, power_nb, base);
return result;
}
// This function computes decimal powers. Probably useless. Just for the
// sake of generality and symmetry.
function power_deci(nb, power_nb) {
var base = "10";
var result = power_general(nb, power_nb, base);
return result;
}
// This functions computes n-th roots of sexagesimal numbers, such as
// square roots or cube roots.
function nth_root(sexa, root) {
// This algorithm was given by Christine Proust. The idea is the
// following: to compute the square root of a number, check if all
// its prime factors have an even number of occurrences; if yes,
// take one of them on two and we multiply them; if not, you can fix
// things for 2, 3 and 5 by multiplying the number by 60.
//
// As Christine has suggested, this algorithm is easy to generalize
// to an arbitrary base. This is what is done below.
//
// This algorithm does not use big numbers. It is quite quick
// (except concerning the factorization) and is not affected by
// JavaScript's limit of 2^53.
// The list of prime factors.
var primes = prime_factors(sexa);
var result = "1";
// Count the occurrences of each prime factor.
var counts = {};
counts["2"] = 0;
counts["3"] = 0;
counts["5"] = 0;
for (var i = 0; i < primes.length; i++) {
var value = primes[i];
if (typeof counts[value] === "undefined") {
counts[value] = 1;
} else {
counts[value]++;
}
}
// All factors (except 2, 3 and 5) must have a number of occurrences
// which is a multiple of the root. Otherwise, the result is
// undefined.
for (var key in counts) {
if (key != "2" && key != "3" && key != "5"
&& counts[key] % root != 0)
return nu;
}
// The numbers of occurrences of 3 and 5 must be congruent with each
// other modulo the root. Otherwise, the result is undefined.
if (counts["3"] % root != counts["5"] % root) {
return nu;
}
// If the number of 3's (and of 5's) is not a multiple of the
// root, and if in floating mode, then multiply the number by
// the right power of 60 (i.e of 2*2*3*5).
if (counts["3"] % root != 0) {
if (sexa_floating) {
var shift = counts["3"];
counts["2"] += 2 * (root - (shift % root));
counts["3"] += root - (shift % root);
counts["5"] += root - (shift % root);
} else {
return nu;
}
}
// Now the numbers of 3's and 5's are multiple of the root. Is it
// still the case for 2's? If not, the result is undefined.
if (counts["2"] % root != 0)
return nu;
// Since everything seems to go well, now we compute the nth root.
for (var key in counts) {
result =
multiplication_sexa(
result,
power_sexa(key,
Deci_to_sexa_absolute(counts[key] / root)));
}
// Return result.
return result;
}
// Sexagesimal square roots.
function square_root_sexa(sexa) {
var root = 2;
result = is_sexa(sexa) ? nth_root(sexa, root) : not_sexa;
return result;
}
// Sexagesimal cubic root.
function cubic_root_sexa(sexa) {
var root = 3;
result = is_sexa(sexa) ? nth_root(sexa, root) : not_sexa;
return result;
}
////////////////////////////////////////////////////////////////
// Powers and root forms
////////////////////////////////////////////////////////////////
// These functions are related with powers and roots forms. They do deal
// with HTML.
function square(form) {
var sexa = form.input.value;
var result = is_sexa(sexa) ?
floating_or_absolute(power_sexa(sexa, "2")) : not_sexa;
display_result(result, "square");
}
function square_root(form) {
var sexa = form.input.value;
var result = floating_or_absolute(square_root_sexa(sexa));
display_result(result, "squareroot");
}
function cube(form) {
var sexa = form.input.value;
var result = is_sexa(sexa) ?
floating_or_absolute(power_sexa(sexa, "3")) : not_sexa;
display_result(result, "cube");
}
function cubic_root(form) {
var sexa = form.input.value;
var result = floating_or_absolute(cubic_root_sexa(sexa));
display_result(result, "cuberoot");
}
////////////////////////////////////////////////////////////////
// Regularity and factorization
////////////////////////////////////////////////////////////////
// This function tests whether the sexa is regular (a regular number is
// a number such as 2^p * 3^q * 5*r).
function is_regular(sexa) {
var division = new Array();
var factors = new Object();
var divisors = ["30", "5", "3", "2"];
factors["nb2"] = 0;
factors["nb3"] = 0;
factors["nb5"] = 0;
// Let us take each prime factor of 60 (i. first 5, then 3, finally 2).
for (var i = 0; i < divisors.length; i++) {
do {
// Try to divide the sexa by the current prime factor of 60.
division = division_sexa_absolute(sexa, divisors[i]);
if (division["remainder"] == "0") {
switch (divisors[i]) {
case "30":
factors["nb2"]++;
factors["nb3"]++;
factors["nb5"]++;
break;
case "2":
factors["nb2"]++;
break;
case "3":
factors["nb3"]++;
break;
case "5":
factors["nb5"]++;
break;
}
sexa = division["quotient"];
}
}
while (division["remainder"] == 0)
}
if (sexa == "1")
return factors;
else
return false;
}
// Return the list of prime factors of a sexagesimal number.
function prime_factors(sexa) {
var divisor = "2";
var result = new Array(); // The result is the array of prime
// factors, such as ["2", "2", "3", "5"].
var i = 0; // Indices for the result array.
// The square of the divisor must be less than the sexa (except in
// the case where the sexa itself is a prime number, see below).
while (less_equal_sexa(multiplication_sexa_absolu(divisor, divisor),
sexa)) {
// Try to divide the sexa by the divisor.
var division = division_sexa_absolute(sexa, divisor);
// If the sexa is a multiple of the divisor, then append the
// divisor to the list of prime factors and take the quotient as
// the new sexa.
if (division["remainder"] == "0") {
result[i++] = divisor;
sexa = division["quotient"];
}
else { // If the sexa is not a multiple of the divisor, try the
// following divisor.
divisor = addition_sexa(divisor, "1");
}
}
// If you have reached the square root of the sexa without having
// "1" as the result, then the sexa itelf is a prime number.
if (sexa != "1")
result[i] = sexa;
// Now, return the array of all prime factors.
return result;
}
// Greatest common divisor. The input numbers are taken as absolute and
// the result is absolute.
function gcd(sexa1, sexa2) {
var sexa1_factors = new Array();
var sexa2_factors = new Array();
var gcd_factors = new Array();
var result = "1";
// Take both numbers as ordered lists of prime factors.
sexa1_factors = prime_factors(sexa1);
sexa2_factors = prime_factors(sexa2);
// We compare the first factor of each list. If they are different,
// the smallest is thrown away. If they are equal, this factor is a
// factor of the GCD.
while (sexa1_factors.length > 0 && sexa2_factors.length > 0) {
if (less_equal_sexa(sexa1_array[0], sexa2_array[0])
&& !less_equal_sexa(sexa2_array[0], sexa1_array[0])) {
sexa1_factors.shift();
}
else if (less_equal_sexa(sexa2_array[0], sexa1_array[0])
&& !less_equal_sexa(sexa1_array[0], sexa2_array[0])) {
sexa2_factors.shift();
}
else {
gcd_factors.push(sexa1_factors[0]);
sexa1_factors.shift();
sexa2_factors.shift();
}
}
// Finally multiply the prime factors of the GCD to get it.
while (gcd_factors.length > 0) {
result = multiplication_sexa_absolu(result, gcd_factors.shift());
}
return result;
}
////////////////////////////////////////////////////////////////
// Approximation by regulars numbers
////////////////////////////////////////////////////////////////
// This function computes the regular approximation of a number. For
// instance, the output for 7 should be :
//
// "6",
// "6.45",
// "6.56.40",
// ...
// "7.6.40",
// "7.12",
// "8"
//
// The problem is that we have to choose between space and time. On my
// computer (in 2016), approximations are quickly computed until three
// places, which is not enough comparing with what Mesopotamian scribes
// needed. For four places or more, my browser freezes.
//
// Space is cheaper today and Internet connections are faster. Taking
// the risk to increase by 500 Ko the present file, I chose to include
// here Mathieu Ossendrijver's list of regular numbers up to 20 places.
// So they have been computed once for all.
//
// Hence, the function "regular_approximation_on_the_fly" below is not
// used. By default, MesoCalc uses
// "regular_approximation_with_database".
function regular_approximation (form) {
var sexa = form.input.value;
var nb_digits = form.nb_digits.value;
if (!is_sexa(sexa)) {
display_result(not_sexa, "regular_approximation");
} else {
// Take two lists: the list "inf" of lower approximations and
// the list "sup" of upper approximations.
var inf = regular_approximation_with_database(sexa, nb_digits)[0];
var sup = regular_approximation_with_database(sexa, nb_digits)[1];
var i;
// Display all lower approximations, except the last one.
var tableau = '<p><table class="center">\n';
tableau += "<tr><th>Regular approximations of " + sexa + "</tr>";
for (i = 0; i < inf.length - 1; i++) {
tableau += "<tr><td>" + inf[i] + "</td></tr>\n";
}
// If there is no upper approximations, this means that the
// approximated number is itself regular. Thus, the one and only
// lower approximation, which is the number itself, is written
// in bold font.
if (sup.length == 0) {
tableau += "<tr><td><strong>"
+ inf[i] + "</strong></td></tr>\n";
} else {
// If there are upper approximations, this means that the
// approximated number is not regular. We thus have to
// compute if its nearest regular approximation is the last
// lower or the first upper number.
var nb1 = inf[i];
var nb2 = sup[0];
var nb_places = Math.max(nb1.split(".").length,
Math.max(sexa.split(".").length,
nb2.split(".").length));
while (nb1.split(".").length < nb_places) {
nb1 += ".0";
}
while (sexa.split(".").length < nb_places) {
sexa += ".0";
}
while (nb2.split(".").length < nb_places) {
nb2 += ".0";
}
if (!less_equal_sexa(subtraction_sexa(sexa, nb2),
subtraction_sexa(sexa, nb1))) {
tableau += "<tr><td><strong>" + inf[i]
+ "</strong></td></tr>\n";
tableau += "<tr><td>" + sup[0] + "</td></tr>\n";
} else if (!less_equal_sexa(subtraction_sexa(sexa, nb1),
subtraction_sexa(sexa, nb2))) {
tableau += "<tr><td>" + inf[i] + "</td></tr>\n";
tableau += "<tr><td><strong>" + sup[0]
+ "</strong></td></tr>\n";
} else {
tableau += "<tr><td><strong>" + inf[i]
+ "</strong></td></tr>\n";
tableau += "<tr><td><strong>" + sup[0]
+ "</strong></td></tr>\n";
}
}
// Now display the rest of the upper approximations.
for (var i = 1; i < sup.length; i++) {
tableau += "<tr><td>" + sup[i] + "</td></tr>\n";
}
tableau += '</table></p>';
document.getElementById('regular_approximation').innerHTML = tableau;
}
}
// By default, the present function is NOT used by MesoCalc.
function regular_approximation_on_the_fly (sexa) {
var approx_list = new Array();
var inf = new Array();
var sup = new Array();
if (!is_sexa(sexa)) {
return not_sexa;
} else if (is_regular(sexa)) {
inf.push(sexa);
} else {
var sexa_array = sexa.split(".");
var limit = 3;
var comp;
// Let us fill empty places with 0's. For instance, 7
// becomes 7.0.0.
if (sexa_array.length < limit) {
for (var i = sexa_array.length; i < limit; i++) {
sexa_array[i] = "0";
}
}
// Find integer numbers as lower and upper bounds. For
// instance, the results for 7 are respectively 6 and 8.
comp = sexa_array[0];
while (!is_regular(comp)) {
comp = subtraction_sexa(comp, "1");
}
var lower_bound = comp;
inf.push(comp);
comp = sexa_array[0];
while (!is_regular(comp)) {
comp = addition_sexa(comp, "1");
}
var upper_bound = comp;
sup.unshift(comp);
// Now we look for the nearest regulars. For instance,
// for 7, we start at 7.0 and decrease the value until we
// find a regular number : 6.59, 6.58, ..., 6.45 ; this
// last value is taken as the new lower bound. Then we take
// numbers with three places : 6.59.59, 6.59.58, ...,
// 6.56.40. The variable "limit" indicates how many places
// must be taken into account.
for (var i = 2; i <= limit; i++) {
var array_tmp = sexa_array.slice(0, i);
comp = array_tmp.join(".");
while (!is_regular(comp)) {
comp = subtraction_sexa(comp, "1");
if (comp == lower_bound) {
continue;
}
}
lower_bound = comp;
inf.push(comp);
}
// Now do the same for upper bounds.
for (var i = 2; i <= limit; i++) {
var array_tmp = sexa_array.slice(0, i);
comp = array_tmp.join(".");
while (!is_regular(comp)) {
comp = addition_sexa(comp, "1");
if (comp == upper_bound) {
continue;
}
}
upper_bound = comp;
sup.unshift(comp);
}
}
// Finally return both lists.
return [inf,sup];
}
// This is the function which is used by MesoCalc to generate an
// approximation by regulars, instead of the function
// "regular_approximation_on_the_fly".
function regular_approximation_with_database (sexa, nb_digits) {
var approx_list = new Array();
var inf = new Array();
var sup = new Array();
if (!is_sexa(sexa)) {
return not_sexa;
} else if (is_regular(sexa)) {
inf.push(sexa);
} else {
// Look for the smallest interval containing the number. For
// instance, the number 7 is between 6.59.54.14.24 and
// 7.0.14.23.35.54.2.32.33.20.18.23.41.46.54.31.13.9.7.12. The
// search is logarithmic.
var nearest_lower = 0;
var nearest_upper = regulars_list.length - 1;
while (nearest_upper - nearest_lower > 1) {
var i = Math.floor((nearest_upper + nearest_lower)/2);
if (less_equal_sexa_floating(regulars_list[i], sexa)) {
nearest_lower = i;
} else {
nearest_upper = i;
}
}
// Now look for the "pyramid" of approximations. For instance,
// starting from 6.59.54.14.24, which is the greatest regular
// number lower than 7, go backwards looking for the first
// one-place regular number, which is 6. Then, take 6 as the
// lower bound of our interval. Starting from 6.59.54.14.24, go
// backwards looking for the first two-places regular number
// higher than 6 (if any), which is 6.45. Do the same to find
// 6.56.40. Then, there is no four-places (and less than
// twenty-places) regular number higher than 6.56.40.
var lower_bound = 0;
var upper_bound = regulars_list.length - 1;
// Add "1" as an approximation if the number to approximate
// really should be at the very beginning or at the very end of
// the list.
if (!less_equal_sexa_floating("2", sexa)) {
inf.push("1");
} else {
if (!less_equal_sexa_floating(sexa,
regulars_list[regulars_list.length
- 1])) {
sup.unshift("1");
}
}
// The maximal number of places is that of the greater regular
// number preceding the number to approximate. For instance, it
// is 5 for 7 since 6.59.54.14.24 has five places.
for (var nb_places = 1; nb_places <= nb_digits; nb_places++) {
for (var j = nearest_lower; lower_bound < j; j--) {
if (regulars_list[j].split(".").length == nb_places) {
lower_bound = j;
inf.push(regulars_list[j]);
break;
}
}
}
// Now, do the same for greater approximations.
for (var nb_places = 1; nb_places <= nb_digits; nb_places++) {
for (var j = nearest_upper; j < upper_bound; j++) {
if (regulars_list[j].split(".").length == nb_places) {
upper_bound = j;
sup.unshift(regulars_list[j]);
break;
}
}
}
}
// Finally return both lists.
return [inf,sup];
}
function regular_numbers_interval_form (form) {
var sexa1 = form.input1.value;
var sexa2 = form.input2.value;
var nb_digits = form.nb_digits.value;
if (!is_sexa(sexa1) || !is_sexa(sexa2)) {
display_result(not_sexas, "regular_numbers_interval");
} else {
var list = regular_numbers_interval(sexa1, sexa2);
var tableau = '<p><table class="center">\n';
for (i = 0; i < list.length; i++) {
if (list[i].split(".").length <= nb_digits) {
tableau += "<tr><td>" + list[i] + "</td></tr>\n";
}
}
tableau += '</table></p>';
document.getElementById('regular_numbers_interval').innerHTML = tableau;
}
}
function regular_numbers_interval (sexa1, sexa2) {
var regular_numbers_list = new Array();
// Find lower and upper bounds.
var nearest_lower1 = 0;
var nearest_upper1 = regulars_list.length - 1;
var nearest_lower2 = 0;
var nearest_upper2 = regulars_list.length - 1;
var lower_bound;
var upper_bound;
while (nearest_upper1 - nearest_lower1 > 1) {
var i = Math.floor((nearest_upper1 + nearest_lower1)/2);
if (less_equal_sexa_floating(regulars_list[i], sexa1)) {
nearest_lower1 = i;
} else {
nearest_upper1 = i;
}
}
if (less_equal_sexa_floating(sexa1, regulars_list[nearest_lower1])) {
lower_bound = nearest_upper1 - 1;
} else {
lower_bound = nearest_upper1 - 1;
}
if (less_equal_sexa_floating(sexa2, "1")
&& less_equal_sexa_floating("1", sexa2)) {
upper_bound = regulars_list.length - 1;
} else {
while (nearest_upper2 - nearest_lower2 > 1) {
var i = Math.floor((nearest_upper2 + nearest_lower2)/2);
if (less_equal_sexa_floating(regulars_list[i], sexa2)) {
nearest_lower2 = i;
} else {
nearest_upper2 = i;
}
}
if (less_equal_sexa_floating(regulars_list[nearest_upper2], sexa2)) {
upper_bound = nearest_lower2 + 1;
} else {
upper_bound = nearest_lower2;
}
}
// Return the list of all regular numbers within the interval.
for (var i = lower_bound; i <= upper_bound; i++) {
regular_numbers_list.push(regulars_list[i]);
}
return regular_numbers_list;
}
////////////////////////////////////////////////////////////////
// Regularity and factorization forms
////////////////////////////////////////////////////////////////
function facteurs(form) {
var sexa = form.input.value;
var result = "";
if (!is_sexa(sexa))
result = not_sexa;
else
result = prime_factors(sexa).join(" × ");
display_result(result, "prime_factors");
}
function regular(form) {
var sexa = form.input.value;
var result = (is_sexa(sexa)) ? (is_regular(sexa) ? "yes" : "no")
: not_sexa;
display_result(result, "regular_number");
}
function gcd_form(form) {
var sexa1 = form.input1.value;
var sexa2 = form.input2.value;
var result = (is_sexa(sexa1) && is_sexa(sexa2)) ?
gcd(sexa1, sexa2) : not_sexas;
display_result(result, "gcd");
}
////////////////////////////////////////////////////////////////
// Comparison of numbers
////////////////////////////////////////////////////////////////
// Minimum of two numbers.
function min_general(nb1, nb2, base) {
if (less_equal(nb1, nb2, base))
return nb1;
else
return nb2;
}
// Minimum of two decimal numbers.
function min_deci(nb1, nb2, base) {
var base = "10";
var result = min_general(nb1, nb2, base);
return result;
}
// Mimimum of two sexagesimal numbers.
function min_sexa(nb1, nb2, base) {
var base = "60";
var result = min_general(nb1, nb2, base);
return result;
}
// This function tests whether the first number is less than or equal to
// the second. (The difference with JavaScript's native "<=" is that
// this algorithm is base-independant and works beyond 2^53).
