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relationes ad locvm simplicem in spatio spectantes.

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Ad calculi confirmationem adiungi poterit

cos cos a cos(£— e) cos S sin rt

cos b

cos l cos Q sin L

Pro determinatione ipsius E inseruient perinde vt in art. praec. aequationessin s cos a sin s cos l

cos

E=-

cos b

cos b cos t^sin E = cos£

cos Ssin b sin S

Variationes differentiales ipsarum /, b hisce formulis exhibebuntur:

d l =

sin j E cos S

da +

cos E

d<$

cos b 1 cos 6

d& = —cosJEcosJda + sinEdtJ

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Exempli caussa ex ascensione recta 355* 45 7 45" 5o — a, declinatione— 8°47'26" =S, obliquitate eclipticae 25°27'5g"26 =£ longitudinem et latitudinemcomputabimus. Est igitur 45 0 + f : a=222 0 5i'52"65, 45° — —3j° 39'42"87,

45° — i (e — S) =28° 52' 17" 87; hinc porro

log cos(45°+-ia).9,865o82o n log sin (45° + ia) ....9,8326803 n

log sin (45° — \ («+<£)).g,7860418 log sin (45° — i (e — <J)).9,6838112

log cos (4 5° — 2 (<s + J)).9,8985222 log cos (45°— i (s — S}) .9,9423572

logsin(45°— ~ £ b) sin§(E—/).g,65ii258 n

log sin(45° — i 6) cos l (E— l) .9,7760375 n

vnde i(E —/) = 216 ° 56' 5" oq-, log sin (45° — jrb) =9,8723171

log cos (45°—| b) sin § (E + /).9,5164916 n

logcos(45° — kb) cos i(E+l) .9,7636042 n

rnde i(E+1) — 203° 5o'Ag" 9-1: log cos(45 °—i b) =9,8239669Fit itaque E— 426 26 55 33, l =—7°2 5 , i 5”’45, siue quod eodem redit E—66 e 26'55' : 55 )/=552° 54'44 5 5; angulus 45° — %b e logarithmo sinus habetur 48°io'58"i2, e log-arithmo cosinus 48° io'58" 17, e tangente, cuius logarithmus illorum differentia est,i8°io'58"i4; hinc b = — 6°2i'56"2S.

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