{"id":622,"date":"2018-06-03T01:03:03","date_gmt":"2018-06-03T01:03:03","guid":{"rendered":"http:\/\/jonvoisey.net\/blog\/?p=622"},"modified":"2024-09-03T11:52:40","modified_gmt":"2024-09-03T16:52:40","slug":"almagest-book-i-ptolemys-table-of-chords","status":"publish","type":"post","link":"https:\/\/jonvoisey.net\/blog\/2018\/06\/almagest-book-i-ptolemys-table-of-chords\/","title":{"rendered":"Almagest Book I: Ptolemy’s Table of Chords"},"content":{"rendered":"

Here displayed in all its glory is Ptolemy’s Table of Chords. Notes to follow.<\/p>\n

<\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
Arc<\/td>\nChord<\/td>\nSixtieths<\/span>1<\/sup><\/a><\/span><\/td>\n<\/tr>\n<\/thead>\n
$\\frac{1}{2}$<\/td>\n0;31;25<\/td>\n0;1,2,50<\/td>\n<\/tr>\n
1<\/td>\n1;2,50<\/td>\n0;1,2,50<\/td>\n<\/tr>\n
$1 \\frac{1}{2}$<\/td>\n1;34,15<\/td>\n0;1,2,50<\/td>\n<\/tr>\n
2<\/td>\n2;5,40<\/td>\n0;1,2,50<\/td>\n<\/tr>\n
$2 \\frac{1}{2}$<\/td>\n2;37,4<\/td>\n0;1,2,48<\/td>\n<\/tr>\n
3<\/td>\n3;8,28<\/td>\n0;1,2,48<\/td>\n<\/tr>\n
$3 \\frac{1}{2}$<\/td>\n3;38,52<\/td>\n0;1,2,48<\/td>\n<\/tr>\n
4<\/td>\n4;11,16<\/td>\n0;1,2,47<\/td>\n<\/tr>\n
$4 \\frac{1}{2}$<\/td>\n4;42,40<\/td>\n\u00a00;1,2,47<\/td>\n<\/tr>\n
5<\/td>\n5;14,4<\/td>\n0;1,2,46<\/td>\n<\/tr>\n
$5 \\frac{1}{2}$<\/td>\n5;45,27<\/td>\n0;1,2,45<\/td>\n<\/tr>\n
6<\/td>\n6;16,49<\/td>\n0;1,2,44<\/td>\n<\/tr>\n
$6 \\frac{1}{2}$<\/td>\n6;48,11<\/td>\n0;1,2,43<\/td>\n<\/tr>\n
7<\/td>\n7;19,33<\/td>\n0;1,2,42<\/td>\n<\/tr>\n
$7 \\frac{1}{2}$<\/td>\n7;50,54<\/td>\n0;1,2,41<\/td>\n<\/tr>\n
8<\/td>\n8;22,15<\/td>\n0;1,2,40<\/td>\n<\/tr>\n
$8 \\frac{1}{2}$<\/td>\n8;53,35<\/td>\n0;1,2,39<\/td>\n<\/tr>\n
9<\/td>\n9;24,54<\/td>\n0;1,2,38<\/td>\n<\/tr>\n
$9 \\frac{1}{2}$<\/td>\n9;56,13<\/td>\n0;1,2,37<\/td>\n<\/tr>\n
10<\/td>\n10;27,32<\/td>\n0;1,2,35<\/td>\n<\/tr>\n
$10 \\frac{1}{2}$<\/td>\n10;58,49<\/td>\n0;1,2,33<\/td>\n<\/tr>\n
11<\/td>\n11;30,5<\/td>\n0;1,2,32<\/td>\n<\/tr>\n
$11 \\frac{1}{2}$<\/td>\n12;1,21<\/td>\n0;1,2,30<\/td>\n<\/tr>\n
12<\/td>\n12;32,36<\/td>\n0;1,2,28<\/td>\n<\/tr>\n
$12 \\frac{1}{2}$<\/td>\n13;3,50<\/td>\n0;1,2,27<\/td>\n<\/tr>\n
13<\/td>\n13;35,4<\/td>\n0;1,2,25<\/td>\n<\/tr>\n
$13 \\frac{1}{2}$<\/td>\n14;6,16<\/td>\n0;1,2,23<\/td>\n<\/tr>\n
14<\/td>\n14;37,27<\/td>\n0;1,2,21<\/td>\n<\/tr>\n
$14 \\frac{1}{2}$<\/td>\n15;8,38<\/td>\n0;1,2,19<\/td>\n<\/tr>\n
15<\/td>\n15;39,47<\/td>\n0;1,2,17<\/td>\n<\/tr>\n
$15 \\frac{1}{2}$<\/td>\n16;10,56<\/td>\n0;1,2,15<\/td>\n<\/tr>\n
16<\/td>\n16;42,3<\/td>\n0;1,2,13<\/td>\n<\/tr>\n
$16 \\frac{1}{2}$<\/td>\n17;13,9<\/td>\n0;1,2,10<\/td>\n<\/tr>\n
17<\/td>\n17;44,14<\/td>\n0;1,2,7<\/td>\n<\/tr>\n
$17 \\frac{1}{2}$<\/td>\n18;15,17<\/td>\n0;1,2,5<\/td>\n<\/tr>\n
18<\/td>\n18;46,19<\/td>\n0;1,2,2<\/td>\n<\/tr>\n
$18 \\frac{1}{2}$<\/td>\n19;17,21<\/td>\n0;1,2,0<\/td>\n<\/tr>\n
19<\/td>\n19;48,21<\/td>\n0;1,1,57<\/td>\n<\/tr>\n
$19 \\frac{1}{2}$<\/td>\n20;19,19<\/td>\n0;1,1,54<\/td>\n<\/tr>\n
20<\/td>\n20;50,16<\/td>\n0;1,1,51<\/td>\n<\/tr>\n