//
// This order relation corresponds to absolute arithmetic. It compares
// numbers after "right-alignment":
//
// ( 1)
// ( 2)
// (1.1)
function less_equal(nb1, nb2, base) {
// The digit separator: "" until 10, "." for higher bases such as 60.
var separator = base <= 10 ? "" : ".";
// Handle numbers as strings of digits.
var array_nb1 = nb1.split(separator);
var array_nb2 = nb2.split(separator);
// If the two numbers do not have the same number of digits.
if (array_nb1.length < array_nb2.length) { // If the second number
// is longer than the first.
return true;
}
if (array_nb1.length > array_nb2.length) { // If the second number
// is longer than the first.
return false;
}
// If both numbers have the same number of digits.
for (var i = 0; i < array_nb1.length; i++) {
if (parseInt(array_nb1[i]) < parseInt(array_nb2[i])) {
return true;
}
if (parseInt(array_nb1[i]) > parseInt(array_nb2[i])) {
return false;
}
}
// If the two numbers are equal.
return true;
}
function less_equal_sexa(nb1, nb2) {
// This order relation corresponds to absolute arithmetic. It
// compares numbers after "right-alignment":
//
// ( 1)
// ( 2)
// (1.1)
var base = 60;
return less_equal(nb1, nb2, base);
}
function less_equal_deci(nb1, nb2) {
var base = 10;
return less_equal(nb1, nb2, base);
}
function less_equal_sexa_floating (nb1, nb2) {
// This order relation corresponds to floating arithmetic. It
// compares numbers after "left-alignment":
//
// (1 )
// (1.1)
// (2 )
var nb1_places = nb1.split(".").length;
var nb2_places = nb2.split(".").length;
if (nb1_places != nb2_places) {
if (nb1_places < nb2_places) {
for (var i = 0; i < nb2_places - nb1_places; i++) {
nb1 = nb1.concat(".0");
}
}
else {
for (var i = 0; i < nb1_places - nb2_places; i++) {
nb2 = nb2.concat(".0");
}
}
}
return less_equal_sexa(nb1, nb2);
}
////////////////////////////////////////////////////////////////
// Tables (in forms)
////////////////////////////////////////////////////////////////
// Sexagesimal multiplication tables, as they were made in Mesopotamia.
function mult_table(form) {
var sexa = form.input.value;
if (!sexa) {
result = "";
} else {
if (!is_sexa(sexa)) {
result = not_sexa;
} else {
var result = '<p><table class=\"center\">'
+ '<th colspan="2">Multiplication table of ' + sexa + '</th>';
// The Mesopotamian multiplication tables contained all
// multiples from 1 to 20, and then 30, 40 and 50.
var i = "1";
while (less_equal_sexa(i, "59")) {
result += "<tr><td>" + i + '</td><td align="right">'
+ multiplication_sexa(sexa, i) // Floating or absolute.
+ "</td></tr>";
i = less_equal_sexa(i, "19") ? i = addition_sexa(i, "1")
: i = addition_sexa(i, "10");
}
result += "</table></p>";
}
}
document.getElementById('mult_tableau').innerHTML = result;
}
function square_table(form) {
if (affiche_table_carres) {
affiche_table_carres = false;
result = "";
} else {
affiche_table_carres = true;
var result = '<p><table class=\"center\">'
+ '<th colspan="2">Table of squares</th>';
for (var i = "1";
less_equal_sexa(i, "59");
i = addition_sexa(i, "1")) {
result += "<tr><td>"
+ floating_or_absolute(i)
+ '</td><td align="right">'
+ floating(multiplication_sexa(i, i))
+ "</td></tr>";
}
result += "</table></p>";
}
document.getElementById('square_tableau').innerHTML = result;
}
function square_root_table(form) {
if (affiche_table_racines_carrees) {
affiche_table_racines_carrees = false;
result = "";
} else {
affiche_table_racines_carrees = true;
var result = "<p><table class=\"center\">"
+ '<th colspan="2">Table of square roots</th>';
var entrees = new Array;
// The table must display the square roots 1 to 59, and then 1,
// 1.1, 1.1.1, 1.1.1.1 (see Christine Proust, _Tablettes
// mathématiques de Nippur_, 2007, p. 323)
var i = "1";
while (less_equal_sexa(i, power_sexa("1.0", "4"))) {
result += "<tr><td>"
+ floating_or_absolute(multiplication_sexa_absolu(i, i))
+ '</td><td align="right">'
+ floating_or_absolute(i)
+ "</td></tr>";
i = less_equal_sexa(i, "1.0") ? addition_sexa(i, "1")
: addition_sexa(multiplication_sexa_absolu(i, "1.0"), "1");
}
result += "</table></p>";
}
document.getElementById('square_root_tableau').innerHTML = result;
}
function cube_root_table(form) {
if (affiche_table_racines_cubiques) {
affiche_table_racines_cubiques = false;
result = "";
} else {
affiche_table_racines_cubiques = true;
var result = "<p><table class=\"center\">"
+ '<th colspan="2">Table of cube roots</th>';
var i = "1";
while (less_equal_sexa(i, "40")) {
result += "<tr><td>"
+ floating(power_sexa(i, "3"))
+ '</td><td align="right">'
+ floating_or_absolute(i)
+ "</td></tr>";
i = less_equal_sexa(i, "19") ? addition_sexa(i, "1")
: addition_sexa(i, "10");
}
result += "</table></p>";
}
document.getElementById('cube_root_tableau').innerHTML = result;
}
function geom(form) {
var first = form.first.value;
var ratio = form.ratio.value;
var terms = form.terms.value;
var result = "";
if (!first)
first = "1";
if (!ratio)
ratio = "1";
if (!terms)
terms = "1";
if (!is_sexa(first) || !is_sexa(ratio)) {
result = "Not sexagesimal numbers.";
} else
if (!is_int(terms) || terms < 1) {
result = "Wrong number of terms.";
return;
} else {
result = "<p><table class=\"center\">"
+ "<tr><th>Term</th><th>Value</th>"
+ "<th>Reciprocal</th></tr>";
for (var i = "0";
less_equal_sexa(i, Deci_to_sexa_absolute(terms));
i = addition_sexa(i, "1")) {
var terme2 = power_sexa(ratio, i);
var terme3 = multiplication_sexa(terme2, first);
result += "<tr><td>"
+ i
+ "</td><td>"
+ terme3
+ "</td><td>"
+ igi(terme3)
+ "</td></tr>";
}
result += "</table></p>";
}
document.getElementById('geom_tableau').innerHTML = result;
}
function inverse_table(form) {
var result = "";
var deci = 0;
var prime_list = new Array();
if (affiche_table_inverse) {
affiche_table_inverse = false;
result = "";
} else {
affiche_table_inverse = true;
var result = '<p><table class="center">'
+ '<tr><th colspan="2">Table of reciprocals</th></tr>';
for (sexa = "2";
less_equal_sexa(sexa, "1.21");
sexa = addition_sexa(sexa, "1")) {
// Do not permute the two following conditions, i.e the
// less_equal_sexa() and the is_regular(). Otherwise, you
// would compute the prime factors of useless numbers.
// Indeed, computing the prime factors takes a lot of time.
if ((less_equal_sexa(sexa, "1.0")
|| sexa == "1.04" || sexa == "1.4"
|| sexa == "1.21"
) && (prime_list = is_regular(sexa))) {
result += "<tr><td>" + sexa + '</td><td align="right">'
+ igi(sexa) + "</td></tr>";
}
}
result += "</table></p>";
}
document.getElementById('inverse_tableau').innerHTML = result;
}
function regular_liste(form) {
var sexa1 = form.input1.value;
var sexa2 = form.input2.value;
var result = "";
if (!sexa1 || !sexa2) {
result = "";
} else {
if (!is_sexa(sexa1) || !is_sexa(sexa2)) {
result = not_sexas;
} else {
if (!less_equal_sexa(sexa1, sexa2)) {
var tmp = sexa1;
sexa1 = sexa2;
sexa2 = tmp;
}
result = '<p><table class="center">'
+ '<tr> '
+ '<th>Regular numbers between '
+ sexa1 + ' and ' + sexa2
+ '</th></tr>';
for (var sexa = sexa1;
less_equal_sexa(sexa, sexa2);
sexa = addition_sexa(sexa, "1")) {
if (is_regular(sexa)) {
result += "<tr><td>" + floating_or_absolute(sexa)
+ "</td>" + '</tr>';
}
}
result += "</table></p>";
}
}
document.getElementById('regular_liste').innerHTML = result;
}
function regular_inverse_liste(form) {
var sexa1 = form.input1.value;
var sexa2 = form.input2.value;
var nb_digits = form.nb_digits.value;
if (!is_sexa(sexa1) || !is_sexa(sexa2)) {
display_result(not_sexas, "regular_inverse_liste");
} else {
var list = regular_numbers_interval(sexa1, sexa2);
var tableau = '<p><table class="center">\n';
tableau += '<tr> '
+ '<th colspan="2">Regular numbers and'
+ ' their reciprocal between '
+ sexa1 + ' and ' + sexa2
+ '</th></tr>'
+ "<tr><th>Regular numbers</th> "
+ " <th>Reciprocal numbers</th></tr> ";
for (var i = 0; i < list.length; i++) {
if (list[i].split(".").length <= nb_digits) {
tableau += "<tr><td>" + list[i] + "</td>\n"
+ "<td>" + igi(list[i]) + "</td></tr>\n";
}
}
tableau += '</table></p>';
document.getElementById('regular_inverse_liste').innerHTML = tableau;
}
}
////////////////////////////////////////////////////////////////
// Measuring units
////////////////////////////////////////////////////////////////
// Conversions into the lower unit.
function conversion_to_lower_unit(values, unit_table) {
// This function takes as input an array of decimal or sexagesimal
// values and an unit table (length_unit, surface_unit, etc.).
// Its output is an array of sexagesimal values given in the lower
// measuring unit (šusi for lengths, še for surfaces, etc.).
// This function is used by all particular conversion functions:
// longueur2susi, surface2se, volume2se, poids2se, capacite2se.
// Computations are performed in sexagesimal, so there is
// practically no limit for big numbers.
var i;
var result = "0";
for (i = 0; i < values.length; i++){
// Take all values as sexagesimal numbers.
values[i] = values[i] ?
(is_sexa(values[i]) ?
values[i] : Deci_to_sexa_absolute(values[i])) :
"0";
// Convert them into the lower unit.
result = multiplication_sexa_absolu(
addition_sexa(result,
values[i]),
unit_table[i][1]);
}
return result;
}
function longueur2susi(values) {
var result = conversion_to_lower_unit(values, length_unit);
return result;
}
function surface2se(values) {
var result = conversion_to_lower_unit(values, surface_unit);
return result;
}
function volume2se(values) {
var result = conversion_to_lower_unit(values, volume_unit);
return result;
}
function poids2se(values) {
var result = conversion_to_lower_unit(values, weight_unit);
return result;
}
function capacite2se(values) {
var result = conversion_to_lower_unit(values, capacity_unit);
return result;
}
function sexa_to_deci_array (sexa_array) {
// This function converts an array of sexagesimal values into an
// array of decimal values.
var deci_array = new Array();
var i;
for (i = 0; i < sexa_array.length; i++) {
deci_array[i] = parseInt(Sexa_vers_deci(sexa_array[i]));
}
return deci_array;
}
function deci_to_sexa_array (deci_array) {
// This function converts an array of decimal values into an array
// of sexagesimal values.
var sexa_array = new Array();
var i;
for (i = 0; i < deci_array.length; i++) {
sexa_array[i] = Deci_to_sexa_absolute(deci_array[i]);
}
return sexa_array;
}
// Conversions into big units.
function format_measure_without_fractions(values, unit_table) {
// This function takes as input an array of (potentially invalid)
// sexagesimal measuring values and produces as output an array of
// VALID sexagesimal measuring values. For instance, 60 šusi will be
// converted into 2 kuš. This is particularly useful when used after
// the function conversion_to_lower_unit or one of its forms
// (longueur2susi, surface2se...).
// First convert all values to the lower unit.
var i = values.length - 1;
values[i] = conversion_to_lower_unit(values, unit_table);
i--;
while (i >= 0) {
values[i] = "0";
i--;
}
// Then convert everything into bigger units.
for (i = values.length - 1; i > 0; i--) {
var ratio = unit_table[i - 1][1];
if (less_equal_sexa(ratio, values[i])) {
var quotient = quotient_sexa_absolute(values[i], ratio);
var reste = remainder_sexa(values[i], ratio);
values[i] = reste;
values[i - 1] = addition_sexa(values[i - 1], quotient);
}
}
return values;
}
function susi2longueur(small_unit) {
var unit_table = length_unit;
var sexa_values = ["0","0","0","0",small_unit];
sexa_values = format_measure_without_fractions(sexa_values, unit_table);
var result = length_with_fractions(sexa_values);
return result;
}
function measure_with_fractions (values, unit_table) {
var result = "";
if (conversion_to_lower_unit(values, unit_table) == "0") {
result = "0 " + unit_table[unit_table.length - 1][0];
} else {
for (var i = 0; i < values.length - 1; i++) {
var current_unit = "";
if (values[i] != "0") {
if ((unit_table == surface_unit || unit_table == volume_unit)
&& unit_table[i][0] == "gan"){
current_unit += systemeG(values[i]) + " ";
} else {
current_unit += decomposition_60(values[i]) + " ";
}
}
// There are sixths only is the ratio is dividable by 6.
var ratio = unit_table[i][1];
if (remainder_sexa(ratio, "6") == "0") {
var sixth_of_ratio = quotient_sexa_absolute(ratio, "6");
var sixths = quotient_sexa_absolute(values[i + 1], sixth_of_ratio);
if (!less_equal_sexa(sixths, "0")) {
current_unit += simplif_fraction(sixths,"6");
values[i + 1] = remainder_sexa(values[i + 1], sixth_of_ratio);
current_unit += " ";
}
}
if (current_unit != "") {
current_unit += unit_table[i][0] + " ";
result += current_unit;
}
}
result += (values[values.length - 1] != "0" ?
values[values.length - 1] + " "
+ unit_table[values.length - 1][0]
+ " "
: "");
}
return result;
}
function length_with_fractions (values) {
var result = measure_with_fractions(values, length_unit);
return result;
}
function surface_with_fractions (values) {
var result = measure_with_fractions(values, surface_unit);
return result;
}
function volume_with_fractions (values) {
var result = measure_with_fractions(values, volume_unit);
return result;
}
function weights_with_fractions (values) {
var result = measure_with_fractions(values, weight_unit);
return result;
}
function capacities_with_fractions (values) {
var result = measure_with_fractions(values, capacity_unit);
return result;
}
function se2surface(small_unit) {
var unit_table = surface_unit;
var sexa_values = ["0","0","0",small_unit];
sexa_values = format_measure_without_fractions(sexa_values, unit_table);
var result = surface_with_fractions(sexa_values);
return result;
}
function se2poids(small_unit) {
var unit_table = weight_unit;
var sexa_values = ["0","0","0",small_unit];
sexa_values = format_measure_without_fractions(sexa_values, unit_table);
var result = weights_with_fractions(sexa_values);
return result;
}
function se2capacite(small_unit) {
var unit_table = capacity_unit;
var sexa_values = ["0","0","0","0","0",small_unit];
sexa_values = format_measure_without_fractions(sexa_values, unit_table);
var result = capacities_with_fractions(sexa_values);
return result;
}
function se2volume(se) {
// Units of volume are computed just like units of surface.
var result = se2surface(se);
return result;
}
// This function apprixmates Mesopotamian mesures with metric units.
function approx_measure(small_unit, ratio_to_metric_unit,
ratio_to_metric_decimals, name_of_metric_unit,
number_of_decimals) {
// Take the number as a string.
small_unit = small_unit.toString();
var small_unit_deci = is_sexa(small_unit) ?
parseInt(Sexa_vers_deci(small_unit)) : small_unit;
// How many decimals are to be displayed.
var scale = Math.pow(10, number_of_decimals);
var zeros = "";
for (var i = 1; i < number_of_decimals; i++) {
zeros += "0";
}
// Separation of the metric unit and its decimals.
var metric_unit = Math.floor(small_unit_deci / ratio_to_metric_unit);
var remaining_small_unit = small_unit_deci % ratio_to_metric_unit;
// Computation of the decimals.
var metric_decimals = ""
+ Math.round((remaining_small_unit
* ratio_to_metric_decimals
* scale) / scale);
// Remove trailing zeros.
var tail = new RegExp("0+$", "");
// Return the result.
var result = metric_unit.toLocaleString()
+ (metric_decimals == 0 ? "" : "."
