Notae Editoris. 
443 
Log. sin. 41° 27' = 9,8208358 
„ „ 59' 30" = 8,23822 14 
„ „ 39' 23" = 8,0590572 (parall. lat. Lunae a Sole) ; 39' 23" -f- 17' 6" 
„ „ 48" 33' = 9,8747911 (ait. nonag.) = 56' 29" (vera lat.) 
„ „ 59' 30" = 8,2382214 
„ „ 44' 35" — 8,1130125 (parall. long.) 
„ „ 37° 31' = 9,7846117 (384° 48' — 347° 17') 
„ „ 27' 9" = 7,8976242 (parall. long. Lunae a Sole) 
26' 40" 
53' 49" vera long. Lunae a Sole 
prius 25' 26" 
1° 19' 15" motus Lunae horis 2. 28'. 
107) p. 372. Huc referantur ea, quae de observatione hac, quam Keplerus per 
errorem Huennae factam dicit, annot. N. 102 dicta sunt. Ad explicandam calculi rationem 
haec addimus: Assumto eclipsis initio hora 10. 3' a. m. deficiunt ad meridiem h. 1. 57', 
quibus progreditur Sol a meridiano per 29° 15'. Jam dantur in A MNV : MV = MA -j- AV 
= 16° 5' + 55" 54' 45" = 71° 59' 45" (72°). Et cum M in 16° 5' —, N in 18° 24' X, 
MN = 348" 24' — 316° 5' = 32" 19' (K. 20'). 
cos. 72" 
Quare cos. NV 
NY = 68° 33' 
cos. 32° 20' ’ 
sin. 68° 33' X sin. 59' 30" = sin. 55' 22" (parall. lat.) 
cos. 68“ 33' X sin. 59' 30" = sin. 21' 45" (parali, long.) 
Kepleri tabula item prodit parall. lat. = 55' 22", neque vero, qualem K. aftert 56' 22". 
Pro fine eclipsis: MV = 1° 47' -j- 55" 54' 45" = 57" 41' 45" (K. 57" 43') 
MN = 387° 43' — 355° 32' = 32° 11' 
cos. NY = C ° S ' 57 ir;^ i NV =' 50" 50' 40" 
COS. 0¿ v 11 
sive, assumto latere MV = 57° 43', NV = 50° 52' 20", Keplerus : 50" 44'. 
Sin. 50" 44' X sin. 59' 30" = sin. lat. parall. Lunae a © 46' 4"; cos. 50“ 44' X sin. 59' 30 
= sin. 37' 39" parall. long. SN = 387° 43' — 346" 50' = 40" 53' 
, 25 
40. 28; 
sin. 40° 28' X sin. 37' 39" = sin. 24' 26" (long. par. J) a ©). 
Pluribus de hoc Kepleri problemate agit celeber Jerome Lalande in Connaissances 
de tems, Par. 1796, p. 238, his verbis concludens: toutes les fois qu’on en calcule, 
on rend un h a m mage a la mémoire de Kepler, dont on suit encore la 
m 6 * \°08) p. 373. In A CFD est CF* = CD* + DF* ; in A FAE : FA* = FE* -j- AE*. 
Si posueris CB = a, AF = CF — b, DE = c, BD = x et FE = y, eritj 
+ (c — y) 3 , b* = x* + y*, unde y = Vb* — x* 
a* -f- 2ax -j - x * "H — 2° Vb* — x* -{- b*—x* 
ergo b ; 
b* = (a -|- x) s 
= (a + x)* + (c - Vb * — x *) * 
0 = a* 2ax 4" c! 
inde 
2c Vb* — 
-0 
4 b* 
a* 4“ c* 
Cum sint a = 17' 16", b = 31' 40", c = 57' 54", prodit x = 0' 28", idem quod 
Ceplerus invenit calculo trigonometrico. Verba Kepleri „ubi cubus et numerus aequatur 
uadratis et positionibus,“ aequationem significant cubicam, hac forma : x* 4~ a = bx* 4~ cx, 
ecundum denominationes Cardani (Ars magna). 
Calculum trigonometricum Keplerus hac ratione absolvit : In A CBA ad B rectángulo 
antur CB = 17' 16" et BA = 57' 54" ergo tg. CAB = - ^ -g~ ; A CAB =■ 16° 36' 20" 
K 30 "), 45 = sec. CAB ; AC = sec. CAB X AB = - = 60,42' = 1° 25"; 
AB 
cos. CAB 
.G 
AC 
30 ' 127 ,".