$20 \\frac{1}{2}$<\/td>\n21;21,11<\/td>\n0;1,1,48<\/td>\n<\/tr>\n
21<\/td>\n21;52,6<\/td>\n0;1,1,45<\/td>\n<\/tr>\n
$21 \\frac{1}{2}$<\/td>\n22;22,58<\/td>\n0;1,1,42<\/td>\n<\/tr>\n
22<\/td>\n22;53,49<\/td>\n0;1,1,39<\/td>\n<\/tr>\n
$22 \\frac{1}{2}$<\/td>\n23;24,39<\/td>\n0;1,1,36<\/td>\n<\/tr>\n
23<\/td>\n23;55,27<\/td>\n0;1,1,33<\/td>\n<\/tr>\n
$23 \\frac{1}{2}$<\/td>\n24;26,13<\/td>\n0;1,1,30<\/td>\n<\/tr>\n
24<\/td>\n24;56,58<\/td>\n0;1,1,26<\/td>\n<\/tr>\n
$24 \\frac{1}{2}$<\/td>\n25;27,41<\/td>\n0;1,1,22<\/td>\n<\/tr>\n
25<\/td>\n25;58,22<\/td>\n0;1,1,19<\/td>\n<\/tr>\n
$25 \\frac{1}{2}$<\/td>\n26;29,1<\/td>\n0;1,1,15<\/td>\n<\/tr>\n
26<\/td>\n26;59,38<\/td>\n0;1,1,11<\/td>\n<\/tr>\n
$26 \\frac{1}{2}$<\/td>\n27;30,14<\/td>\n0;1,1,8<\/td>\n<\/tr>\n
27<\/td>\n28;0,48<\/td>\n0;1,1,4<\/td>\n<\/tr>\n
$27 \\frac{1}{2}$<\/td>\n28;31,20<\/td>\n0;1,1,0<\/td>\n<\/tr>\n
28<\/td>\n29;1,50<\/td>\n0;1,0,56<\/td>\n<\/tr>\n
$28 \\frac{1}{2}$<\/td>\n29;32,18<\/td>\n0;1,0,52<\/td>\n<\/tr>\n
29<\/td>\n30;2,44<\/td>\n0;1,0,48<\/td>\n<\/tr>\n
$29 \\frac{1}{2}$<\/td>\n30;33,8<\/td>\n0;1,0,44<\/td>\n<\/tr>\n
30<\/td>\n31;3,30<\/td>\n0;1,0,40<\/td>\n<\/tr>\n
$30 \\frac{1}{2}$<\/td>\n31;33,50<\/td>\n0;1,0,35<\/td>\n<\/tr>\n
31<\/td>\n32;4,8<\/td>\n0;1,0,31<\/td>\n<\/tr>\n
$31 \\frac{1}{2}$<\/td>\n32;34,22<\/td>\n0;1,0,27<\/td>\n<\/tr>\n
32<\/td>\n33;4,35<\/td>\n0;1,0,22<\/td>\n<\/tr>\n
$32 \\frac{1}{2}$<\/td>\n33;34,46<\/td>\n0;1,0,17<\/td>\n<\/tr>\n
33<\/td>\n34;4,55<\/td>\n0;1,0,12<\/td>\n<\/tr>\n
$33 \\frac{1}{2}$<\/td>\n34;35,1<\/td>\n0;1,0,8<\/td>\n<\/tr>\n
34<\/td>\n35;5,5<\/td>\n0;1,0,3<\/td>\n<\/tr>\n
$34 \\frac{1}{2}$<\/td>\n35;35,6<\/td>\n0;0,59,57<\/td>\n<\/tr>\n
35<\/td>\n36;5,5<\/td>\n0;0,59,52<\/td>\n<\/tr>\n
$35 \\frac{1}{2}$<\/td>\n36;35,1<\/td>\n0;0,59,48<\/td>\n<\/tr>\n
36<\/td>\n37;4,55<\/td>\n0;0,59,43<\/td>\n<\/tr>\n
$36 \\frac{1}{2}$<\/td>\n37;34,47<\/td>\n0;0,59,38<\/td>\n<\/tr>\n
37<\/td>\n38;4,36<\/td>\n0;0,59,32<\/td>\n<\/tr>\n
$37 \\frac{1}{2}$<\/td>\n38;34,22<\/td>\n0;0,59,27<\/td>\n<\/tr>\n
38<\/td>\n39;4,5<\/td>\n0;0,59,22<\/td>\n<\/tr>\n
$38 \\frac{1}{2}$<\/td>\n39;33,46<\/td>\n0;0,59,16<\/td>\n<\/tr>\n
39<\/td>\n40;3,25<\/td>\n0;0,59, 11<\/td>\n<\/tr>\n
$39 \\frac{1}{2}$<\/td>\n40;33,0<\/td>\n0;0,59,5<\/td>\n<\/tr>\n
40<\/td>\n41;2,33<\/td>\n0;0,59,0<\/td>\n<\/tr>\n
$40 \\frac{1}{2}$<\/td>\n41;30,54<\/td>\n0;0,58,54<\/td>\n<\/tr>\n
41<\/td>\n42;1,30<\/td>\n0;0,58,48<\/td>\n<\/tr>\n
$41 \\frac{1}{2}$<\/td>\n42;30,54<\/td>\n0;0,58,42<\/td>\n<\/tr>\n
42<\/td>\n43;0,15<\/td>\n0;0,58,6<\/td>\n<\/tr>\n
$42 \\frac{1}{2}$<\/td>\n43;29,33<\/td>\n0;0,58, 31<\/td>\n<\/tr>\n
43<\/td>\n43;58,49<\/td>\n0;0,58,25<\/td>\n<\/tr>\n
$43 \\frac{1}{2}$<\/td>\n44;28,1<\/td>\n0;0,58,18<\/td>\n<\/tr>\n
44<\/td>\n44;57,10<\/td>\n0;0,58,12<\/td>\n<\/tr>\n
$44 \\frac{1}{2}$<\/td>\n44;26,16<\/td>\n0;0,58,6<\/td>\n<\/tr>\n
45<\/td>\n45;55,19<\/td>\n0;0,58,0<\/td>\n<\/tr>\n
$45 \\frac{1}{2}$<\/td>\n46;24.19<\/td>\n0;0,57,54<\/td>\n<\/tr>\n
46<\/td>\n46;53,16<\/td>\n0;0,57,47<\/td>\n<\/tr>\n