+ (zeros + metric_decimals).slice(-number_of_decimals).replace(tail, ""))
+ " " + name_of_metric_unit + (metric_unit >= 2 ? "s" : "");
return result;
}
function display_measure_with_metric_approx(measure, approx) {
var result = "<pre>"
+ measure
+ "<br/>"
+ '<span class="highlight">'
+ "(≈ "
+ approx
+ ")"
+ '</span>'
+ "</pre>";
return result;
}
function approx_length(susi) {
var result = approx_measure(susi, 60, 50/3, "meter", 3);
return result;
}
function display_length_with_metric_approx (susi) {
var result = display_measure_with_metric_approx(
susi2longueur(susi), approx_length(susi));
return result;
}
function add_longueurs(form) {
var length1 = [form.danna1.value,
form.us1.value,
form.ninda1.value,
form.kus1.value,
form.susi1.value];
var length2 = [form.danna2.value,
form.us2.value,
form.ninda2.value,
form.kus2.value,
form.susi2.value];
var result_susi = addition_sexa(longueur2susi(length1),
longueur2susi(length2));
var result = display_length_with_metric_approx(result_susi);
display_result(result, "add_lengths_output");
}
function soustr_longueurs(form) {
var result = "";
// On récupère les données.
var length1 = [form.danna1.value,
form.us1.value,
form.ninda1.value,
form.kus1.value,
form.susi1.value];
var length2 = [form.danna2.value,
form.us2.value,
form.ninda2.value,
form.kus2.value,
form.susi2.value];
susi1 = longueur2susi(length1);
susi2 = longueur2susi(length2);
if (less_equal_sexa(susi2, susi1)) {
var result_susi = subtraction_sexa(susi1, susi2);
result = display_length_with_metric_approx(result_susi);
}
else {
result = negative;
}
display_result(result, "subtract_lengths_output");
}
function mult_longueur_form(form) {
var length = [form.danna.value,
form.us.value,
form.ninda.value,
form.kus.value,
form.susi.value];
var scalaire = form.scalaire.value ? form.scalaire.value : "1";
var result_susi = multiplication_sexa_absolu(longueur2susi(length),
scalaire);
var result = display_length_with_metric_approx(result_susi);
display_result(result, "mult_length_output");
}
////////////////////////////////////////////////////////////////
// Surfaces
////////////////////////////////////////////////////////////////
function approx_surface(se, reste) {
var se_deci = is_sexa(se) ? parseInt(Sexa_vers_deci(se)) : se;
var square_susi = se_deci * 12;
if (reste != "" || reste != 0) {
var fraction = new Array();
fraction = reste.split("/");
square_susi += 12 * (fraction[0] == "" ? 0 :
parseInt(fraction[0]) / parseInt(fraction[1]));
}
var result = approx_measure(square_susi, 3600, 100000/36,
"square meter", 7);
return result;
}
function display_surface_with_metric_approx (se, remainder) {
var result = display_measure_with_metric_approx(
se2surface(se), approx_surface(se, remainder));
result = remainder ?
result.replace("<br/>", " " + remainder + "<br/>")
: result;
return result;
}
function add_surfaces(form) {
var result = "";
var surface1 = [form.gan1.value,
form.sar1.value,
form.gin1.value,
form.se1.value];
var surface2 = [form.gan2.value,
form.sar2.value,
form.gin2.value,
form.se2.value];
var result_se = addition_sexa(
surface2se(surface1),
surface2se(surface2));
result = display_surface_with_metric_approx(result_se, "");
display_result(result, "add_surfaces_output");
}
function soustr_surfaces(form) {
var result = "";
var surface1 = [form.gan1.value,
form.sar1.value,
form.gin1.value,
form.se1.value];
var surface2 = [form.gan2.value,
form.sar2.value,
form.gin2.value,
form.se2.value];
se1 = surface2se(surface1);
se2 = surface2se(surface2);
if (less_equal_sexa(se2, se1)) {
var se = subtraction_sexa(se1, se2);
result = display_surface_with_metric_approx(se, "");
}
else {
result = negative;
}
display_result(result, "subtract_surfaces_output");
}
function mult_surface_form(form) {
var surface = [form.gan.value,
form.sar.value,
form.gin.value,
form.se.value];
var scalaire = form.scalaire.value ? form.scalaire.value : "1"
var result_se = multiplication_sexa_absolu(
surface2se(surface),
scalaire);
result = display_surface_with_metric_approx(result_se, "");
display_result(result, "mult_surface_output");
}
function mult_longueurs(form) {
var length1 = [form.danna1.value,
form.us1.value,
form.ninda1.value,
form.kus1.value,
form.susi1.value];
var length2 = [form.danna2.value,
form.us2.value,
form.ninda2.value,
form.kus2.value,
form.susi2.value];
var result =
mult_deux_longueurs(longueur2susi(length1),
longueur2susi(length2));
display_result(result, "mult_two_lengths_output");
}
function mult_deux_longueurs(susi1, susi2) {
var result = "";
var ratio = "12"; // 1 se = 12 square susi
if (susi1 == "0" || susi2 == "0") {
result = display_surface_with_metric_approx("0", "");
} else {
var susi_carre = multiplication_sexa_absolu(susi1, susi2);
var se = quotient_sexa_absolute(susi_carre, ratio);
var reste = remainder_sexa(susi_carre, ratio);
reste = reste == 0 ? "" : simplif_fraction(reste, ratio);
result = display_surface_with_metric_approx(se, reste);
}
return result;
}
////////////////////////////////////////////////////////////////
// Volumes
////////////////////////////////////////////////////////////////
function approx_volume(se, reste) {
var se_deci = is_sexa(se) ? parseInt(Sexa_vers_deci(se)) : se;
var cubic_susi = se_deci * 360;
if (reste != "" || reste != 0) {
var fraction = new Array();
fraction = reste.split("/");
cubic_susi += 360 * (fraction[0] == "" ? 0 :
parseInt(fraction[0]) / parseInt(fraction[1]));
}
var result = approx_measure(cubic_susi, 216000, 10000/216,
"cube meter", 7);
return result;
}
function display_volume_with_metric_approx (se, remainder) {
var result = display_measure_with_metric_approx(
se2volume(se), approx_volume(se, remainder));
result = remainder ?
result.replace("<br/>", " " + remainder + "<br/>")
: result;
return result;
}
function add_volumes(form) {
var result = "";
var volume1 = [form.gan1.value,
form.sar1.value,
form.gin1.value,
form.se1.value];
var volume2 = [form.gan2.value,
form.sar2.value,
form.gin2.value,
form.se2.value];
var result_se = addition_sexa(volume2se(volume1),
volume2se(volume2));
result = display_volume_with_metric_approx(result_se, "");
display_result(result, "add_volumes_output");
}
function soustr_volumes(form) {
var result = "";
var surface1 = [form.gan1.value,
form.sar1.value,
form.gin1.value,
form.se1.value];
var surface2 = [form.gan2.value,
form.sar2.value,
form.gin2.value,
form.se2.value];
se1 = surface2se(surface1);
se2 = surface2se(surface2);
if (less_equal_sexa(se2, se1)) {
var se = subtraction_sexa(se1, se2);
result = display_volume_with_metric_approx(se, "");
}
else {
result = negative;
}
display_result(result, "subtract_volumes_output");
}
function mult_volume_form(form) {
var volume = [form.gan.value,
form.sar.value,
form.gin.value,
form.se.value];
var scalaire = form.scalaire.value ? form.scalaire.value : "1";
var result_se = multiplication_sexa_absolu(
volume2se(volume),
scalaire);
result = display_volume_with_metric_approx(result_se, "");
display_result(result, "mult_volume_output");
}
function mult_trois_longueurs_form(form) {
var length1 = [form.danna1.value,
form.us1.value,
form.ninda1.value,
form.kus1.value,
form.susi1.value];
var length2 = [form.danna2.value,
form.us2.value,
form.ninda2.value,
form.kus2.value,
form.susi2.value];
var length3 = [form.danna3.value,
form.us3.value,
form.ninda3.value,
form.kus3.value,
form.susi3.value];
var result = mult_trois_longueurs(longueur2susi(length1),
longueur2susi(length2),
longueur2susi(length3));
display_result(result, "mult_three_lengths_output");
}
function mult_surface_longueur(se, susi) {
var result = "";
var facteur = "12";
var ratio = "6.0"; // 1 se = 360 susi^3
if (se == 0 || susi == 0 || facteur == 0) {
result = display_volume_with_metric_approx("0", "");
} else {
var susi_cube =
multiplication_sexa_absolu(
multiplication_sexa_absolu(se, susi),
facteur);
var se_deci = Math.floor(Sexa_vers_deci(susi_cube) / ratio);
var reste = Sexa_vers_deci(susi_cube) % ratio;
var se_sexa = Deci_to_sexa_absolute(se_deci);
reste = reste == 0 ? "" : " " + simplif_fraction(reste, ratio);
result = display_volume_with_metric_approx(se_sexa, reste);
}
return result;
}
function mult_surface_longueur_form(form) {
var surface = [form.gan.value,
form.sar.value,
form.gin.value,
form.se.value];
var length = [form.danna.value,
form.us.value,
form.ninda.value,
form.kus.value,
form.susi.value];
var result =
mult_surface_longueur(surface2se(surface),
longueur2susi(length));
display_result(result, "mult_surface_length_output");
}
function mult_trois_longueurs(susi1, susi2, susi3) {
var result = "";
var ratio = "6.0"; // 1 se = 360 susi^3
if (susi1 == 0 || susi2 == 0 || susi3 == 0) {
result = display_volume_with_metric_approx("0", "");
} else {
var susi_cube = multiplication_sexa_absolu(
multiplication_sexa_absolu(susi1, susi2), susi3);
var se = quotient_sexa_absolute(susi_cube, ratio);
var reste = remainder_sexa(susi_cube, ratio);
reste = reste == 0 ? "" : simplif_fraction(reste, ratio);
result = display_volume_with_metric_approx(se, reste);
}
return result;
}
////////////////////////////////////////////////////////////////
// Capacités
////////////////////////////////////////////////////////////////
function approx_capacity(se) {
var se_deci = is_sexa(se) ? parseInt(Sexa_vers_deci(se)) : se;
var result = approx_measure(se, 10800, 100/108, "litre", 4);
return result;
}
function display_capacity_with_metric_approx (se) {
var result = display_measure_with_metric_approx(
se2capacite(se), approx_capacity(se));
return result;
}
function add_capacites(form) {
var capacity1 = [form.gur1.value,
form.bariga1.value,
form.ban1.value,
form.sila1.value,
form.gin1.value,
form.se1.value];
var capacity2 = [form.gur2.value,
form.bariga2.value,
form.ban2.value,
form.sila2.value,
form.gin2.value,
form.se2.value];
var result_se = addition_sexa(
capacite2se(capacity1),
capacite2se(capacity2));
result = display_capacity_with_metric_approx(result_se);
display_result(result, "add_capacities_output");
}
function soustr_capacites(form) {
var result = "";
var capacity1 = [form.gur1.value,
form.bariga1.value,
form.ban1.value,
form.sila1.value,
form.gin1.value,
form.se1.value];
var capacity2 = [form.gur2.value,
form.bariga2.value,
form.ban2.value,
form.sila2.value,
form.gin2.value,
form.se2.value];
se1 = capacite2se(capacity1);
se2 = capacite2se(capacity2);
if (less_equal_sexa(se2, se1)) {
var se = subtraction_sexa(se1, se2);
result = display_capacity_with_metric_approx(se);
}
else {
result = negative;
}
display_result(result, "subtract_capacities_output");
}
function mult_capacite_form(form) {
var capacity = [form.gur.value,
form.bariga.value,
form.ban.value,
form.sila.value,
form.gin.value,
form.se.value];
var scalaire = form.scalaire.value ? form.scalaire.value : "1";
var result_se = multiplication_sexa_absolu(
capacite2se(capacity),
scalaire);
result = display_capacity_with_metric_approx(result_se);
display_result(result, "mult_capacity_output");
}
////////////////////////////////////////////////////////////////
// Poids
////////////////////////////////////////////////////////////////
function approx_weight(se) {
var se_deci = is_sexa(se) ? parseInt(Sexa_vers_deci(se)) : se;
var result = approx_measure(se, 21600, 5000/108, "kilogram", 6);
return result;
}
function display_weight_with_metric_approx (se) {
var result = display_measure_with_metric_approx(
se2poids(se), approx_weight(se));
return result;
}
function add_poids(form) {
var result = "";
var weight1 = [form.gu1.value,
form.mana1.value,
form.gin1.value,
form.se1.value];
var weight2 = [form.gu2.value,
form.mana2.value,
form.gin2.value,
form.se2.value];
var result_se = addition_sexa(poids2se(weight1),
poids2se(weight2));
result = display_weight_with_metric_approx(result_se);
display_result(result, "add_weights_output");
}
function soustr_poids(form) {
var result = "";
var weight1 = [form.gu1.value,
form.mana1.value,
form.gin1.value,
form.se1.value];
var weight2 = [form.gu2.value,
form.mana2.value,
form.gin2.value,
form.se2.value];
se1 = poids2se(weight1);
se2 = poids2se(weight2);
if (less_equal_sexa(se2, se1)) {
var se = subtraction_sexa(se1, se2);
result = display_weight_with_metric_approx(se);
}
else {
result = negative;
}
display_result(result, "subtract_weights_output");
}
function mult_poids_form(form) {
var weight = [form.gu.value,
form.mana.value,
form.gin.value,
form.se.value];
var scalaire = form.scalaire.value ? form.scalaire.value : "1";
var result_se = multiplication_sexa_absolu(
poids2se(weight),
scalaire);
result = display_weight_with_metric_approx(result_se);
display_result(result, "mult_weight_output");
}
////////////////////////////////////////////////////////////////
// Système S et système G
////////////////////////////////////////////////////////////////
var sargal2saru_ratio = "6";
var saru2sar_ratio = "10";
var sar2gesu_ratio = "6";
var gesu2ges_ratio = "10";
var ges2u_ratio = "6";
var u2dis_ratio = "10";
var sar2buru_ratio = "6";
var buru2bur_ratio = "10";
var bur2ese_ratio = "6";
var ese2iku_ratio = "10";
function systemS2systemG(form) {
var result = "";
var sargal = form.sargal.value;
var saru = form.saru.value;
var sar = form.sar.value;
var gesu = form.gesu.value;
var ges = form.ges.value;
var u = form.u.value;
var dis = form.dis.value;
dis =
addition_sexa(
dis,
multiplication_sexa_absolu(
u2dis_ratio_deci,
addition_sexa(
u,
multiplication_sexa_absolu(
ges2u_ratio_deci,
addition_sexa(
ges,
multiplication_sexa_absolu(
gesu2ges_ratio_deci,
addition_sexa(
gesu,
multiplication_sexa_absolu(
sar2gesu_ratio_deci,
addition_sexa(
sar,
multiplication_sexa_absolu(
saru2sar_ratio_deci,
addition_sexa(
saru,
multiplication_sexa_absolu(
sargal2saru_ratio_deci,
sargal))))))))))));
result = systemeG(dis);
form.output.value = result;
}
function systemG2systemS_form(form) {
var sargal = form.sargal.value == "" ? "0" : form.sargal.value;
var saru = form.saru.value == "" ? "0" : form.saru.value;
var sar = form.sar.value == "" ? "0" : form.sar.value;
var buru = form.buru.value == "" ? "0" : form.buru.value;
var bur = form.bur.value == "" ? "0" : form.bur.value;
var ese = form.ese.value == "" ? "0" : form.ese.value;
var iku = form.iku.value == "" ? "0" : form.iku.value;
var result = systemG2systemS(sargal, saru, sar, buru, bur, ese, iku);
form.output.value = result;
}
function systemG2systemS(sargal, saru, sar, buru, bur, ese, iku) {
iku =
addition_sexa(
iku,
multiplication_sexa_absolu(
ese2iku_ratio,
addition_sexa(
ese,
multiplication_sexa_absolu(
bur2ese_ratio,
addition_sexa(
bur,
multiplication_sexa_absolu(
buru2bur_ratio,
addition_sexa(
buru,
multiplication_sexa_absolu(
sar2buru_ratio,
addition_sexa(
sar,
multiplication_sexa_absolu(
saru2sar_ratio,
addition_sexa(
saru,
multiplication_sexa_absolu(
sargal2saru_ratio,
sargal))))))))))));
var result = systemeS(iku);
return result;
}
////////////////////////////////////////////////////////////////
// Briques
////////////////////////////////////////////////////////////////
function nalbanum(form) {
var volume = form.input.value;
var result = "";
if (!volume) {
result = "";
} else {
if (!is_sexa(volume)) {
result = not_sexa;
} else {
if (is_regular(volume)) {
result = '<table>' + '<tr> '
+ '<th>Standard volume</th>'
+ ' <th><em>nalbanum</em> (brickage)</th>'
+ '<th><em>nazbalum</em> (carriage)</th></tr>'
+ '<tr><td>' + volume + '</td>'
+ '<td>' + floating(quotient_sexa("5", volume))
+ '</td>'
+ '<td>'
+ floating(multiplication_sexa("37.30",
quotient_sexa("5", volume)))
+ '</td></tr>'
+ "</table> (floating results)";
}
else {
result = "Not regular number of volume.";
}
}
}
document.getElementById('nalbanum_tableau').innerHTML = result;
}
////////////////////////////////////////////////////////////////
// Autres
////////////////////////////////////////////////////////////////
function is_int(value){
if (!isNaN(value) && (parseFloat(value) == parseInt(value)))
return true;
else
return false;
}
function is_sexa(chaine) {
var tableau = chaine.split(".");
for (i = 0; i < tableau.length ; i++) {
if (!is_int(tableau[i]) || parseInt(tableau[i]) >= 60)
return false;
}
return true;
}
function decomposition_60(sexa) {
var number = Sexa_vers_deci(sexa);
var result = new String("");
var divisor = 1;
var ratio = 60;
var quotient;
var reste;
do {
// Before entering this loop, the number is supposed to be
// well-formated.
quotient = Math.floor(number / ratio);
reste = number % ratio;
number = quotient;
result = (reste > 0 ? reste + (divisor > 1 ? "×" + divisor : "")
+ (result != "" ? " + " : "")
: "")
+ result;
divisor *= ratio;
} while (number >= ratio);
if (number != 0)
result = number + "×" + divisor
+ (result != "" ? " + " + result : "");
return result;
}
function systemeS(sexa) {
var number = Sexa_vers_deci(sexa);
var result = new String("");
var divisor = 1;
var ratio = 60;
do {
var quotient = Math.floor(number / ratio);
var reste = number % ratio;
number = quotient;
result = (reste == 0 ? "" : " " + reste
+ (divisor == 1 ? "" : " " + systemS_name(divisor))
) + result;
divisor *= ratio;
} while (number >= ratio);
if (number != 0)
result = number + " " + systemS_name(divisor)
+ (result == "" ? "" : result + " iku");
return result;
}
function systemS_name(divisor) {
var result;
switch (divisor) {
case 216000: result = "šar-gal"; break;
case 36000: result = "šar'u"; break;
case 3600: result = "šar"; break;
case 600: result = "bur'u"; break;
case 60: result = "bur"; break;
case 10: result = "eše"; break;
case 1: result = "iku"; break;
default: result = "× " + divisor;
}
return result;
}
function systemG_name(divisor) {
var result;
switch (divisor) {
case 3888000: result = " šar-gal-šu-nu-tag"; break;
case 64800: result = " šar-gal"; break;
case 10800: result = " šar'u"; break;
case 1080: result = " šar"; break;
case 180: result = " bur'u"; break;
case 18: result = " bur"; break;
case 6: result = " eše"; break;
case 1: result = " iku"; break;
default: result = "×" + divisor;
}
return result;
}
function systemeG(sexa) {
var number = Sexa_vers_deci(sexa);
var result = new String("");
var divisor = 1;
var rapport;
var quotient, reste;
// mod 6
rapport = 6;
quotient = Math.floor(number / rapport);
reste = number % rapport;
number = quotient;
result = (reste == 0 ? "" : reste)
+ result;
divisor *= rapport;
// mod 18
if (number >= 3) {
rapport = 3;
quotient = Math.floor(number / rapport);
reste = number % rapport;
number = quotient;
result = (reste == 0 ? "" : reste
+ systemG_name(divisor)
+ (result == "" ? "" : " ")
+ result);
divisor *= rapport;
}
// 10 et 6, etc.
while (number >= 10) {
rapport = 10;
quotient = Math.floor(number / rapport);
reste = number % rapport;
number = quotient;
result = (reste == 0 ? "" : reste
+ systemG_name(divisor)
+ (result == "" ? "" :
divisor <= 64800 ? " " : " + "))
+ result;
divisor *= rapport;
rapport = 6;
quotient = Math.floor(number / rapport);
reste = number % rapport;
number = quotient;
result = (reste == 0 ? "" : reste
+ (divisor == 1 ? "" : systemG_name(divisor))
+ (result == "" ? "" :
divisor <= 64800 ? " " : " + "))
+ result;
divisor *= rapport;
};
if (number != 0)
result = number + systemG_name(divisor)
+ (result == "" ? "" :
(divisor <= 64800 ? " " : " + ") + result);
return result;
}
function display_result(result, element) {
result = '<span class="result_line">' + result + '</span>';
document.getElementById(element).innerHTML = result;
}
function clear_result(element) {
document.getElementById(element).innerHTML = "";
}
//]]>
// -->
</script>
<!--
################################################################
HTML code of MesoCalc
################################################################
-->
<div id="tout">
<div id="titre">
<h1><a href="http://baptiste.meles.free.fr/site/mesocalc.html">MesoCalc</a></h1>
<hr/>
<p>A Mesopotamian Calculator</p>
</div>
<div id="nav">
<div class="titre"><a href="#note"
onclick="display_intro();">Introduction</a></div>
<div class="titre"><a href="#operations">Arithmetics</a></div>
<form action="" id="form_floating">
<p>Computing system<sup>(<a href="#codes"
onclick="display_intro();">?</a>)</sup>:
<br/>
<input type="radio" name="floating" value="oui"
checked="checked" id="flottant_oui"
onclick="sexa_floating = true;"/>
<label for="flottant_oui">floating
(<span class="system">60F</span>) </label> <br/>
<input type="radio" name="floating" value="non"
id="flottant_non" onclick="sexa_floating = false;"/>
<label for="flottant_non">absolute
(<span class="system">60A</span>) </label>
</p>
</form>
<ul>
<li> <a href="#conversions">Conversion & properties</a></li>
<li> <a href="#multiplication">Multiplicative operations</a></li>
<li> <a href="#powers">Exponential operations</a></li>
<li> <a href="#addition">Additive operations</a></li>
</ul>
<div class="titre"><a href="#units">Measures</a></div>
<ul>
<li> <a href="#lengths">Lengths</a> / <a href="#surfaces">Surfaces</a> /
<a href="#volumes">Volumes</a></li>
<li> <a href="#capacities">Capacities</a></li>
<li> <a href="#weights">Weights</a></li>
<!-- <li> <a href="#systemSsystemG">Systems G/S</a></li> -->
</ul>
<div class="titre"><a href="#dates">Dates</a></div>
</div>
<div id="corps">
<div class="encart">
<p>
MesoCalc is a <strong>Mesopotamian calculator</strong>. It
computes in <a href="#operations">sexagesimal place-value
notation</a>, operates on <a href="#units">measures</a> and converts
<a href="#dates">dates</a>.
