Copernicus's Chord Tables

table

picture

semicircle

page number

1

β=2α

40

	0		1		2		3		4
1	2909	2909	177432	2908	351902	2907	526264	2905	700467	2902	59
2	5818		180341		354809		529169		703368		58
3	8727		183249		357716		532074		706270		57
4	11636		186158		360623		534979		709171		56
5	14544		189066		363530		537883		712073		55
6	17453		191974		366437		540788		714974	2901	54
7	20362		194883		369344		543693		717876		53
8	23271		197791		372251		546597		720777		52
9	26180		200699		375158		549502		723678		51
10	29089		203608		378065		552406	2904	726580		50
11	31998		206516		380971		555311		729481		49
12	34907		209424		383878		558215		732382		48
13	37815		212332		386785		561119		735283		47
14	40724		215241		389692		564024		738184		46
15	43633		218149		392598		566928		741085		45
16	46542		221057		395505		569832		743986		44
17	49451		223965		398411		572736		746887		43
18	52360		226873		401318		575640		749787		42
19	55268		229781		404224		578544		752688		41
20	58177		232690		407131	2906	581448		755589		40
21	61086		235598		410037		584352		758489		39
22	63995		238506		412944		587256		761390	2900	38
23	66904		241414		415850		590160		764290		37
24	69813		244322		418757		593064		767190		36
25	72721		247230		421663		595967		770091		35
26	75630		250138		424569		598871		772991		34
27	78539		253046		427475		601775		775891		33
28	81448		255954		430382		604678		778791		32
29	84357		258862		433288		607582		781691		31
30	87265		261769		436194		610485	2903	784591		30
	89		88		87		86		85

This Demonstration reconstructs Copernicus's chord (sine) table from De lateribus et angulis triangulorum [1], published by Rheticus. Rheticus (1514–1574) was a student of Copernicus (1473–1543). The book contains a table of chords (sines) for every minute of the quadrant and for a radius of

7

10

, that is, using formula

7

10

sin(α)

. So the chords were given to seven places. The differences were also calculated.