$46 \\frac{1}{2}$<\/td>\n47;22,9<\/td>\n0;0,57,41<\/td>\n<\/tr>\n
47<\/td>\n47;51,0<\/td>\n0;0,57,34<\/td>\n<\/tr>\n
$47 \\frac{1}{2}$<\/td>\n48;19,47<\/td>\n0;0,57,27<\/td>\n<\/tr>\n
48<\/td>\n48;48,30<\/td>\n0;0,57,21<\/td>\n<\/tr>\n
$48 \\frac{1}{2}$<\/td>\n49;,17,11<\/td>\n0;0,57,14<\/td>\n<\/tr>\n
49<\/td>\n48;48,60<\/td>\n0;0,57,7<\/td>\n<\/tr>\n
$49 \\frac{1}{2}$<\/td>\n50;14,21<\/td>\n0;0,57,0<\/td>\n<\/tr>\n
50<\/td>\n50;42,51<\/td>\n0;0,56,53<\/td>\n<\/tr>\n
$50 \\frac{1}{2}$<\/td>\n51;11,18<\/td>\n0;0,56,46<\/td>\n<\/tr>\n
51<\/td>\n51;39,42<\/td>\n0;0,56,39<\/td>\n<\/tr>\n
$51 \\frac{1}{2}$<\/td>\n52;8,0<\/td>\n0;0,56,32<\/td>\n<\/tr>\n
52<\/td>\n52;36,16<\/td>\n0;0,56,25<\/td>\n<\/tr>\n
$52 \\frac{1}{2}$<\/td>\n53;4,29<\/td>\n0;0,56,18<\/td>\n<\/tr>\n
53<\/td>\n53;32,38<\/td>\n0;0,56,10<\/td>\n<\/tr>\n
$53 \\frac{1}{2}$<\/td>\n54;0,43<\/td>\n0;0,56,3<\/td>\n<\/tr>\n
54<\/td>\n54;28,44<\/td>\n0;0,55,55<\/td>\n<\/tr>\n
$54 \\frac{1}{2}$<\/td>\n54;56,42<\/td>\n0;0,55,48<\/td>\n<\/tr>\n
55<\/td>\n55;24,36<\/td>\n0;0,55,40<\/td>\n<\/tr>\n
$55 \\frac{1}{2}$<\/td>\n55;52,26<\/td>\n0;0,55,33<\/td>\n<\/tr>\n
56<\/td>\n56;20,12<\/td>\n0;0,55,25<\/td>\n<\/tr>\n
$56 \\frac{1}{2}$<\/td>\n56;47,54<\/td>\n0;0,55,17<\/td>\n<\/tr>\n
57<\/td>\n57;15,33<\/td>\n0;0,55,9<\/td>\n<\/tr>\n
$57 \\frac{1}{2}$<\/td>\n57;43,7<\/td>\n0;0,55,1<\/td>\n<\/tr>\n
58<\/td>\n58;10,38<\/td>\n0;0,54,53<\/td>\n<\/tr>\n
$58 \\frac{1}{2}$<\/td>\n58;38,5<\/td>\n0;0,54,45<\/td>\n<\/tr>\n
59<\/td>\n59;5,27<\/td>\n0;0,54,37<\/td>\n<\/tr>\n
$59 \\frac{1}{2}$<\/td>\n59;32,45<\/td>\n0;0,54,29<\/td>\n<\/tr>\n
60<\/td>\n60;0,0<\/td>\n0;0,54,21<\/td>\n<\/tr>\n
$60 \\frac{1}{2}$<\/td>\n60;27,11<\/td>\n0;0,54,12<\/td>\n<\/tr>\n
61<\/td>\n60;54,17<\/td>\n0;0,54,4<\/td>\n<\/tr>\n
$61 \\frac{1}{2}$<\/td>\n60;21,19<\/td>\n0;0,53,56<\/td>\n<\/tr>\n
62<\/td>\n61;48,17<\/td>\n0;0,53,47<\/td>\n<\/tr>\n
$62 \\frac{1}{2}$<\/td>\n62;15,10<\/td>\n0;0,53,39<\/td>\n<\/tr>\n
63<\/td>\n62;42,0<\/td>\n0;0,53,30<\/td>\n<\/tr>\n
$63 \\frac{1}{2}$<\/td>\n63;8,45<\/td>\n0;0,53,22<\/td>\n<\/tr>\n
64<\/td>\n64;35,25<\/td>\n0;0,53,13<\/td>\n<\/tr>\n
$64 \\frac{1}{2}$<\/td>\n64;2,2<\/td>\n0;0,53,4<\/td>\n<\/tr>\n
65<\/td>\n64;28,34<\/td>\n0;0,52,55<\/td>\n<\/tr>\n
$65 \\frac{1}{2}$<\/td>\n64;55,1<\/td>\n0;0,52,46<\/td>\n<\/tr>\n
66<\/td>\n65;51,24<\/td>\n0;0,52,37<\/td>\n<\/tr>\n
$66 \\frac{1}{2}$<\/td>\n65;47,43<\/td>\n0;0,52,28<\/td>\n<\/tr>\n
67<\/td>\n66;13,57<\/td>\n0;0,52,19<\/td>\n<\/tr>\n
$67 \\frac{1}{2}$<\/td>\n66;40,7<\/td>\n0;0,52,10<\/td>\n<\/tr>\n
68<\/td>\n67;6,12<\/td>\n0;0,52,1<\/td>\n<\/tr>\n
$68 \\frac{1}{2}$<\/td>\n67;62,12<\/td>\n0;0,51,52<\/td>\n<\/tr>\n
69<\/td>\n67;58,8<\/td>\n0;0,51,43<\/td>\n<\/tr>\n
$69 \\frac{1}{2}$<\/td>\n68;23,59<\/td>\n0;0,51,33<\/td>\n<\/tr>\n
70<\/td>\n68;49,45<\/td>\n0;0,51,23<\/td>\n<\/tr>\n
$70 \\frac{1}{2}$<\/td>\n69;15,27<\/td>\n0;0,51,14<\/td>\n<\/tr>\n
71<\/td>\n69;41,4<\/td>\n0;0,51,4<\/td>\n<\/tr>\n
$71 \\frac{1}{2}$<\/td>\n70;6,36<\/td>\n0;0,50,55<\/td>\n<\/tr>\n