</p>
</div>
<p>MesoCalc was created in March 2013
by <a href="http://baptiste.meles.free.fr/">Baptiste MÉLÈS</a>
(CNRS, Archives Henri Poincaré, Université de Lorraine) with
the scientific assistance of <strong>Christine PROUST</strong>
(CNRS, Université Paris-Diderot) in the framework of
the <a href="http://sawerc.hypotheses.org/">SAW Project</a>
(Mathematical Sciences in the Ancient World), headed
by <strong>Karine CHEMLA</strong> (CNRS, Université
Paris-Diderot).</p>
<p>MesoCalc includes computations made by <strong>Mathieu OSSENDRIJVER</strong>
(Humboldt-Universität) and a calendar designed by <strong>Bruno GOMBERT</strong> (Université Paris 1 Panthéon Sorbonne, ARSCAN),
with their benevolent acceptance.</p>
<div class="encart">
<h3>Contents</h3>
<ul>
<li> <a href="#note">Introduction</a> </li>
<li> <a href="#operations">Arithmetics</a>
<ul>
<li><a href="#conversions">Conversion and arithmetical
properties</a>: conversions between decimal and
sexagesimal numbers, regularity test, regular
approximations, list of regular numbers, prime
factors, greatest common divisor;</li>
<li> <a href="#multiplication">Multiplicative operations</a>:
multiplication, quotient, reciprocals, tables... </li>
<li> <a href="#powers">Exponential operations</a>:
square, square root, cube, cube root, geometric
progression, tables... </li>
<li> <a href="#addition">Additive operations</a>: addition,
subtraction; </li>
</ul>
</li>
<li> <a href="#units">Measures</a>
<ul>
<li> <a href="#lengths">Lengths</a>,
<a href="#surfaces">surfaces</a>,
<a href="#volumes">volumes</a>,
<a href="#capacities">capacities</a> and
<a href="#weights">weights</a>: addition,
subtraction, multiplication.</li>
<!-- <li> <a href="#systemSsystemG">System G and
system S</a>: conversions. -->
</ul>
</li>
<li> <a href="#dates">Dates</a>
<ul>
<li><a href="#dates">Date conversion</a></li>
</ul>
</li>
<li> <a href="#faq">About MesoCalc</a>
<ul>
<li> <a href="#download">Can I download
MesoCalc?</a></li>
<li> <a href="#source">Can I read the source
code?</a> </li>
<li><a href="#features">Are there new features in
MesoCalc?</a></li>
<li><a href="#archive">Is MesoCalc's source code
archived?</a></li>
<li> <a href="#license">License</a> </li>
<li> <a href="#contact">Contact</a> </li>
</ul>
</li>
</ul>
</div>
<hr/>
<h2><a name="note"/>Introduction</h2>
<h3><a name="codes"/>Computing systems</h3>
<div class="encart">
<p>
The numbers if the calculator below may belong to different
kinds:
</p>
<table class="center">
<tr>
<th>Code</th>
<th>Numerical system</th>
<th>Examples</th>
</tr>
<tr>
<td><span class="system">10A</span></td>
<td>Decimal place-value notation</td>
<td>7200</td>
</tr>
<tr>
<td><span class="system">60A/F</span></td>
<td>Sexagesimal place-value notation</td>
<td>2.0.0 or 2</td>
</tr>
<tr>
<td><span class="system">60A</span></td>
<td>Absolute sexagesimal place-value notation</td>
<td>2.0.0</td>
</tr>
<tr>
<td><span class="system">60F</span></td>
<td>Floating sexagesimal place-value notation</td>
<td>2</td>
</tr>
<tr>
<td><span class="system">60R</span></td>
<td>Regular number in <span class="system">60F</span></td>
<td>2</td>
</tr>
</table>
</div>
<div id="replie" style="display: block;">
<div class="encart">
<div class="center">
<a href="javascript:void(0);"><span onclick="display_intro();">More
info about this...</span></a>
</div>
</div>
</div>
<div id="deplie" style="display: none;">
<div class="encart">
<div class="center">
<a href="javascript:void(0);"><span onclick="hide_intro();">Less
info about this...</span></a>
</div>
</div>
<h3><a name="spvn"/>Decimal and sexagesimal place-value notation
(<span class="system">10A</span>
and <span class="system">60A/F</span>)</h3>
<div class="encart">
<p> Our numerical system (<span class="system">10A</span>)
is a <strong>decimal</strong> place-value notation. It
means that we use ten digits (0, 1, 2, 3, 4, 5, 6, 7, 8,
9), and that every number containing several digits
(like 1729) is composed of multiples of powers
of <strong>10</strong>. As an example, when we write the
number 1729, we mean the number
(<strong>1</strong> × 1000) + (<strong>7</strong> × 100) + (<strong>2</strong> × 10) + <strong>9</strong>. </p>
<p>
By contrast, Mesopotamian mathematics use
a <strong>sexagesimal</strong> place-value notation
(<span class="system">60A/F</span>). It means that they
used 59 "digits" (they had no 0), and that the
numbers are decomposed into multiples of powers
of <strong>60</strong>, which we can separate with a dot.
As an example, the number 1729 would be noted 28.49, which
means
(<strong>28</strong> × 60) + <strong>49</strong>.
The number 10000 would be noted 2.46.40, which means
(<strong>2</strong> × 3600) + (<strong>46</strong> × 60) + <strong>40</strong>.
</p>
<p>
Unlike 10, which has only two divisors (2 and 5), 60 has a lot
of divisors: 2, 3, 4, 5, 6, 10, 12, 15, 20, 30.
</p>
</div>
<h3><a name="floating"/>What are the absolute and floating notations?
(<span class="system">60A</span>
and <span class="system">60F</span>)</h3>
<div class="encart">
<p>
Whereas our numerical system (<span class="system">10A</span>)
is always absolute, the sexagesimal notation used in
mathematical cuneiform texts can be either
"<strong>absolute</strong>" or
"<strong>floating</strong>" (<span class="system">60A/F</span>). </p>
<p>
Intuitively, the sexagesimal notation is said to be
<strong>floating</strong> (<span class="system">60F</span>)
when we neglect all the "<strong>.0</strong>"s that
we can find at the end of a number,
and <strong>absolute</strong>
(<span class="system">60A</span>) when we can not neglect
them. For instance, in <span class="system">60A</span>, the
decimal number 60 is noted "1.0", since it is
(<strong>1</strong> × 60) + <strong>0</strong>. But
in <span class="system">60F</span>, it would just be
noted "1", since we have to neglect all
final ".0"s! We can say that
60<sup><span class="system">10A</span></sup> = 1.0<sup><span class="system">60A</span></sup> = 1<sup><span class="system">60F</span></sup>.
</p>
<p>
As a consequence, the floating sexagesimal number which is
noted "1" in <span class="system">60F</span> can
correspond to the decimal numbers 1, 60
(= <strong>1</strong> × 60), 3600
(= <strong>1</strong> × 60 × 60), etc.; but it can
also correspond to the fractions 1/60
(= <strong>1</strong> × 1/60), 1/3600
(= <strong>1</strong> × 1/(60 × 60)), etc.
Similarly, the number which is noted "2"
in <span class="system">60F</span> can correspond to the
decimal numbers 2, 120, 7200, etc., but also to the fractions
1/30, 1/1800, etc.
</p>
<p> Here are some more examples of sexagesimal place-value
notation:</p>
<table class="center">
<tr><th><span class="system">10A</span></th>
<th><span class="system">60A</span></th>
<th><span class="system">60F</span></th> </tr>
<tr>
<td>1</td>
<td align="right">1</td>
<td align="right">1</td>
</tr>
<tr>
<td>2</td>
<td align="right">2</td>
<td align="right">2</td>
</tr>
<tr>
<td>59</td>
<td align="right">59</td>
<td align="right">59</td>
</tr>
<tr>
<td><strong>60</strong></td>
<td align="right"><strong>1.0</strong></td>
<td align="right"><strong>1</strong></td>
</tr>
<tr>
<td>61</td>
<td align="right">1.1</td>
<td align="right">1.1</td>
</tr>
<tr>
<td><strong>120</strong></td>
<td align="right"><strong>2.0</strong></td>
<td align="right"><strong>2</strong></td>
</tr>
<tr>
<td><strong>3600</strong></td>
<td align="right"><strong>1.0.0</strong></td>
<td align="right"><strong>1</strong></td>
</tr>
<tr>
<td><strong>7200</strong></td>
<td align="right"><strong>2.0.0</strong></td>
<td align="right"><strong>2</strong></td>
</tr>
<tr>
<td>10000</td>
<td align="right">2.46.40</td>
<td align="right">2.46.40</td>
</tr>
</table>
<p>
The floating system may seem strange, but it has wonderful
mathematical properties. For instance, the square root of 15
in <span class="system">60A</span> is not an integer (it is
someting like 3.87..., just like
in <span class="system">10A</span>); but the square root of 15
in <span class="system">60F</span> is 30, for 15 can also
represent the number 15.0 = 900, which is the square
of 30.</p>
<p> Similarly, the cube root of 7.30
in <span class="system">60A</span> is not an integer (just
like the square root of 450
in <span class="system">10A</span>), but the cube root of 7.30
in
<span class="system">60F</span> is 30, for
7.30<sup><span class="system">60F</span></sup> can represent
the
number 7.30.0<sup><span class="system">60A</span></sup> = 27000<sup><span class="system">10A</span></sup>,
which is the cube of 30.
</p>
</div>
<h3><a name="regular"/>What are reciprocals and regular numbers?
(<span class="system">60R</span>)</h3>
<div class="encart">
<p>
The Mesopotamian "division" is performed as
the <strong>multiplication of the dividend</strong> by what is
called the
<strong>"reciprocal" number of the
divisor</strong>.</p>
<p> The <strong>reciprocal R</strong> of
a <strong>number N</strong> is the number such
that, <strong>in floating notation,
R × N = 1</strong> (be it 1, 1.0, 1.0.0 or any
other power of 60 in absolute notation). For instance, the
reciprocal of 1 is 1, since 1 × 1 = 1. The
reciprocal of 2 is 30, since 2 × 30 = 1.0 (which is
noted 1 in floating notation). The reciprocal of 8
is 7.30, since 7.30 × 8 = 1.0.0 (which is also
noted 1 in floating notation).
</p>
<p> Some numbers do not have any reciprocal. As a matter of
fact, a number has a reciprocal if and only if <strong>all of
its prime factors are prime factors of 60 as well</strong>,
which means that it must be reducible to a product of powers
of 2, 3 and 5. Such a number is called a <strong>regular
number</strong> (<span class="system">60R</span>). The
numbers 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16 etc. are regular
numbers, whereas the numbers 7, 11, 13, 14, 17, 19, 21, 22,
23 etc. are not.
</p>
</div>
<hr/>
<h3><a name="biblio"/>Bibliography</h3>
<div class="encart">
<p>If you want to know more about the sexagesimal place-value
notation and mathematical cuneiform texts:</p>
<ul>
<li> FRIBERG, Jöran (2007), <em>A Remarkable Collection of
Babylonian Mathematical Texts</em>, New York:
Springer. </li>
<li> HØYRUP, Jens (2002), <em>Lengths, Widths, Surfaces. A
Portrait of Old Babylonian Algebra and Its Kin</em>,
Berlin & Londres: Springer. </li>
<li> MELVILLE
Duncan, <a href="http://it.stlawu.edu/~dmelvill/mesomath/biblio/bigbib.html">Bibliography
of Mesopotamian Mathematics</a>.</li>
<li> NEUGEBAUER, Otto (1957), <em>The Exact Sciences in
Antiquity</em> (2th ed.), Providence: Brown University
Press. </li>
<li> NEUGEBAUER, Otto and SACHS, Abraham J.
(1945), <em>Mathematical Cuneiform Texts</em>, New Haven:
American Oriental Series & American Schools of
Oriental Research. </li>
<li>PARKER, R. A. and DUBBERSTEIN, W. H., <em>Babylonian
Chronology, 626 B.C.-A.D. 45</em>, Studies in Ancient Oriental Civilization 24, 1942.</li>
<li> PROUST, Christine (2007), <em>Tablettes mathématiques de
Nippur</em>, Istanbul: Institut Français d'Etudes
Anatoliennes, De Boccard. </li>
<li> PROUST,
Christine, <a href="http://www.math.ens.fr/culturemath/histoire%20des%20maths/htm/calcul%20sexagesimal/calcul%20sexagesimal.htm">Le calcul
sexagésimal en Mésopotamie</a>. </li>
<li> ROBSON, Eleanor (2008), <em>Mathematics in Ancient Iraq:
A Social History</em>, Princeton: Princeton University
Press. </li>
<li> THUREAU-DANGIN, François (1932), <em>Esquisse d'une
histoire du système sexagésimal</em>, Paris:
Geuthner. </li>
<li> <a href="http://cdli.ucla.edu/">Cuneiform Digital
Library Initiative (CDLI)</a>. </li>
<li><a href="http://oracc.museum.upenn.edu/doc/builder/math">Mathematical
Notations</a>: conventions for the translitteration of
Mesopotamian mathematical and astronomical texts.</li>
</ul>
</div>
</div>
<hr/>
<h2><a name="operations"/>Arithmetics</h2>
<h3><a name="conversions"/><a name="properties"/>Conversion and
arithmetical properties</h3>
<h4>Conversions</h4>
<div class="encart">
<form action="" id="form_deci2sexa" onsubmit="return false;">
<p>
Conversion from decimal to sexagesimal
(<span class="system">10A</span> → <span class="system">60A/F</span>):<br/>
<input type="text" size="20" name="input" value=""
onkeypress="if (event.keyCode == 13)
deci2sexa(this.form)" />
<input type="button" name="bouton" value="Sexagesimal →"
onclick="deci2sexa(this.form)" />
<span id="conversion-10-60"/>
</p>
</form>
</div>
<div class="encart">
<form action="" id="form_sexa2deci" onsubmit="return false;">
<p>
Conversion from sexagesimal to decimal
(<span class="system">60A</span> → <span class="system">10A</span>):
<br/>
<input type="text" size="20" name="input" value=""
onkeypress="if (event.keyCode == 13)
sexa2deci(this.form)" />
<input type="button" name="bouton" value="Decimal →"
onclick="sexa2deci(this.form)" />
<span id="conversion-60-10"/>
</p>
</form>
</div>
<h4>Arithmetical properties</h4>
<div class="encart">
<form action="" id="form_regular" onsubmit="return false;">
<p>
Regular number?
(<span class="system">60A/F</span> → yes/no) <br/>
<input type="text" size="20" name="input" value=""
onkeypress="if (event.keyCode == 13)
regular(this.form)" />
<input type="button" name="bouton" value="Regular?"
