Ptolemy's Table of Chords
Arc (°)	Chord60			Chord10	Sixtieths60				Sixtieths10
0.5	0	31	25	0.523611	0	1	2	50	0.017226
1.0	1	2	50	1.047222	0	1	2	50	0.017226
1.5	1	34	15	1.570833	0	1	2	50	0.017226
2.0	2	5	40	2.094444	0	1	2	50	0.017226
2.5	2	37	4	2.617778	0	1	2	48	0.017226
3.0	3	8	28	3.141111	0	1	2	48	0.017226
3.5	3	39	52	3.664444	0	1	2	48	0.017226
4.0	4	11	16	4.187778	0	1	2	47	0.017226
4.5	4	42	40	4.711111	0	1	2	47	0.017226
5.0	5	14	4	5.234444	0	1	2	46	0.017226
5.5	5	45	27	5.757500	0	1	2	45	0.017226
6.0	6	16	49	6.280278	0	1	2	44	0.017226
6.5	6	48	11	6.803056	0	1	2	43	0.017226
7.0	7	19	33	7.325833	0	1	2	42	0.017225
7.5	7	50	54	7.848333	0	1	2	41	0.017225
8.0	8	22	15	8.370833	0	1	2	40	0.017225
8.5	8	53	35	8.893056	0	1	2	39	0.017225
9.0	9	24	54	9.415000	0	1	2	38	0.017225
9.5	9	56	13	9.936944	0	1	2	37	0.017225
10.0	10	27	32	10.458889	0	1	2	35	0.017225
10.5	10	58	49	10.980278	0	1	2	33	0.017225
11.0	11	30	5	11.501389	0	1	2	32	0.017225
11.5	12	1	21	12.022500	0	1	2	30	0.017225
12.0	12	32	36	12.543333	0	1	2	28	0.017224
12.5	13	3	50	13.063889	0	1	2	27	0.017224
13.0	13	35	4	13.584444	0	1	2	25	0.017224
13.5	14	6	16	14.104444	0	1	2	23	0.017224
14.0	14	37	27	14.624167	0	1	2	21	0.017224
14.5	15	8	38	15.143889	0	1	2	19	0.017224
15.0	15	39	47	15.663056	0	1	2	17	0.017224
15.5	16	10	56	16.182222	0	1	2	15	0.017223
16.0	16	42	3	16.700833	0	1	2	13	0.017223
16.5	17	13	9	17.219167	0	1	2	10	0.017223
17.0	17	44	14	17.737222	0	1	2	7	0.017223
17.5	18	15	17	18.254722	0	1	2	5	0.017223
18.0	18	46	19	18.771944	0	1	2	2	0.017222
18.5	19	17	21	19.289167	0	1	2	0	0.017222
19.0	19	48	21	19.805833	0	1	1	57	0.016949
19.5	20	19	19	20.321944	0	1	1	54	0.016949
20.0	20	50	16	20.837778	0	1	1	51	0.016948
20.5	21	21	11	21.353056	0	1	1	48	0.016948
21.0	21	52	6	21.868333	0	1	1	45	0.016948
21.5	22	22	58	22.382778	0	1	1	42	0.016948
22.0	22	53	49	22.896944	0	1	1	39	0.016947
22.5	23	24	39	23.410833	0	1	1	36	0.016947
23.0	23	55	27	23.924167	0	1	1	33	0.016947
23.5	24	26	13	24.436944	0	1	1	30	0.016947
24.0	24	56	58	24.949444	0	1	1	26	0.016946
24.5	25	27	41	25.461389	0	1	1	22	0.016946
25.0	25	58	22	25.972778	0	1	1	19	0.016946
25.5	26	29	1	26.483611	0	1	1	15	0.016946
26.0	26	59	38	26.993889	0	1	1	11	0.016945
26.5	27	30	14	27.503889	0	1	1	8	0.016945
27.0	28	0	48	28.013333	0	1	1	4	0.016945
27.5	28	31	20	28.522222	0	1	1	0	0.016944
28.0	29	1	50	29.030556	0	1	0	56	0.016671
28.5	29	32	18	29.538333	0	1	0	52	0.016671
29.0	30	2	44	30.045556	0	1	0	48	0.016670
29.5	30	33	8	30.552222	0	1	0	44	0.016670
30.0	31	3	30	31.058333	0	1	0	40	0.016670
30.5	31	33	50	31.563889	0	1	0	35	0.016669
31.0	32	4	7	32.068611	0	1	0	31	0.016669