72<\/td>\n70;32,3<\/td>\n0;0,50,45<\/td>\n<\/tr>\n
$72 \\frac{1}{2}$<\/td>\n70;57,26<\/td>\n0;0,50,35<\/td>\n<\/tr>\n
73<\/td>\n71;22,44<\/td>\n0;0,50,26<\/td>\n<\/tr>\n
$73 \\frac{1}{2}$<\/td>\n71;47,56<\/td>\n0;0,50,16<\/td>\n<\/tr>\n
74<\/td>\n72;13,4<\/td>\n0;0,50,6<\/td>\n<\/tr>\n
$74 \\frac{1}{2}$<\/td>\n72;38,7<\/td>\n0;0,49,56<\/td>\n<\/tr>\n
75<\/td>\n73;3,5<\/td>\n0;0,49,46<\/td>\n<\/tr>\n
$75 \\frac{1}{2}$<\/td>\n73;27,58<\/td>\n0;0,49,36<\/td>\n<\/tr>\n
76<\/td>\n73;52,46<\/td>\n0;0,49,26<\/td>\n<\/tr>\n
$76 \\frac{1}{2}$<\/td>\n74;17,29<\/td>\n0;0,49,16<\/td>\n<\/tr>\n
77<\/td>\n74;42,7<\/td>\n0;0,49,6<\/td>\n<\/tr>\n
$77 \\frac{1}{2}$<\/td>\n75;6,39<\/td>\n0;0,48,55<\/td>\n<\/tr>\n
78<\/td>\n75;31,7<\/td>\n0;0,48,45<\/td>\n<\/tr>\n
$78 \\frac{1}{2}$<\/td>\n75;55,29<\/td>\n0;0,48,34<\/td>\n<\/tr>\n
79<\/td>\n76;19,46<\/td>\n0;0,48,24<\/td>\n<\/tr>\n
$79 \\frac{1}{2}$<\/td>\n76;43,58<\/td>\n0;0,48,13<\/td>\n<\/tr>\n
80<\/td>\n77;8,5<\/td>\n0;0,48,3<\/td>\n<\/tr>\n
$80 \\frac{1}{2}$<\/td>\n77;32,6<\/td>\n0;0,47,52<\/td>\n<\/tr>\n
80<\/td>\n77;56,2<\/td>\n0;0,47,41<\/td>\n<\/tr>\n
$81 \\frac{1}{2}$<\/td>\n78;19,52<\/td>\n0;0,47,31<\/td>\n<\/tr>\n
82<\/td>\n78;43,38<\/td>\n0;0,47,20<\/td>\n<\/tr>\n
$82 \\frac{1}{2}$<\/td>\n79;7,18<\/td>\n0;0,47,9<\/td>\n<\/tr>\n
83<\/td>\n79;30,52<\/td>\n0;0,46,58<\/td>\n<\/tr>\n
$83 \\frac{1}{2}$<\/td>\n79;54,21<\/td>\n0;0,46,47<\/td>\n<\/tr>\n
84<\/td>\n80;17,45<\/td>\n0;0,46,36<\/td>\n<\/tr>\n
$84 \\frac{1}{2}$<\/td>\n80;41,3<\/td>\n0;0,46,25<\/td>\n<\/tr>\n
85<\/td>\n81;4,15<\/td>\n0;0,46,14<\/td>\n<\/tr>\n
$85 \\frac{1}{2}$<\/td>\n81;27,22<\/td>\n0;0,46,3<\/td>\n<\/tr>\n
86<\/td>\n81;50,24<\/td>\n0;0,45,52<\/td>\n<\/tr>\n
$86 \\frac{1}{2}$<\/td>\n82;13,19<\/td>\n0;0,45,40<\/td>\n<\/tr>\n
87<\/td>\n82;36,9<\/td>\n0;0,45,29<\/td>\n<\/tr>\n
$87 \\frac{1}{2}$<\/td>\n82;58,54<\/td>\n0;0,45,18<\/td>\n<\/tr>\n
88<\/td>\n83;21,33<\/td>\n0;0,45,6<\/td>\n<\/tr>\n
$88 \\frac{1}{2}$<\/td>\n83;44,4<\/td>\n0;0,44,55<\/td>\n<\/tr>\n
89<\/td>\n84;6,32<\/td>\n0;0,44,43<\/td>\n<\/tr>\n
$89 \\frac{1}{2}$<\/td>\n84;28,54<\/td>\n0;0,44,31<\/td>\n<\/tr>\n
90<\/td>\n84;51,10<\/td>\n0;0,44,20<\/td>\n<\/tr>\n
$90 \\frac{1}{2}$<\/td>\n85;13,20<\/td>\n0;0,44,8<\/td>\n<\/tr>\n
91<\/td>\n85;35,24<\/td>\n0;0,43,57<\/td>\n<\/tr>\n
$91 \\frac{1}{2}$<\/td>\n85;57,23<\/td>\n0;0,43,45<\/td>\n<\/tr>\n
92<\/td>\n86;19,15<\/td>\n0;0,43,33<\/td>\n<\/tr>\n
$92 \\frac{1}{2}$<\/td>\n86;41,2<\/td>\n0;0,43,21<\/td>\n<\/tr>\n
93<\/td>\n87;2,42<\/td>\n0;0,43,9<\/td>\n<\/tr>\n
$93 \\frac{1}{2}$<\/td>\n87;24,17<\/td>\n0;0,42,57<\/td>\n<\/tr>\n
94<\/td>\n87;45,45<\/td>\n0;0,42,45<\/td>\n<\/tr>\n
$94 \\frac{1}{2}$<\/td>\n88;7,7<\/td>\n0;0,42,33<\/td>\n<\/tr>\n
95<\/td>\n88;28,24<\/td>\n0;0,42,21<\/td>\n<\/tr>\n
$95 \\frac{1}{2}$<\/td>\n88;49,34<\/td>\n0;0,42,9<\/td>\n<\/tr>\n
96<\/td>\n89;10,39<\/td>\n0;0,41,57<\/td>\n<\/tr>\n
$96 \\frac{1}{2}$<\/td>\n89;31,37<\/td>\n0;0,41,45<\/td>\n<\/tr>\n
97<\/td>\n89;52,29<\/td>\n0;0,41,33<\/td>\n<\/tr>\n
$97 \\frac{1}{2}$<\/td>\n90;13,15<\/td>\n0;0,41,21<\/td>\n<\/tr>\n