onclick="regular(this.form)" />
<!-- <input type="text" size="25" name="output" value="" /> -->
<span id="regular_number"/>
</p>
</form>
</div>
<div class="encart">
<form action="" id="form_regular_approximation"
onsubmit="return false;">
<p>
Regular approximation <br/>
of <input type="text" size="20" name="input" value=""
onkeypress="if (event.keyCode == 13)
regular_approximation(this.form)" />
(<span class="system">60A/F</span>)
up to <select name="nb_digits">
<option value="1">1</option>
<option value="2">2</option>
<option value="3">3</option>
<option value="4">4</option>
<option value="5">5</option>
<option value="6">6</option>
<option value="7">7</option>
<option value="8">8</option>
<option value="9">9</option>
<option value="10">10</option>
<option value="11">11</option>
<option value="12">12</option>
<option value="13">13</option>
<option value="14">14</option>
<option value="15">15</option>
<option value="16">16</option>
<option value="17">17</option>
<option value="18">18</option>
<option value="19">19</option>
<option value="20" selected="selected">20</option>
</select> sexagesimal digits: <br/>
<input type="button" name="bouton" value="Approximations"
onclick="regular_approximation(this.form)" />
</p>
<div id="regular_approximation"></div>
</form>
</div>
<div class="encart">
<form action="" id="form_facteurs" onsubmit="return false;">
<p>
Prime factors
(<span class="system">60A</span> → <span class="system">60A/F</span>):
<br/>
<input type="text" size="20" name="input" value=""
onkeypress="if (event.keyCode == 13)
facteurs(this.form)" />
<input type="button" name="bouton" value="Prime factors"
onclick="facteurs(this.form)" />
<span id="prime_factors"/>
<!-- <input type="text" size="25" name="output" value="" /> -->
</p>
</form>
</div>
<div class="encart">
<form action="" id="form_gcd" onsubmit="return false;">
<p>
Greatest common divisor
(<span class="system">60A</span>
and <span class="system">60A</span> → <span class="system">60A</span>)
<br/>
<input type="text" size="20" name="input1" value=""
onkeypress="if (event.keyCode == 13)
gcd_form(this.form)" />
and
<input type="text" size="20" name="input2" value=""
onkeypress="if (event.keyCode == 13)
gcd_form(this.form)" />
<input type="button" name="bouton" value="GCD"
onclick="gcd_form(this.form)" />
<span id="gcd"/>
</p>
</form>
</div>
<h3><a name="multiplication"/>Multiplicative operations</h3>
<h4>Multiplication and quotient</h4>
<div class="encart">
<form action="" id="form_multiplication" onsubmit="return false;">
<p>
Multiplication
(<span class="system">60A/F</span>):
</p>
<div class="retrait">
<input type="text" size="10" name="input1"
id="multiplicanda1" value="" onkeypress="if
(event.keyCode == 13) multiplication(this.form)" />
×
<input type="text" size="10" name="input2"
id="multiplicanda2" value="" onkeypress="if
(event.keyCode == 13) multiplication(this.form)" />
<span id="nouv_multiplication"></span>
<br/>
<input type="button" name="bouton" value="Product"
onclick="multiplication(this.form)" />
<input type="button"
onclick="clear_multiplication(this.form)"
value="Clear"/>
</div>
<div class="retrait" id="tableau_multiplication"></div>
</form>
</div>
<div class="encart">
<form action="" id="form_mult_table" onsubmit="return false;">
<p>
Multiplication table
(<span class="system">60A/F</span>): <br/>
<input type="text" size="10" name="input" value=""
onkeypress="if (event.keyCode == 13)
mult_table(this.form)" />
<input type="button" name="bouton" value="Table"
onclick="mult_table(this.form)" />
</p>
<div id="mult_tableau"></div>
</form>
</div>
<div class="encart">
<form action="" id="form_quotient" onsubmit="return false;">
<p>
Quotient
(<span class="system">60F</span>÷<span class="system">60R</span> → <span class="system">60F</span>):
<br/>
<input type="text" size="10" name="input1"
id="quotient_input1" value="" onkeypress="if
(event.keyCode == 13) quotient(this.form)" />
÷
<input type="text" size="10" name="input2" value=""
onkeypress="if (event.keyCode == 13)
quotient(this.form)" />
<br/>
<input type="button" name="bouton" value="Quotient"
onclick="quotient(this.form)" />
<input type="button" onclick="clear_quotient(this.form);"
value="Clear"/>
<span id="quotient"/>
<!-- <input type="text" size="25" name="output" value="" /> -->
</p>
</form>
</div>
<h4>Reciprocal and regular numbers</h4>
<div class="encart">
<form action="" id="form_inverse" onsubmit="return false;">
<p>
Reciprocal number
(<span class="system">60F</span>): <br/>
<input type="text" size="20" name="input" value=""
onkeypress="if (event.keyCode == 13)
inverse(this.form)" />
<input type="button" name="bouton" value="Reciprocal"
onclick="inverse(this.form)" />
<span id="igi"/>
</p>
</form>
</div>
<div class="encart">
<form action="" id="form_inverse_table">
<p>
<input type="button" name="bouton"
value="Reciprocal table"
onclick="inverse_table(this.form)" />
(<span class="system">60F</span>) </p>
<div id="inverse_tableau"></div>
</form>
</div>
<div class="encart">
<form action="" id="form_regular_numbers_interval"
onsubmit="return false;">
<p>
Table of regular numbers
(<span class="system">60A/F</span>
and
<span class="system">60A/F</span>) <br/>
between
<input type="text" size="20" name="input1" value=""
onkeypress="if (event.keyCode == 13)
regular_numbers_interval_form(this.form)" />
and
<input type="text" size="20" name="input2" value=""
onkeypress="if (event.keyCode == 13)
regular_numbers_interval_form(this.form)" />
<br/>
up to <select name="nb_digits">
<option value="1">1</option>
<option value="2">2</option>
<option value="3">3</option>
<option value="4">4</option>
<option value="5">5</option>
<option value="6">6</option>
<option value="7">7</option>
<option value="8">8</option>
<option value="9">9</option>
<option value="10">10</option>
<option value="11">11</option>
<option value="12">12</option>
<option value="13">13</option>
<option value="14">14</option>
<option value="15">15</option>
<option value="16">16</option>
<option value="17">17</option>
<option value="18">18</option>
<option value="19">19</option>
<option value="20" selected="selected">20</option>
</select> sexagesimal digits: <br/>
<input type="button" name="bouton" value="Table"
onclick="regular_numbers_interval_form(this.form)"/>
</p>
<div id="regular_numbers_interval"></div>
</form>
</div>
<div class="encart">
<form action="" id="form_regular_inverse_liste"
onsubmit="return false;">
<p>
Table of regular and reciprocal numbers <br/>
from
<input type="text" size="10" name="input1" value=""
onkeypress="if (event.keyCode == 13)
regular_inverse_liste(this.form)" />
to
<input type="text" size="10" name="input2" value=""
onkeypress="if (event.keyCode == 13)
regular_inverse_liste(this.form)" />
(<span class="system">60A/F</span>) <br/>
up to <select name="nb_digits">
<option value="1">1</option>
<option value="2" selected="selected">2</option>
<option value="3">3</option>
<option value="4">4</option>
<option value="5">5</option>
<option value="6">6</option>
<option value="7">7</option>
<option value="8">8</option>
<option value="9">9</option>
<option value="10">10</option>
<option value="11">11</option>
<option value="12">12</option>
<option value="13">13</option>
<option value="14">14</option>
<option value="15">15</option>
<option value="16">16</option>
<option value="17">17</option>
<option value="18">18</option>
<option value="19">19</option>
<option value="20">20</option>
</select> sexagesimal digits: <br/>
<input type="button"
name="bouton" value="Table"
onclick="regular_inverse_liste(this.form)" />
</p>
<div id="regular_inverse_liste"></div>
</form>
</div>
<h3><a name="powers"/>Exponential operations</h3>
<h4>Squares and square roots</h4>
<div class="encart">
<form action="" id="form_carre" onsubmit="return false;">
<p>
Square
(<span class="system">60A/F</span>): <br/>
<input type="text" size="20" name="input" value=""
onkeypress="if (event.keyCode == 13)
square(this.form)" />
<input type="button" name="bouton" value="Square"
onclick="square(this.form)" />
<span id="square"/>
</p>
</form>
</div>
<div class="encart">
<form action="" id="form_square_root" onsubmit="return false;">
<p>
Square root
(<span class="system">60A/F</span>): <br/>
<input type="text" size="20" name="input" value=""
onkeypress="if (event.keyCode == 13)
square_root(this.form)" />
<input type="button" name="bouton" value="Square root"
onclick="square_root(this.form)" />
<span id="squareroot" />
<!-- <input type="text" size="25" name="output" value="" /> -->
</p>
</form>
</div>
<div class="encart">
<form action="" id="form_square_table" onsubmit="return false;">
<p>
<input type="button" name="bouton" value="Table of squares"
onclick="square_table(this.form)" />
(<span class="system">60F</span>)
</p>
<div id="square_tableau"></div>
</form>
</div>
<div class="encart">
<form action="" id="form_square_root_table" onsubmit="return false;">
<p>
<input type="button" name="bouton"
value="Table of square roots"
onclick="square_root_table(this.form)" />
(<span class="system">60F</span>)
</p>
<div id="square_root_tableau"></div>
</form>
</div>
<h4>Cubes and cube roots</h4>
<div class="encart">
<form action="" id="form_cube" onsubmit="return false;">
<p>
Cube
(<span class="system">60A/F</span>): <br/>
<input type="text" size="20" name="input" value=""
onkeypress="if (event.keyCode == 13)
cube(this.form)" />
<input type="button" name="bouton" value="Cube"
onclick="cube(this.form)" />
<span id="cube"/>
<!-- <input type="text" size="25" name="output" value="" /> -->
</p>
</form>
</div>
<div class="encart">
<form action="" id="form_cubic_root" onsubmit="return false;">
<p>
Cube root
(<span class="system">60A/F</span>): <br/>
<input type="text" size="20" name="input" value=""
onkeypress="if (event.keyCode == 13)
cubic_root(this.form)" />
<input type="button" name="bouton" value="Cube root"
onclick="cubic_root(this.form)" />
<span id="cuberoot"/>
<!-- <input type="text" size="25" name="output" value="" /> -->
</p>
</form>
</div>
<div class="encart">
<form action="" id="form_cube_root_table" onsubmit="return false;">
<p>
<input type="button" name="bouton"
value="Table of cube roots"
onclick="cube_root_table(this.form)" />
(<span class="system">60F</span>)
</p>
<div id="cube_root_tableau"></div>
</form>
</div>
<h4>Geometric progression</h4>
<div class="encart">
<form action="" id="form_geom" onsubmit="return false;">
<p>
Geometric progression
(<em>a × b<sup>n</sup></em>): <br/>
<em>a</em> = <input type="text" size="20" name="first"
value="" onkeypress="if (event.keyCode
== 13) geom(this.form)"
/><sup><span class="system">60A/F</span></sup>
(first term) <br/>
<em>b</em> = <input type="text" size="20" name="ratio"
value="" onkeypress="if (event.keyCode
== 13) geom(this.form)"
/><sup><span class="system">60A/F</span></sup>
(common ratio) <br/>
<em>n</em> = <input type="text" size="20" name="terms"
value="" onkeypress="if (event.keyCode
== 13) geom(this.form)"
/><sup><span class="system">10A</span></sup>
(number of terms) <br/>
<input type="button" name="bouton" value="Table"
onclick="geom(this.form)" />
</p>
<div id="geom_tableau"></div>
</form>
</div>
<h3><a name="addition"/>Additive operations</h3>
<div class="encart">
<form action="" id="form_addition" onsubmit="return false;">
<p>
Addition
(<span class="system">60A</span>):
</p>
<div class="retrait">
<input type="text" size="10" name="input1" id="addenda1"
value="" onkeypress="if (event.keyCode == 13)
addition(this.form)" /> +
<input type="text" size="10" name="input2" id="addenda2"
value="" onkeypress="if (event.keyCode == 13)
addition(this.form)" />
<span id="nouv_addition"></span>
<br/>
<input type="button" name="bouton" value="Sum"
onclick="addition(this.form)" />
<input type="button" onclick="clear_addition(this.form)"
value="Clear"/>
</div>
<div class="retrait" id="tableau_addition"></div>
</form>
</div>
<div class="encart">
<form action="" id="form_soustraction" onsubmit="return false;">
<p>
Subtraction
(<span class="system">60A</span>):
</p>
<div class="retrait">
<input type="text" size="10" name="input1"
id="subtrahenda1" value="" onkeypress="if
(event.keyCode == 13) soustraction(this.form)" />
−
<input type="text" size="10" name="input2"
id="subtrahenda2" value="" onkeypress="if
(event.keyCode == 13) soustraction(this.form)" />
<span id="nouv_soustraction"></span>
<br/>
<input type="button" name="bouton" value="Difference"
onclick="soustraction(this.form)" />
<!-- <input type="text" size="25" name="output" value="" /> -->
<input type="button" onclick="clear_soustraction(this.form)"
value="Clear"/>
</div>
<div class="retrait" id="tableau_soustraction"></div>
</form>
</div>
<hr/>
<h2><a name="units"/>Measures</h2>
<h3><a name="lengths"/>Lengths</h3>
<p>Units of length:</p>
<div class="retrait">
<table class="encadre">
<tr>
<td><strong><em>danna</em></strong></td> <td> ← 30
← </td>
<td><strong><em>uš</em></strong></td> <td> ← 60 ← </td>
<td><strong><em>ninda</em></strong></td> <td> ← 12
← </td>
<td><strong><em>kuš</em></strong></td> <td> ← 30
← </td>
<td><strong><em>šusi</em></strong></td>
</tr>
<tr>
<td>10.8 km</td> <td> </td>
<td>360 m</td> <td> </td>
<td>6 m</td> <td> </td>
<td>50 cm</td> <td> </td>
<td>17 mm</td>
</tr>
</table>
</div>
<div class="encart">
<form action="" id="form_add_longueurs" onsubmit="return false;">
<p>
Add lengths:
</p>
<div class="retrait">
<table class="encadre">
<tr>
<th></th>
<th><em>danna</em></th>
<th><em>uš</em></th>
<th><em>ninda</em></th>
<th><em>kuš</em></th>
<th><em>šusi</em></th>
</tr>
<tr>
<td></td>
<td>
<input type="text" name="danna1"
id="add_length_danna1" value="" size="8"
onkeypress="if (event.keyCode == 13)
add_longueurs(this.form)" />
</td>
<td>
<input type="text" name="us1" id="add_length_us1"
value="" size="8" onkeypress="if
(event.keyCode == 13)
add_longueurs(this.form)" />
</td>
<td>
<input type="text" name="ninda1" value="" size="8"
onkeypress="if (event.keyCode == 13)
add_longueurs(this.form)" />
</td>
<td>
<input type="text" name="kus1" id="add_length_kus1"
value="" size="8" onkeypress="if
(event.keyCode == 13)
add_longueurs(this.form)" />
</td>
<td>
<input type="text" name="susi1"
id="add_length_susi1" value="" size="8"
onkeypress="if (event.keyCode == 13)
add_longueurs(this.form)" />
</td>
</tr>
<tr>
<td align="center">+</td>
<td>
<input type="text" name="danna2"
id="add_length_danna2" value="" size="8"
onkeypress="if (event.keyCode == 13)
add_longueurs(this.form)" />
</td>
<td>
<input type="text" name="us2" id="add_length_us2"
value="" size="8" onkeypress="if
(event.keyCode == 13)
add_longueurs(this.form)" />
</td>
<td>
<input type="text" name="ninda2"
id="add_length_ninda2" value="" size="8"
onkeypress="if (event.keyCode == 13)
add_longueurs(this.form)" />
</td>
<td>
<input type="text" name="kus2" id="add_length_kus2"
value="" size="8" onkeypress="if
(event.keyCode == 13)
add_longueurs(this.form)" />
</td>
<td>
<input type="text" name="susi2"
id="add_length_susi2" value="" size="8"
onkeypress="if (event.keyCode == 13)
add_longueurs(this.form)" />
</td>
</tr>
<tr>
<td colspan="6"><hr/></td>
</tr>
<tr>
<td>
<input type="button" name="bouton" value="="
onclick="add_longueurs(this.form)" />
</td>
<td colspan="4">
<span id="add_lengths_output" />
<!-- <input type="text" name="output" value=""
size="45" /> -->
</td>
<td>
<input type="button" onclick="this.form.reset();
clear_result('add_lengths_output');
document.getElementById('add_length_danna1').focus();" value="Clear"/>
</td>
</tr>
</table>
</div>
<div class="retrait" id="tableau_add_longueurs"></div>
</form>
</div>
<div class="encart">
<form action="" id="form_soustr_longueurs" onsubmit="return false;">
<p>
Subtract lengths:
</p>
<div class="retrait">
<table class="encadre">
<tr>
<th></th>
<th><em>danna</em></th>
<th><em>uš</em></th>
<th><em>ninda</em></th>
<th><em>kuš</em></th>
<th><em>šusi</em></th>
</tr>
<tr>
<td></td>
<td>
<input type="text" name="danna1" value="" size="8"
id="subtract_length_danna1"
onkeypress="if (event.keyCode == 13)
soustr_longueurs(this.form)" />
</td>
<td>
<input type="text" name="us1" value="" size="8"
id="subtract_length_us1"
onkeypress="if (event.keyCode == 13)
soustr_longueurs(this.form)" />
</td>
<td>
<input type="text" name="ninda1" value="" size="8"
id="subtract_length_ninda1"
onkeypress="if (event.keyCode == 13)
soustr_longueurs(this.form)" />
</td>
<td>
<input type="text" name="kus1" value="" size="8"
id="subtract_length_kus1"
onkeypress="if (event.keyCode == 13)
soustr_longueurs(this.form)" /> </td>
<td>
<input type="text" name="susi1" value="" size="8"
id="subtract_length_susi1"
onkeypress="if (event.keyCode == 13)
soustr_longueurs(this.form)" />
</td>
</tr>
<tr>
<td align="center">− </td>
<td>
<input type="text" name="danna2" value="" size="8"
id="subtract_length_danna2"
onkeypress="if (event.keyCode == 13)
soustr_longueurs(this.form)" /> </td>
<td>
<input type="text" name="us2" value="" size="8"
id="subtract_length_us2"
onkeypress="if (event.keyCode == 13)
soustr_longueurs(this.form)" /> </td>
<td>
<input type="text" name="ninda2" value="" size="8"
id="subtract_length_ninda2"
onkeypress="if (event.keyCode == 13)