31.5	32	34	22	32.572778	0	1	0	27	0.016669
32.0	33	4	35	33.076389	0	1	0	22	0.016668
32.5	33	34	46	33.579444	0	1	0	17	0.016668
33.0	34	4	55	34.081944	0	1	0	12	0.016668
33.5	34	35	1	34.583611	0	1	0	8	0.016667
34.0	35	5	5	35.084722	0	1	0	3	0.016667
34.5	35	35	6	35.585000	0	0	59	57	0.016393
35.0	36	5	5	36.084722	0	0	59	52	0.016393
35.5	36	35	1	36.583611	0	0	59	48	0.016393
36.0	37	4	55	37.081944	0	0	59	43	0.016392
36.5	37	34	47	37.579722	0	0	59	38	0.016392
37.0	38	4	36	38.076667	0	0	59	32	0.016391
37.5	38	34	22	38.572778	0	0	59	27	0.016391
38.0	39	4	5	39.068056	0	0	59	22	0.016391
38.5	39	33	46	39.562778	0	0	59	16	0.016390
39.0	40	3	25	40.056944	0	0	59	11	0.016390
39.5	40	33	0	40.550000	0	0	59	5	0.016389
40.0	41	2	33	41.042500	0	0	59	0	0.016389
40.5	41	32	3	41.534167	0	0	58	54	0.016115
41.0	42	1	30	42.025000	0	0	58	48	0.016115
41.5	42	30	54	42.515000	0	0	58	42	0.016114
42.0	43	0	15	43.004167	0	0	58	36	0.016114
42.5	43	29	33	43.492500	0	0	58	31	0.016114
43.0	43	58	49	43.980278	0	0	58	25	0.016113
43.5	44	28	1	44.466944	0	0	58	18	0.016113
44.0	44	57	10	44.952778	0	0	58	12	0.016112
44.5	45	26	16	45.437778	0	0	58	6	0.016112
45.0	45	55	19	45.921944	0	0	58	0	0.016111
45.5	46	24	19	46.405278	0	0	57	54	0.015838
46.0	46	53	16	46.887778	0	0	57	47	0.015837
46.5	47	22	9	47.369167	0	0	57	41	0.015836
47.0	47	51	0	47.850000	0	0	57	34	0.015836
47.5	48	19	47	48.329722	0	0	57	27	0.015835
48.0	48	48	30	48.808333	0	0	57	21	0.015835
48.5	49	17	11	49.286389	0	0	57	14	0.015834
49.0	49	45	48	49.763333	0	0	57	7	0.015834
49.5	50	14	21	50.239167	0	0	57	0	0.015833
50.0	50	42	51	50.714167	0	0	56	53	0.015560
50.5	51	11	18	51.188333	0	0	56	46	0.015559
51.0	51	39	41	51.661389	0	0	56	39	0.015559
51.5	52	8	0	52.133333	0	0	56	32	0.015558
52.0	52	36	16	52.604444	0	0	56	25	0.015557
52.5	53	4	29	53.074722	0	0	56	18	0.015557
53.0	53	32	38	53.543889	0	0	56	10	0.015556
53.5	54	0	43	54.011944	0	0	56	3	0.015556
54.0	54	28	44	54.478889	0	0	55	55	0.015282
54.5	54	56	42	54.945000	0	0	55	48	0.015281
55.0	55	24	36	55.410000	0	0	55	40	0.015281
55.5	55	52	26	55.873889	0	0	55	33	0.015280
56.0	56	50	12	56.836667	0	0	55	25	0.015280
56.5	56	47	54	56.798333	0	0	55	17	0.015279
57.0	57	15	33	57.259167	0	0	55	9	0.015278
57.5	57	43	7	57.718611	0	0	55	1	0.015278
58.0	58	10	38	58.177222	0	0	54	53	0.015004
58.5	58	38	5	58.634722	0	0	54	45	0.015003
59.0	59	5	27	59.090833	0	0	54	37	0.015003
59.5	59	32	45	59.545833	0	0	54	29	0.015002
60.0	60	0	0	60.000000	0	0	54	31	0.015002
60.5	60	27	11	60.453056	0	0	54	12	0.015001
61.0	60	54	17	60.904722	0	0	54	4	0.015000
61.5	61	21	19	61.355278	0	0	53	56	0.014727
62.0	61	48	17	61.804722	0	0	53	47	0.014726