98<\/td>\n90;33,55<\/td>\n0;0,41,8<\/td>\n<\/tr>\n
$98 \\frac{1}{2}$<\/td>\n90;54,29<\/td>\n0;0,40,55<\/td>\n<\/tr>\n
99<\/td>\n91;14,56<\/td>\n0;0,40,42<\/td>\n<\/tr>\n
$99 \\frac{1}{2}$<\/td>\n91;35,17<\/td>\n0;0,40,30<\/td>\n<\/tr>\n
100<\/td>\n91;55,32<\/td>\n0;0,40,17<\/td>\n<\/tr>\n
$100 \\frac{1}{2}$<\/td>\n92;15,40<\/td>\n0;0,40,4<\/td>\n<\/tr>\n
101<\/td>\n92;35,42<\/td>\n0;0,39,52<\/td>\n<\/tr>\n
$101 \\frac{1}{2}$<\/td>\n92;55,38<\/td>\n0;0,39,39<\/td>\n<\/tr>\n
102<\/td>\n93;15,27<\/td>\n0;0,39,26<\/td>\n<\/tr>\n
$102 \\frac{1}{2}$<\/td>\n93;35,11<\/td>\n0;0,39,13<\/td>\n<\/tr>\n
103<\/td>\n93;54,47<\/td>\n0;0,39,0<\/td>\n<\/tr>\n
$103 \\frac{1}{2}$<\/td>\n94;14,17<\/td>\n0;0,38,47<\/td>\n<\/tr>\n
104<\/td>\n94;33,41<\/td>\n0;0,38,34<\/td>\n<\/tr>\n
$104 \\frac{1}{2}$<\/td>\n94;52,58<\/td>\n0;0,38,21<\/td>\n<\/tr>\n
105<\/td>\n95;12,9<\/td>\n0;0,38,8<\/td>\n<\/tr>\n
$105 \\frac{1}{2}$<\/td>\n95;31,13<\/td>\n0;0,37,55<\/td>\n<\/tr>\n
106<\/td>\n95;50,11<\/td>\n0;0,37,42<\/td>\n<\/tr>\n
$106 \\frac{1}{2}$<\/td>\n96;9,2<\/td>\n0;0,37,29<\/td>\n<\/tr>\n
107<\/td>\n96;27,47<\/td>\n0;0,37,16<\/td>\n<\/tr>\n
$107 \\frac{1}{2}$<\/td>\n96;46,24<\/td>\n0;0,37,3<\/td>\n<\/tr>\n
108<\/td>\n97;4,55<\/td>\n0;0,36,50<\/td>\n<\/tr>\n
$108 \\frac{1}{2}$<\/td>\n97;23,20<\/td>\n0;0,36,36<\/td>\n<\/tr>\n
109<\/td>\n97;41,38<\/td>\n0;0,36,23<\/td>\n<\/tr>\n
$109 \\frac{1}{2}$<\/td>\n97;59,49<\/td>\n0;0,36,9<\/td>\n<\/tr>\n
110<\/td>\n98;17,54<\/td>\n0;0,35,56<\/td>\n<\/tr>\n
$110 \\frac{1}{2}$<\/td>\n98;35,52<\/td>\n0;0,35,42<\/td>\n<\/tr>\n
111<\/td>\n98;53,43<\/td>\n0;0,35,29<\/td>\n<\/tr>\n
$111 \\frac{1}{2}$<\/td>\n99;11,27<\/td>\n0;0,35,15<\/td>\n<\/tr>\n
112<\/td>\n99;29,5<\/td>\n0;0,35,1<\/td>\n<\/tr>\n
$112 \\frac{1}{2}$<\/td>\n99;46,35<\/td>\n0;0,34,48<\/td>\n<\/tr>\n
113<\/td>\n100;3,59<\/td>\n0;0,34,34<\/td>\n<\/tr>\n
$113 \\frac{1}{2}$<\/td>\n100;21,16<\/td>\n0;0,34,20<\/td>\n<\/tr>\n
114<\/td>\n100;38,26<\/td>\n0;0,34,6<\/td>\n<\/tr>\n
$114 \\frac{1}{2}$<\/td>\n100;55,28<\/td>\n0;0,33,52<\/td>\n<\/tr>\n
115<\/td>\n101;12,25<\/td>\n0;0,33,39<\/td>\n<\/tr>\n
$115 \\frac{1}{2}$<\/td>\n101;29,15<\/td>\n0;0,33,25<\/td>\n<\/tr>\n
116<\/td>\n101;45,57<\/td>\n0;0,33,11<\/td>\n<\/tr>\n
$116 \\frac{1}{2}$<\/td>\n102;2,33<\/td>\n0;0,32,57<\/td>\n<\/tr>\n
117<\/td>\n102;19,1<\/td>\n0;0,32,43<\/td>\n<\/tr>\n
$117 \\frac{1}{2}$<\/td>\n102;35,22<\/td>\n0;0,32,29<\/td>\n<\/tr>\n
118<\/td>\n102;51,37<\/td>\n0;0,32,15<\/td>\n<\/tr>\n
$118 \\frac{1}{2}$<\/td>\n103;7,44<\/td>\n0;0,32,0<\/td>\n<\/tr>\n
119<\/td>\n103;23,44<\/td>\n0;0,31,46<\/td>\n<\/tr>\n
$119 \\frac{1}{2}$<\/td>\n103;39,37<\/td>\n0;0,31,32<\/td>\n<\/tr>\n
120<\/td>\n103;55,23<\/td>\n0;0,31,18<\/td>\n<\/tr>\n
$120 \\frac{1}{2}$<\/td>\n104;11,2<\/td>\n0;0,31,4<\/td>\n<\/tr>\n
121<\/td>\n104;26,34<\/td>\n0;0,30,49<\/td>\n<\/tr>\n
$121 \\frac{1}{2}$<\/td>\n104;41,59<\/td>\n0;0,30,35<\/td>\n<\/tr>\n
122<\/td>\n104;57,16<\/td>\n0;0,30,21<\/td>\n<\/tr>\n