soustr_longueurs(this.form)" /> </td>
<td>
<input type="text" name="kus2" value="" size="8"
id="subtract_length_kus2"
onkeypress="if (event.keyCode == 13)
soustr_longueurs(this.form)" /> </td>
<td>
<input type="text" name="susi2" value="" size="8"
id="subtract_length_susi2"
onkeypress="if (event.keyCode == 13)
soustr_longueurs(this.form)" />
</td>
</tr>
<tr>
<td colspan="6"><hr/></td>
</tr>
<tr>
<td>
<input type="button" name="bouton" value="="
onclick="soustr_longueurs(this.form)" />
</td>
<td colspan="4">
<span id="subtract_lengths_output" />
</td>
<td>
<input type="button" onclick="this.form.reset();
clear_result('subtract_lengths_output');
document.getElementById('subtract_length_danna1').focus();" value="Clear"/>
</td>
</tr>
</table>
</div>
</form>
</div>
<div class="encart">
<form action="" id="form_mult_longueur" onsubmit="return false;">
<p>
Multiply a length:
</p>
<div class="retrait">
<table class="encadre">
<tr>
<td>
<input type="text" name="danna"
id="mult_longueur_danna" value="" size="8"
onkeypress="if (event.keyCode == 13)
mult_longueur_form(this.form)" />
<strong><em>danna</em></strong>
</td>
<td>
<input type="text" name="us" id="mult_longueur_us"
value="" size="8" onkeypress="if
(event.keyCode == 13)
mult_longueur_form(this.form)" />
<strong><em>uš</em></strong>
</td>
<td>
<input type="text" name="ninda" value="" size="8"
onkeypress="if (event.keyCode == 13)
mult_longueur_form(this.form)" />
<strong><em>ninda</em></strong>
</td>
<td>
<input type="text" name="kus" id="mult_longueur_kus"
value="" size="8" onkeypress="if
(event.keyCode == 13)
mult_longueur_form(this.form)" />
<strong><em>kuš</em></strong>
</td>
<td>
<input type="text" name="susi"
id="mult_longueur_susi" value="" size="8"
onkeypress="if (event.keyCode == 13)
mult_longueur_form(this.form)" />
<strong><em>šusi</em></strong>
</td>
</tr>
<tr>
<td colspan="5">
×
<input type="text" name="scalaire"
id="mult_longueur_scalaire" value="" size="8"
onkeypress="if (event.keyCode == 13)
mult_longueur_form(this.form)" />
times
</td>
</tr>
<tr>
<td colspan="5"><hr/></td>
</tr>
<tr>
<td>
<input type="button" name="bouton" value="="
onclick="mult_longueur_form(this.form)" />
</td>
<td colspan="3">
<span id="mult_length_output"></span>
<!-- <input type="text" name="output" value=""
size="45" /> -->
</td>
<td>
<input type="button" onclick="this.form.reset();
clear_result('mult_length_output');
document.getElementById('mult_longueur_danna').focus();" value="Clear"/>
</td>
</tr>
</table>
</div>
</form>
</div>
<h3><a name="surfaces"/>Surfaces</h3>
<p>
Units of surface:
</p>
<div class="retrait">
<table class="encadre">
<tr>
<td><strong><em>gan</em></strong></td>
<td> ← 100 ← </td>
<td><strong><em>sar</em></strong></td>
<td> ← 60 ← </td>
<td><strong><em>gin</em></strong></td>
<td> ← 180 ← </td>
<td><strong><em>še</em></strong></td>
</tr>
<tr>
<td>3600 m²</td> <td> </td>
<td>36 m²</td> <td> </td>
<td>0.6 m²</td> <td> </td>
<td>33 cm²</td>
</tr>
<tr>
<td></td> <td> </td>
<td>1 ninda × 1 ninda</td> <td> </td>
<td></td> <td> </td>
<td></td>
</tr>
</table>
</div>
<div class="encart">
<form action="" id="form_mult_longueurs" onsubmit="return false;">
<p>
Multiply lengths to get a surface:
</p>
<div class="retrait">
<table class="encadre">
<tr>
<th></th>
<th><em>danna</em></th>
<th><em>uš</em></th>
<th><em>ninda</em></th>
<th><em>kuš</em></th>
<th><em>šusi</em></th>
</tr>
<tr>
<td></td>
<td>
<input type="text" name="danna1"
id="mult_length_danna1" value="" size="8"
onkeypress="if (event.keyCode == 13)
mult_longueurs(this.form)" /> </td>
<td>
<input type="text" name="us1" id="mult_length_us1"
value="" size="8" onkeypress="if
(event.keyCode == 13)
mult_longueurs(this.form)" />
</td>
<td>
<input type="text" name="ninda1" value="" size="8"
onkeypress="if (event.keyCode == 13)
mult_longueurs(this.form)" />
</td>
<td>
<input type="text" name="kus1" id="mult_length_kus1"
value="" size="8" onkeypress="if
(event.keyCode == 13)
mult_longueurs(this.form)" />
</td>
<td>
<input type="text" name="susi1"
id="mult_length_susi1" value="" size="8"
onkeypress="if (event.keyCode == 13)
mult_longueurs(this.form)" />
</td>
</tr>
<tr>
<td align="center">× </td>
<td>
<input type="text" name="danna2"
id="mult_length_danna2" value="" size="8"
onkeypress="if (event.keyCode == 13)
mult_longueurs(this.form)" />
</td>
<td>
<input type="text" name="us2" id="mult_length_us2"
value="" size="8" onkeypress="if
(event.keyCode == 13)
mult_longueurs(this.form)" />
</td>
<td>
<input type="text" name="ninda2"
id="mult_length_ninda2" value="" size="8"
onkeypress="if (event.keyCode == 13)
mult_longueurs(this.form)" />
</td>
<td>
<input type="text" name="kus2" id="mult_length_kus2"
value="" size="8" onkeypress="if
(event.keyCode == 13)
mult_longueurs(this.form)" />
</td>
<td>
<input type="text" name="susi2"
id="mult_length_susi2" value="" size="8"
onkeypress="if (event.keyCode == 13)
mult_longueurs(this.form)" />
</td>
</tr>
<tr>
<td colspan="6"><hr/></td>
</tr>
<tr>
<td>
<input type="button" name="bouton" value="="
onclick="mult_longueurs(this.form)" />
</td>
<td colspan="4">
<span id="mult_two_lengths_output"></span>
<!-- <input type="text" name="output" value=""
size="45" /> -->
</td>
<td>
<input type="button" onclick="form.reset();
clear_result('mult_two_lengths_output');
document.getElementById('mult_length_danna1').focus();"
value="Clear"/>
</td>
</tr>
</table>
</div>
</form>
</div>
<div class="encart">
<form action="" id="form_add_surfaces" onsubmit="return false;">
<p>
Add surfaces:
</p>
<div class="retrait">
<table class="encadre">
<tr>
<th></th>
<th><em>gan</em></th>
<th><em>sar</em></th>
<th><em>gin</em></th>
<th><em>še</em></th>
</tr>
<tr>
<td> </td>
<td>
<input type="text" name="gan1" value="" size="8"
id="add_surfaces_gan1"
onkeypress="if (event.keyCode == 13)
add_surfaces(this.form)" />
</td>
<td>
<input type="text" name="sar1" value="" size="8"
id="add_surfaces_sar1"
onkeypress="if (event.keyCode == 13)
add_surfaces(this.form)" />
</td>
<td>
<input type="text" name="gin1" value="" size="8"
id="add_surfaces_gin1"
onkeypress="if (event.keyCode == 13)
add_surfaces(this.form)" />
</td>
<td>
<input type="text" name="se1" value="" size="8"
id="add_surfaces_se1"
onkeypress="if (event.keyCode == 13)
add_surfaces(this.form)" />
</td>
</tr>
<tr>
<td align="center">+</td>
<td>
<input type="text" name="gan2" value="" size="8"
id="add_surfaces_gan2"
onkeypress="if (event.keyCode == 13)
add_surfaces(this.form)" />
</td>
<td>
<input type="text" name="sar2" value="" size="8"
id="add_surfaces_sar2"
onkeypress="if (event.keyCode == 13)
add_surfaces(this.form)" />
</td>
<td>
<input type="text" name="gin2" value="" size="8"
id="add_surfaces_gin2"
onkeypress="if (event.keyCode == 13)
add_surfaces(this.form)" />
</td>
<td>
<input type="text" name="se2" value="" size="8"
id="add_surfaces_se2"
onkeypress="if (event.keyCode == 13)
add_surfaces(this.form)" />
</td>
</tr>
<tr>
<td colspan="5"><hr/></td>
</tr>
<tr>
<td>
<input type="button" name="bouton" value="="
onclick="add_surfaces(this.form)" />
</td>
<td colspan="3">
<span id="add_surfaces_output"></span>
<!-- <input type="text" name="output" value=""
size="45" /> -->
</td>
<td>
<input type="button" onclick="this.form.reset();
clear_result('add_surfaces_output');
document.getElementById('add_surfaces_gan1').focus();" value="Clear"/>
</td>
</tr>
</table>
</div>
</form>
</div>
<div class="encart">
<form action="" id="form_soustr_surfaces" onsubmit="return false;">
<p>
Subtract surfaces:
</p>
<div class="retrait">
<table class="encadre">
<tr>
<th></th>
<th><em>gan</em></th>
<th><em>sar</em></th>
<th><em>gin</em></th>
<th><em>še</em></th>
</tr>
<tr>
<td> </td>
<td>
<input type="text" name="gan1" value="" size="8"
id="subtract_surfaces_gan1"
onkeypress="if (event.keyCode == 13)
soustr_surfaces(this.form)" />
</td>
<td>
<input type="text" name="sar1" value="" size="8"
id="subtract_surfaces_sar1"
onkeypress="if (event.keyCode == 13)
soustr_surfaces(this.form)" />
</td>
<td>
<input type="text" name="gin1" value="" size="8"
id="subtract_surfaces_gin1"
onkeypress="if (event.keyCode == 13)
soustr_surfaces(this.form)" />
</td>
<td>
<input type="text" name="se1" value="" size="8"
id="subtract_surfaces_se1"
onkeypress="if (event.keyCode == 13)
soustr_surfaces(this.form)" />
</td>
</tr>
<tr>
<td align="center">− </td>
<td>
<input type="text" name="gan2" value="" size="8"
id="subtract_surfaces_gan2"
onkeypress="if (event.keyCode == 13)
soustr_surfaces(this.form)" />
</td>
<td>
<input type="text" name="sar2" value="" size="8"
id="subtract_surfaces_sar2"
onkeypress="if (event.keyCode == 13)
soustr_surfaces(this.form)" />
</td>
<td>
<input type="text" name="gin2" value="" size="8"
id="subtract_surfaces_gin2"
onkeypress="if (event.keyCode == 13)
soustr_surfaces(this.form)" />
</td>
<td>
<input type="text" name="se2" value="" size="8"
id="subtract_surfaces_se2"
onkeypress="if (event.keyCode == 13)
soustr_surfaces(this.form)" />
</td>
</tr>
<tr>
<td colspan="5"><hr/></td>
</tr>
<tr>
<td>
<input type="button" name="bouton" value="="
onclick="soustr_surfaces(this.form)" />
</td>
<td colspan="3">
<span id="subtract_surfaces_output"></span>
<!-- <input type="text" name="output" value=""
size="45" /> -->
</td>
<td>
<input type="button" onclick="this.form.reset();
clear_result('subtract_surfaces_output');
document.getElementById('subtract_surfaces_gan1').focus();" value="Clear"/>
</td>
</tr>
</table>
</div>
</form>
</div>
<div class="encart">
<form action="" id="form_mult_surface" onsubmit="return false;">
<p>
Multiply a surface:
</p>
<div class="retrait">
<table class="encadre">
<tr>
<td>
<input type="text" name="gan" id="mult_surface_gan"
value="" size="8" onkeypress="if
(event.keyCode == 13)
mult_surface_form(this.form)" />
</td>
<td>
<input type="text" name="sar" id="mult_surface_sar"
value="" size="8" onkeypress="if
(event.keyCode == 13)
mult_surface_form(this.form)" />
</td>
<td>
<input type="text" name="gin" value="" size="8"
onkeypress="if (event.keyCode == 13)
mult_surface_form(this.form)" />
</td>
<td>
<input type="text" name="se" id="mult_surface_se"
value="" size="8" onkeypress="if
(event.keyCode == 13)
mult_surface_form(this.form)" />
</td>
</tr>
<tr>
<td> <strong><em>gan</em></strong></td>
<td> <strong><em>sar</em></strong></td>
<td> <strong><em>gin</em></strong> </td>
<td> <strong><em>še</em></strong> </td>
</tr>
<tr>
<td colspan="4"> ×
<input type="text" name="scalaire"
id="mult_surface_scalaire" value="" size="8"
onkeypress="if (event.keyCode == 13)
mult_surface_form(this.form)" />
times
</td>
</tr>
<tr>
<td colspan="4"><hr/></td>
</tr>
<tr>
<td>
<input type="button" name="bouton" value="="
onclick="mult_surface_form(this.form)" />
</td>
<td colspan="2">
<span id="mult_surface_output"></span>
<!-- <input type="text" name="output" value=""
size="45" /> -->
</td>
<td>
<input type="button" onclick="form.reset();
clear_result('mult_surface_output');
document.getElementById('mult_surface_gan').focus();"
value="Clear"/>
</td>
</tr>
</table>
</div>
</form>
</div>
<h3><a name="volumes"/>Volumes</h3>
<p>
Units of volume:
</p>
<div class="retrait">
<table class="encadre">
<tr>
<td><strong><em>gan</em></strong> </td>
<td> ← 100 ← </td>
<td><strong><em>sar</em></strong> </td>
<td> ← 60 ← </td>
<td><strong><em>gin</em></strong> </td>
<td> ← 180 ← </td>
<td><strong><em>še</em></strong> </td>
</tr>
<tr>
<td>1800 m³ </td>
<td> </td>
<td>18 m³ </td>
<td> </td>
<td>300 dm³ </td>
<td> </td>
<td>1.66 dm³ </td>
</tr>
<tr>
<td> </td>
<td> </td>
<td>1 (surface-)sar × 1 kuš </td>
<td> </td>
<td> </td>
<td> </td>
<td> </td>
</tr>
</table>
</div>
<div class="encart">
<form action="" id="form_mult_trois_longueurs"
onsubmit="return false;">
<p>
Multiply lengths to get a volume:
</p>
<div class="retrait">
<table class="encadre">
<tr>
<th></th>
<th><em>danna</em></th>
<th><em>uš</em></th>
<th><em>ninda</em></th>
<th><em>kuš</em></th>
<th><em>šusi</em></th>
</tr>
<tr>
<td> </td>
<td>
<input type="text" name="danna1"
id="mult_3length_danna1" value="" size="8"
onkeypress="if (event.keyCode == 13)
mult_trois_longueurs_form(this.form)" />
</td>
<td>
<input type="text" name="us1" id="mult_3length_us1"
value="" size="8" onkeypress="if
(event.keyCode == 13)
mult_trois_longueurs_form(this.form)" />
</td>
<td>
<input type="text" name="ninda1" value="" size="8"
onkeypress="if (event.keyCode == 13)
mult_trois_longueurs_form(this.form)" />
</td>
<td>
<input type="text" name="kus1"
id="mult_3length_kus1" value="" size="8"
onkeypress="if (event.keyCode == 13)
mult_trois_longueurs_form(this.form)" />
</td>
<td>
<input type="text" name="susi1"
id="mult_3length_susi1" value="" size="8"
onkeypress="if (event.keyCode == 13)
mult_trois_longueurs_form(this.form)" />
</td>
</tr>
<tr>
<td align="center">× </td>
<td>
<input type="text" name="danna2"
id="mult_3length_danna2" value="" size="8"
onkeypress="if (event.keyCode == 13)
mult_trois_longueurs_form(this.form)" />
</td>
<td>
<input type="text" name="us2" id="mult_3length_us2"
value="" size="8" onkeypress="if
(event.keyCode == 13)
mult_trois_longueurs_form(this.form)" />
</td>
<td>
<input type="text" name="ninda2"
id="mult_3length_ninda2" value="" size="8"
onkeypress="if (event.keyCode == 13)
mult_trois_longueurs_form(this.form)" />
</td>
<td>
<input type="text" name="kus2"
id="mult_3length_kus2" value="" size="8"
onkeypress="if (event.keyCode == 13)
mult_trois_longueurs_form(this.form)" />
</td>
<td>
<input type="text" name="susi2"
id="mult_3length_susi2" value="" size="8"
onkeypress="if (event.keyCode == 13)
mult_trois_longueurs_form(this.form)" />
</td>
</tr>
<tr>
<td align="center">×
</td>
<td>
<input type="text" name="danna3"
id="mult_3length_danna3" value="" size="8"
onkeypress="if (event.keyCode == 13)
mult_trois_longueurs_form(this.form)" />
</td>
<td>
<input type="text" name="us3" id="mult_3length_us3"
value="" size="8" onkeypress="if
(event.keyCode == 13)
mult_trois_longueurs_form(this.form)" />
</td>
<td>
<input type="text" name="ninda3"
id="mult_3length_ninda3" value="" size="8"
onkeypress="if (event.keyCode == 13)
mult_trois_longueurs_form(this.form)" />
</td>
<td>
<input type="text" name="kus3"
id="mult_3length_kus3" value="" size="8"
onkeypress="if (event.keyCode == 13)
mult_trois_longueurs_form(this.form)" />
</td>
<td>
<input type="text" name="susi3"
id="mult_3length_susi3" value="" size="8"
onkeypress="if (event.keyCode == 13)
mult_trois_longueurs_form(this.form)" />
</td>
</tr>
<tr>
<td colspan="6"><hr/></td>
</tr>
<tr>
<td>
<input type="button" name="bouton" value="="
onclick="mult_trois_longueurs_form(this.form)"
/>
</td>
<td colspan="4">
<span id="mult_three_lengths_output"></span>
<!-- <input type="text" name="output" value=""
size="45" /> -->
</td>
<td>
<input type="button" onclick="form.reset();
clear_result('mult_three_lengths_output');
document.getElementById('mult_3length_danna1').focus();"
value="Clear"/>
</td>
</tr>
</table>
</div>
</form>
</div>
<div class="encart">
<form action="" id="form_mult_surface_longueur"
onsubmit="return false;">
<p>
Multiply length and surface to get a volume:
</p>
<div class="retrait">
<table class="encadre">
<tr>
<td>
<input type="text" name="danna"
id="mult_surface_length_danna" value=""
size="8" onkeypress="if (event.keyCode == 13)
mult_surface_longueur_form(this.form)" />
<strong><em>danna</em></strong>
</td>
<td>
<input type="text" name="us"
id="mult_surface_length_us" value="" size="8"
onkeypress="if (event.keyCode == 13)
mult_surface_longueur_form(this.form)" />
<strong><em>uš</em></strong>
</td>
<td>
<input type="text" name="ninda" value="" size="8"
onkeypress="if (event.keyCode == 13)
mult_surface_longueur_form(this.form)" />
<strong><em>ninda</em></strong>
</td>
<td>
<input type="text" name="kus"
id="mult_surface_length_kus" value=""
size="8" onkeypress="if (event.keyCode == 13)
mult_surface_longueur_form(this.form)" />
<strong><em>kuš</em></strong>
</td>
<td>
<input type="text" name="susi"
id="mult_surface_length_susi" value=""
size="8" onkeypress="if (event.keyCode == 13)
mult_surface_longueur_form(this.form)" />
<strong><em>šusi</em></strong>
</td>
</tr>
<tr>
<td> × </td>
<td>
<input type="text" name="gan"
id="mult_surface_length_gan" value=""
size="8" onkeypress="if (event.keyCode == 13)
mult_surface_longueur_form(this.form)" />
<strong><em>gan</em></strong>
</td>
<td>
<input type="text" name="sar"
id="mult_surface_length_sar" value=""
size="8" onkeypress="if (event.keyCode == 13)
mult_surface_longueur_form(this.form)" />
<strong><em>sar</em></strong>
</td>
<td>
<input type="text" name="gin" value="" size="8"
onkeypress="if (event.keyCode == 13)
mult_surface_longueur_form(this.form)"
/> <strong><em>gin</em></strong>
</td>
<td>
<input type="text" name="se"
id="mult_surface_length_se" value="" size="8"
onkeypress="if (event.keyCode == 13)
mult_surface_longueur_form(this.form)" />
<strong><em>še</em></strong>
</td>
</tr>
<tr>
<td colspan="5"><hr/></td>
</tr>
<tr>
<td>
<input type="button" name="bouton" value="="
onclick="mult_surface_longueur_form(this.form)"/>
</td>
<td colspan="3">
<span id="mult_surface_length_output"></span>