62.5	62	15	10	62.252778	0	0	53	39	0.014725
63.0	62	42	0	62.700000	0	0	53	30	0.014725
63.5	63	8	45	63.145833	0	0	53	22	0.014724
64.0	63	35	26	63.590556	0	0	53	13	0.014723
64.5	64	2	2	64.033889	0	0	53	4	0.014723
65.0	64	28	34	64.476111	0	0	52	55	0.014449
65.5	64	55	1	64.916944	0	0	52	46	0.014448
66.0	65	21	24	65.356667	0	0	52	37	0.014447
66.5	65	47	43	65.795278	0	0	52	28	0.014447
67.0	66	13	57	66.232500	0	0	52	19	0.014446
67.5	66	40	7	66.668611	0	0	52	10	0.014445
68.0	67	6	12	67.103333	0	0	52	1	0.014445
68.5	67	32	12	67.536667	0	0	51	52	0.014171
69.0	67	58	8	67.968889	0	0	51	43	0.014170
69.5	68	23	59	68.399722	0	0	51	33	0.014169
70.0	68	49	45	68.829167	0	0	51	21	0.014168
70.5	69	15	27	69.257500	0	0	51	14	0.014168
71.0	69	41	4	69.684444	0	0	51	4	0.014167
71.5	70	6	36	70.110000	0	0	50	55	0.013893
72.0	70	32	4	70.534444	0	0	50	45	0.013892
72.5	70	57	26	70.957222	0	0	50	35	0.013892
73.0	71	22	44	71.378889	0	0	50	26	0.013891
73.5	71	47	56	71.798889	0	0	50	16	0.013890
74.0	72	13	4	72.217778	0	0	50	6	0.013889
74.5	72	38	7	72.635278	0	0	49	56	0.013615
75.0	73	3	5	73.051389	0	0	49	46	0.013615
75.5	73	27	58	73.466111	0	0	49	36	0.013614
76.0	73	52	46	73.879444	0	0	49	26	0.013613
76.5	74	17	29	74.291389	0	0	49	16	0.013612
77.0	74	42	7	74.701944	0	0	49	6	0.013612
77.5	75	6	39	75.110833	0	0	48	55	0.013338
78.0	75	31	7	75.518611	0	0	48	45	0.013337
78.5	75	55	29	75.924722	0	0	48	34	0.013336
79.0	76	19	46	76.329444	0	0	48	24	0.013335
79.5	76	43	58	76.732778	0	0	48	13	0.013334
80.0	77	8	5	77.134722	0	0	48	3	0.013334
80.5	77	32	6	77.535000	0	0	47	52	0.013060
81.0	77	56	2	77.933889	0	0	47	41	0.013059
81.5	78	19	52	78.331111	0	0	47	31	0.013058
82.0	78	43	38	78.727222	0	0	47	20	0.013057
82.5	79	7	18	79.121667	0	0	47	9	0.013056
83.0	79	30	52	79.514444	0	0	46	58	0.012782
83.5	79	54	21	79.905833	0	0	46	47	0.012781
84.0	80	17	45	80.295833	0	0	46	36	0.012781
84.5	80	41	3	80.684167	0	0	46	25	0.012780
85.0	81	4	15	81.070833	0	0	46	14	0.012779
85.5	81	27	22	81.456111	0	0	46	3	0.012778
86.0	81	50	24	81.840000	0	0	45	52	0.012504
86.5	82	13	19	82.221944	0	0	45	40	0.012503
87.0	82	36	9	82.602500	0	0	45	29	0.012502
87.5	82	58	54	82.981667	0	0	45	18	0.012501
88.0	83	21	33	83.359167	0	0	45	6	0.012500
88.5	83	44	6	83.735000	0	0	44	55	0.012226
89.0	84	6	33	84.109167	0	0	44	43	0.012226
89.5	84	28	54	84.481667	0	0	44	31	0.012225
90.0	84	51	10	84.852778	0	0	44	20	0.012224
90.5	85	13	20	85.222222	0	0	44	8	0.012223
91.0	85	35	24	85.590000	0	0	43	57	0.011949
91.5	85	57	23	85.956389	0	0	43	45	0.011948
92.0	86	19	15	86.320833	0	0	43	33	0.011947
92.5	86	41	2	86.683889	0	0	43	21	0.011946
93.0	87	2	42	87.045000	0	0	43	9	0.011945