$122 \\frac{1}{2}$<\/td>\n105;12,26<\/td>\n0;0,30,7<\/td>\n<\/tr>\n
123<\/td>\n105;27,30<\/td>\n0;0,29,52<\/td>\n<\/tr>\n
$123 \\frac{1}{2}$<\/td>\n105;42,26<\/td>\n0;0,29,37<\/td>\n<\/tr>\n
124<\/td>\n105;57,14<\/td>\n0;0,29,23<\/td>\n<\/tr>\n
$124 \\frac{1}{2}$<\/td>\n106;11,55<\/td>\n0;0,29,8<\/td>\n<\/tr>\n
125<\/td>\n106;26,29<\/td>\n0;0,28,54<\/td>\n<\/tr>\n
$125 \\frac{1}{2}$<\/td>\n106;40,56<\/td>\n0;0,28,39<\/td>\n<\/tr>\n
126<\/td>\n106;55,15<\/td>\n0;0,28,24<\/td>\n<\/tr>\n
$126 \\frac{1}{2}$<\/td>\n107;9,27<\/td>\n0;0,28,10<\/td>\n<\/tr>\n
127<\/td>\n107;23,32<\/td>\n0;0,27,56<\/td>\n<\/tr>\n
$127 \\frac{1}{2}$<\/td>\n107;37,30<\/td>\n0;0,27,40<\/td>\n<\/tr>\n
128<\/td>\n107;51,20<\/td>\n0;0,27,25<\/td>\n<\/tr>\n
$128 \\frac{1}{2}$<\/td>\n108;5,2<\/td>\n0;0,27,10<\/td>\n<\/tr>\n
129<\/td>\n108;18,37<\/td>\n0;0,26,56<\/td>\n<\/tr>\n
$129 \\frac{1}{2}$<\/td>\n108;32,5<\/td>\n0;0,26,41<\/td>\n<\/tr>\n
130<\/td>\n108;45,25<\/td>\n0;0,26,26<\/td>\n<\/tr>\n
$130 \\frac{1}{2}$<\/td>\n108;58,38<\/td>\n0;0,26,11<\/td>\n<\/tr>\n
131<\/td>\n109;11,44<\/td>\n0;0,25,56<\/td>\n<\/tr>\n
$131 \\frac{1}{2}$<\/td>\n109;24,42<\/td>\n0;0,25,41<\/td>\n<\/tr>\n
132<\/td>\n109;37,32<\/td>\n0;0,25,26<\/td>\n<\/tr>\n
$132 \\frac{1}{2}$<\/td>\n109;50,15<\/td>\n0;0,25,11<\/td>\n<\/tr>\n
133<\/td>\n110;2,50<\/td>\n0;0,24,56<\/td>\n<\/tr>\n
$133 \\frac{1}{2}$<\/td>\n110;15,18<\/td>\n0;0,24,41<\/td>\n<\/tr>\n
134<\/td>\n110;27,39<\/td>\n0;0,24,26<\/td>\n<\/tr>\n
$134 \\frac{1}{2}$<\/td>\n110;39,52<\/td>\n0;0,24,10<\/td>\n<\/tr>\n
135<\/td>\n110;51,57<\/td>\n0;0,23,55<\/td>\n<\/tr>\n
$135 \\frac{1}{2}$<\/td>\n111;3,54<\/td>\n0;0,23,40<\/td>\n<\/tr>\n
136<\/td>\n111;15,44<\/td>\n0;0,23,25<\/td>\n<\/tr>\n
$136 \\frac{1}{2}$<\/td>\n111;27,26<\/td>\n0;0,23,9<\/td>\n<\/tr>\n
137<\/td>\n111;39,1<\/td>\n0;0,22,54<\/td>\n<\/tr>\n
$137 \\frac{1}{2}$<\/td>\n111;50,29<\/td>\n0;0,22,39<\/td>\n<\/tr>\n
138<\/td>\n112;1,47<\/td>\n0;0,22,24<\/td>\n<\/tr>\n
$138 \\frac{1}{2}$<\/td>\n112;12,59<\/td>\n0;0,22,8<\/td>\n<\/tr>\n
139<\/td>\n112;24,3<\/td>\n0;0,21,53<\/td>\n<\/tr>\n
$139 \\frac{1}{2}$<\/td>\n112;35,0<\/td>\n0;0,21,37<\/td>\n<\/tr>\n
140<\/td>\n112;45,48<\/td>\n0;0,21,22<\/td>\n<\/tr>\n
$140 \\frac{1}{2}$<\/td>\n112;56,29<\/td>\n0;0,21,7<\/td>\n<\/tr>\n
141<\/td>\n113;7,2<\/td>\n0;0,20,51<\/td>\n<\/tr>\n
$141 \\frac{1}{2}$<\/td>\n113;17,25<\/td>\n0;0,20,36<\/td>\n<\/tr>\n
142<\/td>\n113;27,44<\/td>\n0;0,20,20<\/td>\n<\/tr>\n
$142 \\frac{1}{2}$<\/td>\n113;37,54<\/td>\n0;0,20,4<\/td>\n<\/tr>\n
143<\/td>\n113;47,56<\/td>\n0;0,19,49<\/td>\n<\/tr>\n
$143 \\frac{1}{2}$<\/td>\n113;57,50<\/td>\n0;0,19,33<\/td>\n<\/tr>\n
144<\/td>\n114;7,37<\/td>\n0;0,19,17<\/td>\n<\/tr>\n
$144 \\frac{1}{2}$<\/td>\n114;17,15<\/td>\n0;0,19,2<\/td>\n<\/tr>\n
145<\/td>\n114;26,46<\/td>\n0;0,18,46<\/td>\n<\/tr>\n
$145 \\frac{1}{2}$<\/td>\n114;36,9<\/td>\n0;0,18,30<\/td>\n<\/tr>\n
146<\/td>\n114;45,24<\/td>\n0;0,18,14<\/td>\n<\/tr>\n
$146 \\frac{1}{2}$<\/td>\n114;54,31<\/td>\n0;0,17,59<\/td>\n<\/tr>\n
147<\/td>\n115;3,30<\/td>\n0;0,17,43<\/td>\n<\/tr>\n