<!-- <input type="text" name="output" value=""
size="45" /> -->
</td>
<td>
<input type="button" onclick="form.reset();
clear_result('mult_surface_length_output');
document.getElementById('mult_surface_length_danna').focus();"
value="Clear"/>
</td>
</tr>
</table>
</div>
</form>
</div>
<div class="encart">
<form action="" id="form_add_volumes" onsubmit="return false;">
<p>
Add volumes:
</p>
<div class="retrait">
<table class="encadre">
<tr>
<th></th>
<th><em>gan</em></th>
<th><em>sar</em></th>
<th><em>gin</em></th>
<th><em>še</em></th>
</tr>
<tr>
<td> </td>
<td>
<input type="text" name="gan1" value="" size="8"
id="add_volumes_gan1"
onkeypress="if (event.keyCode == 13)
add_volumes(this.form)" />
</td>
<td>
<input type="text" name="sar1" value="" size="8"
id="add_volumes_sar1"
onkeypress="if (event.keyCode == 13)
add_volumes(this.form)" />
</td>
<td>
<input type="text" name="gin1" value="" size="8"
id="add_volumes_gin1"
onkeypress="if (event.keyCode == 13)
add_volumes(this.form)" />
</td>
<td>
<input type="text" name="se1" value="" size="8"
id="add_volumes_se1"
onkeypress="if (event.keyCode == 13)
add_volumes(this.form)" />
</td>
</tr>
<tr>
<td align="center">+ </td>
<td>
<input type="text" name="gan2" value="" size="8"
id="add_volumes_gan2"
onkeypress="if (event.keyCode == 13)
add_volumes(this.form)" />
</td>
<td>
<input type="text" name="sar2" value="" size="8"
id="add_volumes_sar2"
onkeypress="if (event.keyCode == 13)
add_volumes(this.form)" />
</td>
<td>
<input type="text" name="gin2" value="" size="8"
id="add_volumes_gin2"
onkeypress="if (event.keyCode == 13)
add_volumes(this.form)" />
</td>
<td>
<input type="text" name="se2" value="" size="8"
id="add_volumes_se2"
onkeypress="if (event.keyCode == 13)
add_volumes(this.form)" />
</td>
</tr>
<tr>
<td colspan="5"><hr/></td>
</tr>
<tr>
<td>
<input type="button" name="bouton" value="="
onclick="add_volumes(this.form)" />
</td>
<td colspan="3">
<span id="add_volumes_output"></span>
<!-- <input type="text" name="output" value=""
size="45" /> -->
</td>
<td>
<input type="button" onclick="this.form.reset();
clear_result('add_volumes_output');
document.getElementById('add_volumes_gan1').focus();" value="Clear"/>
</td>
</tr>
</table>
</div>
</form>
</div>
<div class="encart">
<form action="" id="form_soustr_volumes" onsubmit="return false;">
<p>
Subtract volumes:
</p>
<div class="retrait">
<table class="encadre">
<tr>
<th></th>
<th><em>gan</em></th>
<th><em>sar</em></th> <th><em>gin</em></th>
<th><em>še</em></th>
</tr>
<tr>
<td> </td>
<td>
<input type="text" name="gan1" value="" size="8"
id="subtract_volumes_gan1"
onkeypress="if (event.keyCode == 13)
soustr_volumes(this.form)" />
</td>
<td>
<input type="text" name="sar1" value="" size="8"
id="subtract_volumes_sar1"
onkeypress="if (event.keyCode == 13)
soustr_volumes(this.form)" />
</td>
<td>
<input type="text" name="gin1" value="" size="8"
id="subtract_volumes_gin1"
onkeypress="if (event.keyCode == 13)
soustr_volumes(this.form)" />
</td>
<td>
<input type="text" name="se1" value="" size="8"
id="subtract_volumes_se1"
onkeypress="if (event.keyCode == 13)
soustr_volumes(this.form)" />
</td>
</tr>
<tr>
<td align="center">− </td>
<td>
<input type="text" name="gan2" value="" size="8"
id="subtract_volumes_gan2"
onkeypress="if (event.keyCode == 13)
soustr_volumes(this.form)" />
</td>
<td>
<input type="text" name="sar2" value="" size="8"
id="subtract_volumes_sar2"
onkeypress="if (event.keyCode == 13)
soustr_volumes(this.form)" />
</td>
<td>
<input type="text" name="gin2" value="" size="8"
id="subtract_volumes_gin2"
onkeypress="if (event.keyCode == 13)
soustr_volumes(this.form)" />
</td>
<td>
<input type="text" name="se2" value="" size="8"
id="subtract_volumes_se2"
onkeypress="if (event.keyCode == 13)
soustr_volumes(this.form)" />
</td>
</tr>
<tr>
<td colspan="5"><hr/></td>
</tr>
<tr>
<td>
<input type="button" name="bouton" value="="
onclick="soustr_volumes(this.form)" />
</td>
<td colspan="3">
<span id="subtract_volumes_output"></span>
<!-- <input type="text" name="output" value=""
size="45" /> -->
</td>
<td>
<input type="button" onclick="this.form.reset();
clear_result('subtract_volumes_output');
document.getElementById('subtract_volumes_gan1').focus();" value="Clear"/>
</td>
</tr>
</table>
</div>
</form>
</div>
<div class="encart">
<form action="" id="form_mult_volume" onsubmit="return false;">
<p>
Multiply a volume:
</p>
<div class="retrait">
<table class="encadre">
<tr>
<td>
<input type="text" name="gan" id="mult_volume_gan"
value="" size="8" onkeypress="if
(event.keyCode == 13)
mult_volume_form(this.form)" />
</td>
<td>
<input type="text" name="sar" id="mult_volume_sar"
value="" size="8" onkeypress="if
(event.keyCode == 13)
mult_volume_form(this.form)" />
</td>
<td>
<input type="text" name="gin" value="" size="8"
onkeypress="if (event.keyCode == 13)
mult_volume_form(this.form)" />
</td>
<td>
<input type="text" name="se" id="mult_volume_se"
value="" size="8" onkeypress="if
(event.keyCode == 13)
mult_volume_form(this.form)" />
</td>
</tr>
<tr>
<td> <strong><em>gan</em></strong> </td>
<td> <strong><em>sar</em></strong> </td>
<td> <strong><em>gin</em></strong> </td>
<td> <strong><em>še</em></strong> </td>
</tr>
<tr>
<td colspan="4">
×
<input type="text" name="scalaire"
id="mult_volume_scalaire" value="" size="8"
onkeypress="if (event.keyCode == 13)
mult_volume_form(this.form)" />
times
</td>
</tr>
<tr>
<td colspan="4"><hr/></td>
</tr>
<tr>
<td>
<input type="button" name="bouton" value="="
onclick="mult_volume_form(this.form)" />
</td>
<td colspan="2">
<span id="mult_volume_output"></span>
<!-- <input type="text" name="output" value=""
size="45" /> -->
</td>
<td>
<input type="button" onclick="form.reset();
clear_result('mult_volume_output');
document.getElementById('mult_volume_gan').focus();" value="Clear"/>
</td>
</tr>
</table>
</div>
</form>
</div>
<h3><a name="capacities"/>Capacities</h3>
<p>
Units of capacity:
</p>
<div class="retrait">
<table class="encadre">
<tr>
<td><strong><em>gur</em></strong> </td>
<td> ← 5 ← </td>
<td><strong><em>bariga</em></strong> </td>
<td> ← 6 ← </td>
<td><strong><em>ban</em></strong> </td>
<td> ← 10 ← </td>
<td><strong><em>sila</em></strong> </td>
<td> ← 60 ← </td>
<td><strong><em>gin</em></strong> </td>
<td> ← 180 ← </td>
<td><strong><em>še</em></strong> </td>
</tr>
<tr>
<td>300 L</td>
<td> </td>
<td>60 L </td>
<td> </td>
<td>10 L </td>
<td> </td>
<td>1 L </td>
<td> </td>
<td>16.6 mL </td>
<td> </td>
<td>0.092 mL </td>
</tr>
</table>
</div>
<div class="encart">
<form action="" id="form_add_capacites" onsubmit="return false;">
<p>
Add capacities:
</p>
<div class="retrait">
<table class="encadre">
<tr>
<th></th>
<th><em>gur</em></th>
<th><em>bariga</em></th>
<th><em>ban</em></th>
<th><em>sila</em></th>
<th><em>gin</em></th> <th><em>še</em></th>
</tr>
<tr>
<td> </td>
<td>
<input type="text" name="gur1" value="" size="8"
id="add_capacities_gur1"
onkeypress="if (event.keyCode == 13)
add_capacites(this.form)" />
</td>
<td>
<input type="text" name="bariga1" value="" size="8"
id="add_capacities_bariga1"
onkeypress="if (event.keyCode == 13)
add_capacites(this.form)" />
</td>
<td>
<input type="text" name="ban1" value="" size="8"
id="add_capacities_ban1"
onkeypress="if (event.keyCode == 13)
add_capacites(this.form)" />
</td>
<td>
<input type="text" name="sila1" value="" size="8"
id="add_capacities_sila1"
onkeypress="if (event.keyCode == 13)
add_capacites(this.form)" />
</td>
<td>
<input type="text" name="gin1" value="" size="8"
id="add_capacities_gin1"
onkeypress="if (event.keyCode == 13)
add_capacites(this.form)" />
</td>
<td>
<input type="text" name="se1" value="" size="8"
id="add_capacities_se1"
onkeypress="if (event.keyCode == 13)
add_capacites(this.form)" />
</td>
</tr>
<tr>
<td align="center">+
</td>
<td>
<input type="text" name="gur2" value="" size="8"
id="add_capacities_gur2"
onkeypress="if (event.keyCode == 13)
add_capacites(this.form)" />
</td>
<td>
<input type="text" name="bariga2" value="" size="8"
id="add_capacities_bariga2"
onkeypress="if (event.keyCode == 13)
add_capacites(this.form)" />
</td>
<td>
<input type="text" name="ban2" value="" size="8"
id="add_capacities_ban2"
onkeypress="if (event.keyCode == 13)
add_capacites(this.form)" />
</td>
<td>
<input type="text" name="sila2" value="" size="8"
id="add_capacities_sila2"
onkeypress="if (event.keyCode == 13)
add_capacites(this.form)" />
</td>
<td>
<input type="text" name="gin2" value="" size="8"
id="add_capacities_gin2"
onkeypress="if (event.keyCode == 13)
add_capacites(this.form)" />
</td>
<td>
<input type="text" name="se2" value="" size="8"
id="add_capacities_se2"
onkeypress="if (event.keyCode == 13)
add_capacites(this.form)" />
</td>
</tr>
<tr>
<td colspan="7"><hr/></td>
</tr>
<tr>
<td>
<input type="button" name="bouton" value="="
onclick="add_capacites(this.form)" />
</td>
<td colspan="5">
<span id="add_capacities_output"></span>
<!-- <input type="text" name="output" value=""
size="45" /> -->
</td>
<td>
<input type="button" onclick="this.form.reset();
clear_result('add_capacities_output');
document.getElementById('add_capacities_gur1').focus();" value="Clear"/>
</td>
</tr>
</table>
</div>
</form>
</div>
<div class="encart">
<form action="" id="form_soustr_capacites" onsubmit="return false;">
<p>
Subtract capacities:
</p>
<div class="retrait">
<table class="encadre">
<tr>
<th></th>
<th><em>gur</em></th>
<th><em>bariga</em></th>
<th><em>ban</em></th>
<th><em>sila</em></th>
<th><em>gin</em></th>
<th><em>še</em></th>
</tr>
<tr>
<td> </td>
<td>
<input type="text" name="gur1" value="" size="8"
id="subtract_capacities_gur1"
onkeypress="if (event.keyCode == 13)
soustr_capacites(this.form)" />
</td>
<td>
<input type="text" name="bariga1" value="" size="8"
id="subtract_capacities_bariga1"
onkeypress="if (event.keyCode == 13)
soustr_capacites(this.form)" />
</td>
<td>
<input type="text" name="ban1" value="" size="8"
id="subtract_capacities_ban1"
onkeypress="if (event.keyCode == 13)
soustr_capacites(this.form)" />
</td>
<td>
<input type="text" name="sila1" value="" size="8"
id="subtract_capacities_sila1"
onkeypress="if (event.keyCode == 13)
soustr_capacites(this.form)" />
</td>
<td>
<input type="text" name="gin1" value="" size="8"
id="subtract_capacities_gin1"
onkeypress="if (event.keyCode == 13)
soustr_capacites(this.form)" />
</td>
<td>
<input type="text" name="se1" value="" size="8"
id="subtract_capacities_se1"
onkeypress="if (event.keyCode == 13)
soustr_capacites(this.form)" />
</td>
</tr>
<tr>
<td align="center">−</td>
<td>
<input type="text" name="gur2" value="" size="8"
id="subtract_capacities_gur2"
onkeypress="if (event.keyCode == 13)
soustr_capacites(this.form)" />
</td>
<td>
<input type="text" name="bariga2" value="" size="8"
id="subtract_capacities_bariga2"
onkeypress="if (event.keyCode == 13)
soustr_capacites(this.form)" />
</td>
<td>
<input type="text" name="ban2" value="" size="8"
id="subtract_capacities_ban2"
onkeypress="if (event.keyCode == 13)
soustr_capacites(this.form)" />
</td>
<td>
<input type="text" name="sila2" value="" size="8"
id="subtract_capacities_sila2"
onkeypress="if (event.keyCode == 13)
soustr_capacites(this.form)" />
</td>
<td>
<input type="text" name="gin2" value="" size="8"
id="subtract_capacities_gin2"
onkeypress="if (event.keyCode == 13)
soustr_capacites(this.form)" />
</td>
<td>
<input type="text" name="se2" value="" size="8"
id="subtract_capacities_se2"
onkeypress="if (event.keyCode == 13)
soustr_capacites(this.form)" />
</td>
</tr>
<tr>
<td colspan="7"><hr/></td>
</tr>
<tr>
<td>
<input type="button" name="bouton" value="="
onclick="soustr_capacites(this.form)" />
</td>
<td colspan="5">
<span id="subtract_capacities_output"></span>
<!-- <input type="text" name="output" value=""
size="45"/> -->
</td>
<td>
<input type="button" onclick="this.form.reset();
clear_result('subtract_capacities_output');
document.getElementById('subtract_capacities_gur1').focus();" value="Clear"/>
</td>
</tr>
</table>
</div>
</form>
</div>
<div class="encart">
<form action="" id="form_mult_capacite" onsubmit="return false;">
<p>
Multiply a capacity:
</p>
<div class="retrait">
<table class="encadre">
<tr>
<td>
<input type="text" name="gur" id="mult_capacite_gur"
value="" size="8" onkeypress="if
(event.keyCode == 13)
mult_capacite_form(this.form)" />
</td>
<td>
<input type="text" name="bariga"
id="mult_capacite_bariga" value="" size="8"
onkeypress="if (event.keyCode == 13)
mult_capacite_form(this.form)" />
</td>
<td>
<input type="text" name="ban" value="" size="8"
onkeypress="if (event.keyCode == 13)
mult_capacite_form(this.form)" />
</td>
<td>
<input type="text" name="sila"
id="mult_capacite_sila" value="" size="8"
onkeypress="if (event.keyCode == 13)
mult_capacite_form(this.form)" />
</td>
<td>
<input type="text" name="gin" id="mult_capacite_gin"
value="" size="8" onkeypress="if
(event.keyCode == 13)
mult_capacite_form(this.form)"
/>
</td>
<td>
<input type="text" name="se" id="mult_capacite_se"
value="" size="8" onkeypress="if
(event.keyCode == 13)
mult_capacite_form(this.form)" />
</td>
</tr>
<tr>
<td> <strong><em>gur</em></strong> </td>
<td> <strong><em>bariga</em></strong> </td>
<td> <strong><em>ban</em></strong> </td>
<td> <strong><em>sila</em></strong> </td>
<td> <strong><em>gin</em></strong> </td>
<td> <strong><em>še</em></strong> </td>
</tr>
<tr>
<td colspan="6"> ×
<input type="text" name="scalaire"
id="mult_capacite_scalaire" value="" size="8"
onkeypress="if (event.keyCode == 13)
mult_capacite_form(this.form)" />
times
</td>
</tr>
<tr>
<td colspan="6"><hr/></td>
</tr>
<tr>
<td>
<input type="button" name="bouton" value="="
onclick="mult_capacite_form(this.form)" />
</td>
<td colspan="4">
<span id="mult_capacity_output"></span>
<!-- <input type="text" name="output" value=""
size="45" /> -->
</td>
<td>
<input type="button" onclick="form.reset();
clear_result('mult_capacity_output');
document.getElementById('mult_capacite_gur').focus();"
value="Clear"/>
</td>
</tr>
</table>
</div>
</form>
</div>
<h3><a name="weights"/>Weights</h3>
<p>
Units of weight:
</p>
<div class="retrait">
<table class="encadre">
<tr>
<td><strong><em>gu</em></strong> </td>
<td> ← 60 ← </td>
<td><strong><em>mana</em></strong> </td>
<td> ← 60 ← </td>
<td><strong><em>gin</em></strong> </td>
<td> ← 180 ← </td>
<td><strong><em>še</em></strong> </td>
</tr>
<tr>
<td>30 kg
</td>
<td> </td>
<td>500 g
</td>
<td> </td>
<td>8.33 g </td>
<td> </td>
<td>0.046 g </td>
</tr>
</table>
</div>
<div class="encart">
<form action="" id="form_add_poids" onsubmit="return false;">
<p>
Add weights:
</p>
<div class="retrait">
<table class="encadre">
<tr>
<th></th>
<th><em>gu</em></th>
<th><em>mana</em></th>
<th><em>gin</em></th>
<th><em>še</em></th>
</tr>
<tr>
<td> </td>
<td>
<input type="text" name="gu1" value="" size="8"
id="add_weights_gu1"
onkeypress="if (event.keyCode == 13)
add_poids(this.form)" />
</td>
<td>
<input type="text" name="mana1" value="" size="8"
id="add_weights_mana1"
onkeypress="if (event.keyCode == 13)
add_poids(this.form)" />
</td>
<td>
<input type="text" name="gin1" value="" size="8"
id="add_weights_gin1"
onkeypress="if (event.keyCode == 13)
add_poids(this.form)" />
</td>
<td>
<input type="text" name="se1" value="" size="8"
id="add_weights_se1"
onkeypress="if (event.keyCode == 13)
add_poids(this.form)" />
</td>
</tr>
<tr>
<td align="center">+ </td>
<td>
<input type="text" name="gu2" value="" size="8"
id="add_weights_gu2"
onkeypress="if (event.keyCode == 13)
add_poids(this.form)" />
</td>
<td>
<input type="text" name="mana2" value="" size="8"
id="add_weights_mana2"
onkeypress="if (event.keyCode == 13)
add_poids(this.form)" />
</td>
<td>
<input type="text" name="gin2" value="" size="8"
id="add_weights_gin2"
onkeypress="if (event.keyCode == 13)
add_poids(this.form)" />
</td>
<td>
<input type="text" name="se2" value="" size="8"
id="add_weights_se2"
onkeypress="if (event.keyCode == 13)
add_poids(this.form)" />
</td>
</tr>
<tr>
<td colspan="5"><hr/></td>
</tr>
<tr>
<td>
<input type="button" name="bouton" value="="
onclick="add_poids(this.form)" />
</td>
<td colspan="3">
<span id="add_weights_output"></span>
<!-- <input type="text" name="output" value=""
size="45"/>-->
</td>
<td>
<input type="button" onclick="this.form.reset();
clear_result('add_weights_output');
document.getElementById('add_weights_gu1').focus();" value="Clear"/>
</td>
</tr>
</table>
</div>
</form>
</div>
<div class="encart">
<form action="" id="form_soustr_poids" onsubmit="return false;">
<p>
Subtract weights:
</p>
<div class="retrait">
<table class="encadre">
<tr>
<th></th>
<th><em>gu</em></th>
<th><em>mana</em></th>
<th><em>gin</em></th>
<th><em>še</em></th>
</tr>
<tr>
<td> </td>
<td>
<input type="text" name="gu1" value="" size="8"
id="subtract_weights_gu1"
onkeypress="if (event.keyCode == 13)
soustr_poids(this.form)" />
</td>
<td>
<input type="text" name="mana1" value="" size="8"
id="subtract_weights_mana1"
onkeypress="if (event.keyCode == 13)
soustr_poids(this.form)" />
</td>
<td>
<input type="text" name="gin1" value="" size="8"
id="subtract_weights_gin1"
onkeypress="if (event.keyCode == 13)
soustr_poids(this.form)" />
</td>
<td>