93.5	87	24	17	87.404722	0	0	42	57	0.011671
94.0	87	45	45	87.762500	0	0	42	45	0.011670
94.5	88	7	7	88.118611	0	0	42	33	0.011669
95.0	88	28	24	88.473333	0	0	42	21	0.011668
95.5	88	49	34	88.826111	0	0	42	9	0.011667
96.0	89	10	39	89.177500	0	0	41	57	0.011393
96.5	89	31	37	89.526944	0	0	41	45	0.011392
97.0	89	52	29	89.874722	0	0	41	33	0.011391
97.5	90	13	15	90.220833	0	0	41	21	0.011391
98.0	90	33	55	90.565278	0	0	41	8	0.011390
98.5	90	54	29	90.908056	0	0	40	55	0.011115
99.0	91	14	56	91.248889	0	0	40	42	0.011114
99.5	91	35	17	91.588056	0	0	40	30	0.011113
100.0	91	55	32	91.925556	0	0	40	17	0.011112
100.5	92	15	40	92.261111	0	0	40	4	0.011111
101.0	92	35	42	92.595000	0	0	39	52	0.010837
101.5	92	55	38	92.927222	0	0	39	39	0.010836
102.0	93	15	27	93.257500	0	0	39	26	0.010835
102.5	93	35	11	93.586389	0	0	39	13	0.010834
103.0	93	54	47	93.913056	0	0	39	0	0.010833
103.5	94	15	17	94.254722	0	0	38	47	0.010559
104.0	94	33	41	94.561389	0	0	38	34	0.010558
104.5	94	52	58	94.882778	0	0	38	21	0.010557
105.0	95	12	9	95.202500	0	0	38	8	0.010556
105.5	95	31	13	95.520278	0	0	37	55	0.010282
106.0	95	50	11	95.836389	0	0	37	42	0.010281
106.5	96	9	2	96.150556	0	0	37	29	0.010280
107.0	96	27	47	96.463056	0	0	37	16	0.010279
107.5	96	46	24	96.773333	0	0	37	3	0.010278
108.0	97	4	56	97.082222	0	0	36	50	0.010004
108.5	97	23	20	97.388889	0	0	36	36	0.010003
109.0	97	41	38	97.693889	0	0	36	23	0.010002
109.5	97	59	49	97.996944	0	0	36	9	0.010001
110.0	98	19	54	98.331667	0	0	35	56	0.009727
110.5	98	35	52	98.597778	0	0	35	42	0.009725
111.0	98	53	43	98.895278	0	0	35	29	0.009724
111.5	99	11	27	99.190833	0	0	35	15	0.009723
112.0	99	29	5	99.484722	0	0	34	48	0.009448
112.5	99	46	35	99.776389	0	0	34	34	0.009447
113.0	100	3	59	100.066389	0	0	34	34	0.009447
113.5	100	21	16	100.354444	0	0	34	20	0.009446
114.0	100	38	26	100.640556	0	0	34	6	0.009445
114.5	100	55	38	100.927222	0	0	33	53	0.009171
115.0	101	12	25	101.206944	0	0	33	39	0.009170
115.5	101	29	15	101.487500	0	0	33	25	0.009169
116.0	101	45	57	101.765833	0	0	33	11	0.009168
116.5	102	2	33	102.042500	0	0	32	57	0.008893
117.0	102	19	1	102.316944	0	0	32	43	0.008892
117.5	102	35	22	102.589444	0	0	32	29	0.008891
118.0	102	51	37	102.860278	0	0	32	15	0.008890
118.5	103	7	44	103.128889	0	0	32	0	0.008889
119.0	103	23	44	103.395556	0	0	31	46	0.008615
119.5	103	39	37	103.660278	0	0	31	32	0.008614
120.0	103	55	23	103.923056	0	0	31	18	0.008613
120.5	104	11	2	104.183889	0	0	31	4	0.008611
121.0	104	26	34	104.442778	0	0	30	49	0.008337
121.5	104	41	59	104.699722	0	0	30	35	0.008336
122.0	104	57	16	104.954444	0	0	30	21	0.008335
122.5	105	12	26	105.207222	0	0	30	7	0.008334