$147 \\frac{1}{2}$<\/td>\n115;12,22<\/td>\n0;0,17,27<\/td>\n<\/tr>\n
148<\/td>\n115;21,6<\/td>\n0;0,17,11<\/td>\n<\/tr>\n
$148 \\frac{1}{2}$<\/td>\n115;29,41<\/td>\n0;0,16,55<\/td>\n<\/tr>\n
149<\/td>\n115;38,9<\/td>\n0;0,16,40<\/td>\n<\/tr>\n
$149 \\frac{1}{2}$<\/td>\n115;46,29<\/td>\n0;0,16,24<\/td>\n<\/tr>\n
150<\/td>\n115;54,40<\/td>\n0;0,16,8<\/td>\n<\/tr>\n
$150 \\frac{1}{2}$<\/td>\n116;2,44<\/td>\n0;0,15,52<\/td>\n<\/tr>\n
151<\/td>\n116;10,40<\/td>\n0;0,15,36<\/td>\n<\/tr>\n
$151 \\frac{1}{2}$<\/td>\n116;18,28<\/td>\n0;0,15,20<\/td>\n<\/tr>\n
152<\/td>\n116;26,8<\/td>\n0;0,15,4<\/td>\n<\/tr>\n
$152 \\frac{1}{2}$<\/td>\n116;33,40<\/td>\n0;0,14,48<\/td>\n<\/tr>\n
153<\/td>\n116;41,4<\/td>\n0;0,14,32<\/td>\n<\/tr>\n
$153 \\frac{1}{2}$<\/td>\n116;48,20<\/td>\n0;0,14,16<\/td>\n<\/tr>\n
154<\/td>\n116;55,28<\/td>\n0;0,14,0<\/td>\n<\/tr>\n
$154 \\frac{1}{2}$<\/td>\n117;2,28<\/td>\n0;0,13,44<\/td>\n<\/tr>\n
155<\/td>\n117;9,20<\/td>\n0;0,13,28<\/td>\n<\/tr>\n
$155 \\frac{1}{2}$<\/td>\n117;16,4<\/td>\n0;0,13,12<\/td>\n<\/tr>\n
156<\/td>\n117;22,40<\/td>\n0;0,12,56<\/td>\n<\/tr>\n
$156 \\frac{1}{2}$<\/td>\n117;29,8<\/td>\n0;0,12,40<\/td>\n<\/tr>\n
157<\/td>\n117;35,28<\/td>\n0;0,12,24<\/td>\n<\/tr>\n
$157 \\frac{1}{2}$<\/td>\n117;41,40<\/td>\n0;0,12,7<\/td>\n<\/tr>\n
158<\/td>\n117;47,43<\/td>\n0;0,11,51<\/td>\n<\/tr>\n
$158 \\frac{1}{2}$<\/td>\n117;53,39<\/td>\n0;0,11,35<\/td>\n<\/tr>\n
159<\/td>\n117;59,27<\/td>\n0;0,11,19<\/td>\n<\/tr>\n
$159 \\frac{1}{2}$<\/td>\n118;5,7<\/td>\n0;0,11,3<\/td>\n<\/tr>\n
160<\/td>\n118;10,37<\/td>\n0;0,10,47<\/td>\n<\/tr>\n
$160 \\frac{1}{2}$<\/td>\n118;16,1<\/td>\n0;0,10,31<\/td>\n<\/tr>\n
161<\/td>\n118;21,16<\/td>\n0;0,10,14<\/td>\n<\/tr>\n
$161 \\frac{1}{2}$<\/td>\n118;26,23<\/td>\n0;0,9,58<\/td>\n<\/tr>\n
162<\/td>\n118;31,22<\/td>\n0;0,9,42<\/td>\n<\/tr>\n
$162 \\frac{1}{2}$<\/td>\n118;36,13<\/td>\n0;0,9,25<\/td>\n<\/tr>\n
163<\/td>\n118;40,55<\/td>\n0;0,9,9<\/td>\n<\/tr>\n
$163 \\frac{1}{2}$<\/td>\n118;45,30<\/td>\n0;0,8,53<\/td>\n<\/tr>\n
164<\/td>\n118;49,56<\/td>\n0;0,8,37<\/td>\n<\/tr>\n
$164 \\frac{1}{2}$<\/td>\n118;54,15<\/td>\n0;0,8,20<\/td>\n<\/tr>\n
165<\/td>\n118;58,25<\/td>\n0;0,8,4<\/td>\n<\/tr>\n
$165 \\frac{1}{2}$<\/td>\n119;2,26<\/td>\n0;0,7,48<\/td>\n<\/tr>\n
166<\/td>\n119;6,20<\/td>\n0;0,7,31<\/td>\n<\/tr>\n
$166 \\frac{1}{2}$<\/td>\n119;10,6<\/td>\n0;0,7,15<\/td>\n<\/tr>\n
167<\/td>\n119;13,44<\/td>\n0;0,6,59<\/td>\n<\/tr>\n
$167 \\frac{1}{2}$<\/td>\n119;17,13<\/td>\n0;0,6,42<\/td>\n<\/tr>\n
168<\/td>\n119;20,34<\/td>\n0;0,6,26<\/td>\n<\/tr>\n
$168 \\frac{1}{2}$<\/td>\n119;23,47<\/td>\n0;0,6,10<\/td>\n<\/tr>\n
169<\/td>\n119;26,52<\/td>\n0;0,5,53<\/td>\n<\/tr>\n
$169 \\frac{1}{2}$<\/td>\n119;29,49<\/td>\n0;0,5,37<\/td>\n<\/tr>\n
170<\/td>\n119;32,37<\/td>\n0;0,5,20<\/td>\n<\/tr>\n
$170 \\frac{1}{2}$<\/td>\n119;35,17<\/td>\n0;0,5,4<\/td>\n<\/tr>\n
171<\/td>\n119;37,49<\/td>\n0;0,4,48<\/td>\n<\/tr>\n
$171 \\frac{1}{2}$<\/td>\n119;40,13<\/td>\n0;0,4,31<\/td>\n<\/tr>\n
172<\/td>\n119;42,28<\/td>\n0;0,4,14<\/td>\n<\/tr>\n
