208

In Mysterium Cosmographicum

Inde similiter transit ad reliquas distantias sic :

3) 0,74139: 0,69628 = 0,7617 : x ; x = ?’ 696 n 2 |^’ 7617 = 0,7155 = 0«42'55" (dist. min.0)

u,74109 ^

4) 1,393:1,6478 = 1,311 :x;x = ^3 ^ = 1,5508 = 1°33'2" (dist.max.c?)

5) 1: 0,707 = 0,7155 : x ; x = 0,707X0,7155 = 0,5058 = 0°30'21" (dist max.£)

1 5508

6) 1: 0,333 = x: 1,5508; x = = 4,6524 = 4"39'8" (dist. min. !(.)

7) 4,99944: 4,6524 = 5,49256:x; x = = 5,1108 = 5°6'39" (dist.max.lt)

8) 1 : 0,57735 =x: 5,1108 ; x = = 8 ’ 8521 = 8 Ü 51'8" (dist. min. $)

9) 8,3416:8,8521 = 9,9874:x; x = = 10,599 = 10»35'56"(dist.max.b)

8,341b

Quartus denique ordo tabulae Keplerianae simili ratione qua tertius e secundo compu-tatur, addita ad Terrenam distantiam maximam quantitate semidiametri orbis Lunaris = 0,06(3'36''), eademque subtracta a minima Terrae distantia; v. c. 0" 57' 30" —0°3'36" =0° 53' 54" = 0,8983 ; radius globi icosaedro inscripti = 0,795. Ergo :

1 : 0,795 = 0,8983 : x

x = 0,795 X 0,8983 = 0,714 = 0°42' 50" (max. dist. 9).

Sic 1° 2' 30" + 0° 3' 36" = 1° 6' 6" = 1,10166,ergo 1 : 0,795 = x : 1,10166; = 1,3863 = 1°23' 11" (min. dist. tf) &c.

52) p. 157. Angulos, quos haec exhibet tabella, sic elicit Keplerus e tabula praecedente :1) Distantiae f> 10,599; = 9,9874; = 11,3044 . . .

Media Terrae distantia = 1.

10,599 : 1 = sin. tot. : x.

5 ° 25 ' ;

similiter :

9,9874

1

11,3044

2) Pro OJ: 1

= 0,10012 = sin. 5° 45' ;

= 0,08846 = sin. 5° 4'.

0,19566 = sin. 11° 17' (K. 10° 17'),

5,1108

= 0,18207 = ,b. 10" 29-,

1

5,4505

3) Pro cJ: 1

1,5508

1

1,64777

1

1,65361

= 0,18347 = sin. 10° 34' (K. 23').0,6448 = sin. 40° 9',

= 0,60687 = sin. 37° 22',

0,60474 = sin. 37° 13' (K. 52').

4) Pro 9 ipsi numeri tabulae p. 156 in fractiones decimales reducti sunt sinus quaesiti.Quippe

0,7617 = sin. 49° 36'

0,74139 = sin. 47° 51'

0,71388 = sin. 45° 33'

5) Similiter pro $: 0,5058 = sin. 30° 23'

0,48861 = sin. 29° 15'

(0,48961 = sin. 29° 19')

0,47416 = sin. 28M8'.

53) p. 158. Quae Maestlinus in praemissis tabulis earumque explicatione addiderit, exhis ipsius verbis elucet: quid ego praestiterim, paucis recensere conveniet. Schemata ego,