<input type="text" name="se1" value="" size="8"
id="subtract_weights_se1"
onkeypress="if (event.keyCode == 13)
soustr_poids(this.form)" />
</td>
</tr>
<tr>
<td align="center"> − </td>
<td>
<input type="text" name="gu2" value="" size="8"
id="subtract_weights_gu2"
onkeypress="if (event.keyCode == 13)
soustr_poids(this.form)" />
</td>
<td>
<input type="text" name="mana2" value="" size="8"
id="subtract_weights_mana2"
onkeypress="if (event.keyCode == 13)
soustr_poids(this.form)" />
</td>
<td>
<input type="text" name="gin2" value="" size="8"
id="subtract_weights_gin2"
onkeypress="if (event.keyCode == 13)
soustr_poids(this.form)" />
</td>
<td>
<input type="text" name="se2" value="" size="8"
id="subtract_weights_se2"
onkeypress="if (event.keyCode == 13)
soustr_poids(this.form)" />
</td>
</tr>
<tr>
<td colspan="5"><hr/></td>
</tr>
<tr>
<td>
<input type="button" name="bouton" value="="
onclick="soustr_poids(this.form)" />
</td>
<td colspan="3">
<span id="subtract_weights_output"></span>
<!-- <input type="text" name="output" value=""
size="45"/> -->
</td>
<td>
<input type="button" onclick="this.form.reset();
clear_result('subtract_weights_output');
document.getElementById('subtract_weights_gu1').focus();" value="Clear"/>
</td>
</tr>
</table>
</div>
</form>
</div>
<div class="encart">
<form action="" id="form_mult_poids" onsubmit="return false;">
<p>
Multiply a weight:
</p>
<div class="retrait">
<table class="encadre">
<tr>
<td>
<input type="text" name="gu" id="mult_poids_gu"
value="" size="8" onkeypress="if
(event.keyCode == 13)
mult_poids_form(this.form)" />
</td>
<td>
<input type="text" name="mana" id="mult_poids_mana"
value="" size="8" onkeypress="if
(event.keyCode == 13)
mult_poids_form(this.form)" />
</td>
<td>
<input type="text" name="gin" value="" size="8"
onkeypress="if (event.keyCode == 13)
mult_poids_form(this.form)" />
</td>
<td>
<input type="text" name="se" id="mult_poids_se"
value="" size="8" onkeypress="if
(event.keyCode == 13)
mult_poids_form(this.form)" />
</td>
</tr>
<tr>
<td> <strong><em>gu</em></strong> </td>
<td> <strong><em>mana</em></strong> </td>
<td> <strong><em>gin</em></strong> </td>
<td> <strong><em>še</em></strong> </td>
</tr>
<tr>
<td colspan="4"> ×
<input type="text" name="scalaire"
id="mult_poids_scalaire" value="" size="8"
onkeypress="if (event.keyCode == 13)
mult_poids_form(this.form)" />
times
</td>
</tr>
<tr>
<td colspan="4"><hr/></td>
</tr>
<tr>
<td>
<input type="button" name="bouton" value="="
onclick="mult_poids_form(this.form)" />
</td>
<td colspan="2">
<span id="mult_weight_output"></span>
<!-- <input type="text" name="output" value=""
size="45" /> -->
</td>
<td>
<input type="button" onclick="form.reset();
clear_result('mult_weight_output');
document.getElementById('mult_poids_gu').focus();"
value="Clear"/>
</td>
</tr>
</table>
</div>
</form>
</div>
<h3><a name="systemSsystemG"/>System G and system S</h3>
<p>System G:</p>
<div class="retrait">
<table class="encadre">
<tr>
<td> <strong><em>šar-gal</em></strong></td>
<td> ← 6 ← </td>
<td><strong><em>šar'u</em></strong></td>
<td> ← 10 ← </td>
<td><strong><em>šar</em></strong></td>
<td> ← 6 ← </td>
<td><strong><em>bur'u</em></strong></td>
<td> ← 10 ← </td>
<td><strong><em>bur</em></strong></td>
<td> ← 3 ← </td>
<td><strong><em>eše</em></strong></td>
<td> ← 6 ← </td>
<td><strong><em>iku</em></strong> </td>
</tr>
<tr>
<td>64800</td>
<td> </td>
<td>10800</td>
<td> </td>
<td>1080</td>
<td> </td>
<td>180</td>
<td> </td>
<td>18</td>
<td> </td>
<td>6</td>
<td> </td>
<td>1 </td>
</tr>
</table>
</div>
<p>System S:</p>
<div class="retrait">
<table class="encadre">
<tr>
<td><strong><em>šar-gal</em></strong></td>
<td> ← 6 ← </td>
<td><strong><em>šar'u</em></strong></td>
<td> ← 10 ← </td>
<td><strong><em>šar</em></strong></td>
<td> ← 6 ← </td>
<td><strong><em>gešu</em></strong></td>
<td> ← 10 ← </td>
<td><strong><em>geš</em></strong></td>
<td> ← 6 ← </td>
<td><strong><em>u</em></strong></td>
<td> ← 10 ← </td>
<td><strong><em>diš</em></strong> </td>
</tr>
<tr>
<td>216000</td>
<td> </td>
<td>36000</td>
<td> </td>
<td>3600</td>
<td> </td>
<td>600</td>
<td> </td>
<td>60</td>
<td> </td>
<td>10</td>
<td> </td>
<td>1 </td>
</tr>
</table>
</div>
<!-- <div class="encart">
<form action="" id="form_systemS2systemG" onsubmit="return false;">
<p> Conversion from system S to system G: </p>
<div class="retrait">
<table class="encadre">
<tr>
<th>šar-gal</th> <th><em>šar'u</em></th> <th><em>šar</em></th> <th><em>gešu</em></th>
<th><em>geš</em></th> <th><em>u</em></th> <th><em>diš</em></th>
</tr>
<tr>
<td> <input type="text" name="sargal" id="systemS2systemG_sargal" value="" size="7"
onkeypress="if (event.keyCode == 13) systemS2systemG(this.form)" />
</td>
<td> <input type="text" name="saru" value="" size="7"
onkeypress="if (event.keyCode == 13) systemS2systemG(this.form)" />
</td>
<td> <input type="text" name="sar" value="" size="7"
onkeypress="if (event.keyCode == 13) systemS2systemG(this.form)" />
</td>
<td> <input type="text" name="gesu" value="" size="7"
onkeypress="if (event.keyCode == 13)
systemS2systemG(this.form)" />
</td>
<td> <input type="text" name="ges" value="" size="7"
onkeypress="if (event.keyCode == 13) systemS2systemG(this.form)" />
</td>
<td> <input type="text" name="u" value="" size="7"
onkeypress="if (event.keyCode == 13) systemS2systemG(this.form)" />
</td>
<td> <input type="text" name="dis" value="" size="7"
onkeypress="if (event.keyCode == 13)
systemS2systemG(this.form)" />
</td>
</tr>
<tr>
<td colspan="7">
<input type="button" name="bouton" value="G →"
onclick="systemS2systemG(this.form)" />
<input type="text" name="output" value="" size="45" />
<input type="button" onclick="form.reset(); document.getElementById('systemS2systemG_sargal').focus();" value="Clear"/>
</td>
</tr>
</table>
</div>
</form>
</div> -->
<!-- <div class="encart">
<form action="" id="form_systemG2systemS" onsubmit="return false;">
<p> Conversion from system G to system S: </p>
<div class="retrait">
<table class="encadre">
<tr>
<th><em>šar-gal</em></th> <th><em>šar'u</em></th> <th><em>šar</em></th> <th><em>bur'u</em></th>
<th><em>bur</em></th> <th><em>eše</em></th> <th><em>iku</em></th>
</tr>
<tr>
<td> <input type="text" name="sargal" id="systemG2systemS_sargal" value="" size="6"
onkeypress="if (event.keyCode == 13) systemG2systemS_form(this.form)" />
</td>
<td> <input type="text" name="saru" value="" size="6"
onkeypress="if (event.keyCode == 13) systemG2systemS_form(this.form)" />
</td>
<td> <input type="text" name="sar" value="" size="6"
onkeypress="if (event.keyCode == 13) systemG2systemS_form(this.form)" />
</td>
<td> <input type="text" name="buru" value="" size="6"
onkeypress="if (event.keyCode == 13)
systemG2systemS_form(this.form)" />
</td>
<td> <input type="text" name="bur" value="" size="6"
onkeypress="if (event.keyCode == 13) systemG2systemS_form(this.form)" />
</td>
<td> <input type="text" name="ese" value="" size="6"
onkeypress="if (event.keyCode == 13) systemG2systemS_form(this.form)" />
</td>
<td> <input type="text" name="iku" value="" size="6"
onkeypress="if (event.keyCode == 13)
systemG2systemS_form(this.form)" />
</td>
</tr>
<tr>
<td colspan="7">
<input type="button" name="bouton" value="S →"
onclick="systemG2systemS_form(this.form)" />
<input type="text" name="output" value="" size="45" />
<input type="button" onclick="form.reset(); document.getElementById('systemG2systemS_sargal').focus();" value="Clear"/>
</td>
</tr>
</table>
</div>
</form>
</div> -->
<hr/>
<h2><a name="dates"/>Dates</h2>
<div class="encart">
<form action="" id="form_date"
onsubmit="return false;">
<p>
Date conversion: <br/>
King <select id="date_king" onchange="date_update_years();">
<option value="null" selected="selected">-- select --</option>
<option value="Nabopolassar">Nabopolassar</option>
<option value="Nebuchadnezzar">Nebuchadnezzar</option>
<option value="EvilMerodach">Evil-Merodach</option>
<option value="Neriglissar">Neriglissar</option>
<option value="Nabonidus">Nabonidus</option>
<option value="Cyrus">Cyrus</option>
<option value="Cambyses">Cambyses</option>
<option value="Bardiya">Bardiya</option>
<option value="NebuchadnezzarIII">Nebuchadnezzar III</option>
<option value="Darius">Darius</option>
<option value="NebuchadnezzarIV">Nebuchadnezzar IV</option>
<option value="Darius">Darius</option>
<option value="Xerxes">Xerxes</option>
<option value="Artaxerxes">Artaxerxes</option>
<option value="DariusII">Darius II</option>
<option value="ArtaxerxesII">Artaxerxes II</option>
<option value="ArtaxerxesIII">Artaxerxes III</option>
<option value="Arses">Arses</option>
<option value="DariusIII">Darius III</option>
</select>
Year <select id="date_year" onchange="date_update_months();">
<option value=""/>
</select>
Month <select id="date_month" onchange="date_update_days();">
<option value=""/>
</select>
Day <select id="date_day" onchange="date_display_result();">
<option value=""/>
</select>
<!-- <input type="button" name="bouton" value="Date"
onclick="date_display_result()" /> -->
</p>
<div id="date_result"></div>
</form>
</div>
<p>During the Neo Babylonian and Persian periods, which
are concerned by this converter, the year was based on the
revolution of the Earth around the Sun, that is 365 days. It
was beginning in spring, during the Babylonian month of
<em>nisannu</em> (1), and ending during month <em>addaru</em>
(12). Years’ calculation was based on Kings’ reigns which are
well known, thanks to <em>Ptolemy's Canon</em>. This
fundamental document allows us establishing equivalences
between Babylonian and Gregorian dates.</p>
<p>The year in which a king acceded to the throne, is
recorded as “Year 0” in this converter, then subsequent regnal
years are numbered until the next King. A year consisted of
12 lunar months, each of them corresponding to the interval
between two new moons, thus 12 × 29 or 30 days : </p>
<ul>
<li>1: <em>nisannu</em></li>
<li>2: <em>aiāru</em></li>
<li>3: <em>simānu</em></li>
<li>4: <em>dūzu</em></li>
<li>5: <em>abu</em></li>
<li>6: <em>ulūlu</em></li>
<li>7: <em>tašrītu</em></li>
<li>8: <em>arahsamnu</em></li>
<li>9: <em>kislīmu</em></li>
<li>10: <em>ṭebētu</em></li>
<li>11: <em>šabāṭu</em></li>
<li>12: <em>addaru</em></li>
</ul>
<p>However, 11 days are lacking to complete the solar year. To
fill this gap, Mesopotamians used empirically to add from time
to time a 13th month. This intercalary month was added either
after the 6th (month 6b), or the 12th (month 12b).
</p>
<p>
A mathematical scheme enabling a regular cycle of intercalary
months was elaborated during Achaemenid Period, based on the
fact that 19 solar years and 235 lunar months have the same
number of days. Seven intercalary months were added over a
period of 19 years, on year 1, 3, 6, 9, 11, 14, and 17 year.
Only the 1st year had an intercalary month <em>ulūlu</em> (6b), all the
others had an <em>addaru</em> (12b).</p>
<p> Chronological equivalences between Babylonian and Gregorian dates of
this converter have been taken from the book of R. A. Parker and
W. H. Dubberstein, <em>Babylonian Chronology, 626 B.C. - A.D. 45</em>,
Studies in Ancient Oriental Civilization 24, 1942 and encoded by Bruno
Gombert (Université Paris 1 Panthéon Sorbonne, ARSCAN).</p>
<h2><a name="faq"/>About MesoCalc</h2>
<h3><a name="download"/>Can I download MesoCalc?</h3>
<div class="encart">
<p> Yes, you can! You can download MesoCalc and use it offline
on your computer or smartphone.</p>
<ul>
<li> To download the <strong>current version</strong>,
select "File > Save As" in your web browser
while it is displaying the present page.</li>
<li>
To get the <strong>latest version</strong>, <a href="https://archive.softwareheritage.org/browse/origin/?origin_url=https://github.com/BapMel/mesocalc">download
the latest version of the file <code>mesocalc.html</code></a> from <a href="https://www.softwareheritage.org/">Software Heritage</a>,
the universal software archive.
</li>
</ul>
</div>
<h3><a name="source"/>Can I read MesoCalc's source code?</h3>
<div class="encart">
<p>Yes, you can! MesoCalc is a free software. You can read the
source code of the present web page. You can even modify the
source code and then redistribute your own modifications
under the terms of the GNU General Public License (see
the <a href="#license">license</a> below). </p>
<p> You can see the source code of this program. It is written
in HTML, CSS and JavaScript.</p>
<ul>
<li> To see the <strong>current version</strong>'s source
code, go to "View > Page Source" or
"Tools > Source Code" in your web browser while
displaying the present web page.</li>
<li>
To see the <strong>latest version</strong> or any older, <a href="https://archive.softwareheritage.org/browse/origin/?origin_url=https://github.com/BapMel/mesocalc">display
the latest version of the file <code>mesocalc.html</code></a> on <a href="https://www.softwareheritage.org/">Software Heritage</a>,
the universal software archive.
</li>
</ul>
</div>
<h3><a name="archive"/>Is MesoCalc's source code archived?</h3>
<div class="encart">
<p> Yes, it is. Archiving software is crucial because
programmers are not aware that this part of scientific
culture disappears more easily than clay tablets. The
programs and source codes of the first decades of computer
science are already lost at the beginning of the
XXIth century.</p>
<p> This is the reason why MesoCalc'c source code is archived.
You can find its successive versions (since 2016)
on <a href="https://github.com/BapMel/mesocalc">Github</a> and
<a href="https://archive.softwareheritage.org/browse/origin/?origin_url=https://github.com/BapMel/mesocalc">Software Heritage</a>,
the universal software archive.
</p>
<p> <a href="https://archive.softwareheritage.org/swh:1:dir:422f91faa6324f6bc1593fdc1387d0c8fea6603a;origin=https://github.com/BapMel/mesocalc;visit=swh:1:snp:8e33bcb11b630dbd2b9fb108ace63f2660985a14;anchor=swh:1:rev:89c3703de074a6eee90efd54e3f8ba26ae48a42e">
<img src="https://archive.softwareheritage.org/badge/swh:1:dir:422f91faa6324f6bc1593fdc1387d0c8fea6603a/" alt="Archived | swh:1:dir:422f91faa6324f6bc1593fdc1387d0c8fea6603a"/>
</a>
</p>
</div>
<h3><a name="features"/>Are there new features in MesoCalc?</h3>
<div class="encart">
<p>Yes, very frequently! Month after month, MesoCalc gets new
features and new bug corrections. In case you downloaded
MesoCalc to use it offline, make sure that you have the
newest version.</p>
<p>Last modifications:</p>
<ul>
<li><strong>10th February 2023:</strong> <a href="https://www.softwareheritage.org/">Software Heritage</a> links.
<p><a href="https://archive.softwareheritage.org/swh:1:dir:422f91faa6324f6bc1593fdc1387d0c8fea6603a;origin=https://github.com/BapMel/mesocalc;visit=swh:1:snp:8e33bcb11b630dbd2b9fb108ace63f2660985a14;anchor=swh:1:rev:89c3703de074a6eee90efd54e3f8ba26ae48a42e">
<img src="https://archive.softwareheritage.org/badge/swh:1:dir:422f91faa6324f6bc1593fdc1387d0c8fea6603a/" alt="Archived | swh:1:dir:422f91faa6324f6bc1593fdc1387d0c8fea6603a"/></a></p></li>
<li><strong>16th May 2017:</strong> integration of Bruno
Gombert's calendar, designed after R. A. Parker and W. H. Dubberstein, <em>Babylonian Chronology,
626 B.C.-A.D. 45</em>, Studies in Ancient Oriental
Civilization 24, 1942.</li>
<li><strong>7th May 2016:</strong> metric approximation of
measuring units (metres, litres, etc.). Bug correction in
system G (1 šar-gal = 64800, not 34800). Cleaning of the
HTML code. "Clear" buttons for all operations on measuring
units. Verification of the XHTML 1.0 Strict validity :
<p>
<a href="http://validator.w3.org/check?uri=referer"><img src="http://www.w3.org/Icons/valid-xhtml10"
alt="Valid XHTML 1.0 Strict" height="31" width="88" /></a>
</p>
</li>
<li><strong>15th January 2016:</strong> two new features. 1)
Regular approximation of a number; 2) a new algorithm to
list regular numbers, made possible by Mathieu
Ossendrijver's huge database of regular numbers.</li>
<li><strong>16th September 2015:</strong> bug correction in
measurement units. Now, input numbers can be either
decimal or sexagesimal (until recently, only sexagesimal
numbers were accepted).
</li>
</ul>
</div>
<h3><a name="license"/>License</h3>
<div class="encart">
<p>MesoCalc: a Mesopotamian calculator.</p>
<p>Copyright (C) <a href="http://baptiste.meles.free.fr/">Baptiste
MÉLÈS</a> 2013.</p>
<p> Latest version: 11th April 2024.</p>
<p>This program is free software: you can redistribute it and/or
modify it under the terms of the GNU General Public License as
published by the Free Software Foundation, either version 3 of the
License, or any later version.</p>
<p>This program is distributed in the hope that it will be useful,
but WITHOUT ANY WARRANTY; without even the implied warranty of
MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See
the <a href="http://www.gnu.org/licenses/">GNU General Public
License</a> for more details.</p>
</div>
<h3><a name="contact"/>Contact</h3>
<div class="encart">
<p>If you see bugs or want new features,
please <a href="mailto:baptiste.meles@univ-lorraine.fr">contact
Baptiste Mélès</a>. All comments and suggestions are
welcome! </p>
</div>
</div>
</div>
</body>
</html>