$172 \\frac{1}{2}$<\/td>\n119;44,35<\/td>\n0;0,3,58<\/td>\n<\/tr>\n
173<\/td>\n119;46,35<\/td>\n0;0,3,42<\/td>\n<\/tr>\n
$173 \\frac{1}{2}$<\/td>\n119;48,26<\/td>\n0;0,3,26<\/td>\n<\/tr>\n
174<\/td>\n119;50,8<\/td>\n0;0,3,9<\/td>\n<\/tr>\n
$174 \\frac{1}{2}$<\/td>\n119;51,43<\/td>\n0;0,2,53<\/td>\n<\/tr>\n
175<\/td>\n119;53,10<\/td>\n0;0,2,36<\/td>\n<\/tr>\n
$175 \\frac{1}{2}$<\/td>\n119;54,27<\/td>\n0;0,2,20<\/td>\n<\/tr>\n
176<\/td>\n119;55,38<\/td>\n0;0,2,3<\/td>\n<\/tr>\n
$176 \\frac{1}{2}$<\/td>\n119;56,39<\/td>\n0;0,1,47<\/td>\n<\/tr>\n
177<\/td>\n119;57,32<\/td>\n0;0,1,30<\/td>\n<\/tr>\n
$177 \\frac{1}{2}$<\/td>\n119;58,18<\/td>\n0;0,1,14<\/td>\n<\/tr>\n
178<\/td>\n11958,55<\/td>\n0;0,0,57<\/td>\n<\/tr>\n
$178 \\frac{1}{2}$<\/td>\n119;59,24<\/td>\n0;0,0,41<\/td>\n<\/tr>\n
179<\/td>\n119;59,44<\/td>\n0;0,0,25<\/td>\n<\/tr>\n
$179 \\frac{1}{2}$<\/td>\n119;59,56<\/td>\n0;0,0,9<\/td>\n<\/tr>\n
180<\/td>\n120;0,0<\/td>\n0;0,0,0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

The table here is reproduced from the Toomer translation of\u00a0The Almagest<\/em>. In turn, it was reproduced from Glowatzki and Gottsche who recomputed the table using a computer algorithm meant to mimic Ptolemy’s methods, but avoiding arithmetic and scribal errors<\/span>2<\/sup><\/a><\/span>.<\/p>\n

In print publications of this table (and all tables in the Almagest<\/em>), it is broken up into 45 rows per page. This dates back to the oldest copes of the table available and is suspected to be related to the standard height of a piece of papyrus.<\/p>\n

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Here displayed in all its glory is Ptolemy’s Table of Chords. Notes to follow.<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[24],"tags":[29,26,14],"class_list":["post-622","post","type-post","status-publish","format-standard","hentry","category-almagest","tag-chords","tag-mathematics","tag-ptolemy"],"acf":[],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p9ZpvC-a2","_links":{"self":[{"href":"https:\/\/jonvoisey.net\/blog\/wp-json\/wp\/v2\/posts\/622","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/jonvoisey.net\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/jonvoisey.net\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/jonvoisey.net\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/jonvoisey.net\/blog\/wp-json\/wp\/v2\/comments?post=622"}],"version-history":[{"count":27,"href":"https:\/\/jonvoisey.net\/blog\/wp-json\/wp\/v2\/posts\/622\/revisions"}],"predecessor-version":[{"id":4866,"href":"https:\/\/jonvoisey.net\/blog\/wp-json\/wp\/v2\/posts\/622\/revisions\/4866"}],"wp:attachment":[{"href":"https:\/\/jonvoisey.net\/blog\/wp-json\/wp\/v2\/media?parent=622"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/jonvoisey.net\/blog\/wp-json\/wp\/v2\/categories?post=622"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/jonvoisey.net\/blog\/wp-json\/wp\/v2\/tags?post=622"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}