123.0	105	27	30	105.458333	0	0	29	52	0.008060
123.5	105	42	26	105.707222	0	0	29	37	0.008058
124.0	105	57	14	105.953889	0	0	29	23	0.008057
124.5	106	11	55	106.198611	0	0	29	8	0.008056
125.0	106	26	29	106.441389	0	0	28	54	0.007782
125.5	106	40	56	106.682222	0	0	28	39	0.007781
126.0	106	55	15	106.920833	0	0	28	24	0.007780
126.5	107	9	27	107.157500	0	0	28	10	0.007779
127.0	107	23	32	107.392222	0	0	27	56	0.007504
127.5	107	37	30	107.625000	0	0	27	40	0.007503
128.0	107	51	20	107.855556	0	0	27	25	0.007502
128.5	108	5	2	108.083889	0	0	27	10	0.007501
129.0	108	18	37	108.310278	0	0	26	56	0.007227
129.5	108	32	5	108.534722	0	0	26	41	0.007225
130.0	108	45	25	108.756944	0	0	26	26	0.007224
130.5	108	58	38	108.977222	0	0	26	11	0.007223
131.0	109	11	44	109.195556	0	0	25	56	0.006949
131.5	109	24	42	109.411667	0	0	25	41	0.006948
132.0	109	37	32	109.625556	0	0	25	26	0.006946
132.5	109	50	15	109.837500	0	0	25	11	0.006945
133.0	110	2	50	110.047222	0	0	24	56	0.006671
133.5	110	15	18	110.255000	0	0	24	41	0.006670
134.0	110	27	39	110.460833	0	0	24	26	0.006669
134.5	110	39	52	110.664444	0	0	24	10	0.006667
135.0	110	51	57	110.865833	0	0	23	55	0.006393
135.5	111	3	54	111.065000	0	0	23	40	0.006392
136.0	111	15	44	111.262222	0	0	23	25	0.006391
136.5	111	27	26	111.457222	0	0	23	9	0.006390
137.0	111	39	1	111.650278	0	0	22	54	0.006115
137.5	111	50	28	111.841111	0	0	22	39	0.006114
138.0	112	1	47	112.029722	0	0	22	24	0.006113
138.5	112	12	59	112.216389	0	0	22	8	0.006112
139.0	112	24	3	112.400833	0	0	21	53	0.005837
139.5	112	35	0	112.583333	0	0	21	37	0.005836
140.0	112	45	48	112.763333	0	0	21	22	0.005835
140.5	112	56	29	112.941389	0	0	21	7	0.005834
141.0	113	7	2	113.117222	0	0	20	51	0.005559
141.5	113	17	26	113.290556	0	0	20	36	0.005558
142.0	113	27	44	113.462222	0	0	20	20	0.005557
142.5	113	37	54	113.631667	0	0	20	4	0.005556
143.0	113	47	56	113.798889	0	0	19	49	0.005282
143.5	113	57	50	113.963889	0	0	19	33	0.005280
144.0	114	7	37	114.126944	0	0	19	17	0.005279
144.5	114	17	15	114.287500	0	0	19	2	0.005278
145.0	114	26	46	114.446111	0	0	18	46	0.005004
145.5	114	36	9	114.602500	0	0	18	30	0.005002
146.0	114	45	24	114.756667	0	0	18	14	0.005001
146.5	114	54	31	114.908611	0	0	17	59	0.004727
147.0	115	3	30	115.058333	0	0	17	43	0.004726
147.5	115	12	22	115.206111	0	0	17	27	0.004724
148.0	115	21	6	115.351667	0	0	17	11	0.004723
148.5	115	29	41	115.494722	0	0	16	55	0.004449
149.0	115	38	9	115.635833	0	0	16	40	0.004448
149.5	115	46	29	115.774722	0	0	16	24	0.004446
150.0	115	54	40	115.911111	0	0	16	8	0.004445
150.5	116	2	44	116.045556	0	0	15	52	0.004171
151.0	116	10	40	116.177778	0	0	15	36	0.004169
151.5	116	18	28	116.307778	0	0	15	20	0.004168
152.0	116	26	8	116.435556	0	0	15	4	0.004167
152.5	116	33	40	116.561111	0	0	14	48	0.003893
153.0	116	41	4	116.684444	0	0	14	32	0.003891
153.5	116	48	20	116.805556	0	0	14	16	0.003890
154.0	116	55	28	116.924444	0	0	14	0	0.003889
154.5	117	2	28	117.041111	0	0	13	44	0.003615
155.0	117	9	20	117.155556	0	0	13	28	0.003613
155.5	117	16	4	117.267778	0	0	13	12	0.003612
156.0	117	22	40	117.377778	0	0	12	56	0.003338
156.5	117	29	8	117.485556	0	0	12	40	0.003336
157.0	117	35	28	117.591111	0	0	12	24	0.003335
157.5	117	41	40	117.694444	0	0	12	7	0.003334
158.0	117	47	43	117.795278	0	0	11	51	0.003059
158.5	117	53	39	117.894167	0	0	11	35	0.003058
159.0	117	59	27	117.990833	0	0	11	19	0.003057
159.5	118	5	7	118.085278	0	0	10	53	0.002782
160.0	118	10	37	118.176944	0	0	10	47	0.002781
160.5	118	16	1	118.266944	0	0	10	31	0.002780
161.0	118	21	16	118.354444	0	0	10	14	0.002779
161.5	118	26	23	118.439722	0	0	9	58	0.002504
162.0	118	31	22	118.522778	0	0	9	42	0.002503
162.5	118	36	13	118.603611	0	0	9	25	0.002502
163.0	118	40	55	118.681944	0	0	9	9	0.002501
163.5	118	45	30	118.758333	0	0	8	53	0.002226
164.0	118	49	56	118.832222	0	0	8	37	0.002225
164.5	118	54	15	118.904167	0	0	8	20	0.002224
165.0	118	58	25	118.973611	0	0	8	4	0.002223
165.5	119	2	26	119.040556	0	0	7	48	0.001948
166.0	119	6	20	119.105556	0	0	7	31	0.001947
166.5	119	10	6	119.168333	0	0	7	15	0.001946
167.0	119	13	44	119.228889	0	0	6	59	0.001671
167.5	119	17	13	119.286944	0	0	6	42	0.001670
168.0	119	20	34	119.342778	0	0	6	26	0.001669
168.5	119	23	47	119.396389	0	0	6	10	0.001667
169.0	119	26	52	119.447778	0	0	5	53	0.001393
169.5	119	29	49	119.496944	0	0	5	37	0.001392
170.0	119	32	37	119.543611	0	0	5	20	0.001390
170.5	119	35	17	119.588056	0	0	5	4	0.001389
171.0	119	37	49	119.630278	0	0	4	48	0.001115
171.5	119	40	13	119.670278	0	0	4	31	0.001114
172.0	119	42	28	119.707778	0	0	4	14	0.001112
172.5	119	44	35	119.743056	0	0	3	58	0.000838
173.0	119	46	35	119.776389	0	0	3	42	0.000837
173.5	119	48	26	119.807222	0	0	3	26	0.000835
174.0	119	50	8	119.835556	0	0	3	9	0.000834
174.5	119	51	43	119.861944	0	0	2	53	0.000560
175.0	119	53	10	119.886111	0	0	2	36	0.000558
175.5	119	54	27	119.907500	0	0	2	20	0.000557
176.0	119	55	38	119.927222	0	0	2	3	0.000556
176.5	119	56	39	119.944167	0	0	1	47	0.000281
177.0	119	57	32	119.958889	0	0	1	30	0.000280
177.5	119	58	18	119.971667	0	0	1	14	0.000279
178.0	119	58	55	119.981944	0	0	0	57	0.000004
178.5	119	59	24	119.990000	0	0	0	41	0.000003
179.0	119	59	44	119.995556	0	0	0	25	0.000002
179.5	119	59	56	119.998889	0	0	0	9	0.000001
180.0	120	0	0	120.000000	0	0	0	0	0.000000