380 L. EULEIU OPERA POSTHUMA. Astronom 



Pro hoc tempore ex tabulis meis colli^itur 



longitudo nodi media . . 9'8H5'38" 



hinc erit x = — 10 3 II. 



S 8. Jam est porro r= iri^''^^' 30" cos r=-i- cos lO^^^r^O" 



v= 4 12 54 33 cosp=:: — cos47 5 27 



2c= 8 25 49 6 cos2p=: — cos 85 kd 6 



v—F= 4 23 16 3 cos(p-r) = --cos36 43 57 



Unde invenitur: diameter solis apparens =31' 41" 



parallaxis solis horizontalis = 12 



motus horarius solis = 2 23 =/w= 143'" jm 



diameter lunae apparens = 32 55 ™ 



parallaxis lunae horizontalis = 59 38 



motus lunae horarius =36 35 =n=2195 



Ex his fiet: semidiameter umbrae « = 44 — |- 



semidiam. lunae apparens ^= 16 27 -4-4- 



ergo a -f- /? = 60 27 = /* 

 duratio porro eclipsis est h= 1,4389 horas 



atque ob a=^h {n-*-k) fiet a= 1585" = 26' 25" , 



et b = ^h{m-i-k) h= 109= 149 



§9. Gum jam sit « — »1 = 2052 et »i-h7i-h2/c = 2354 atque 2£C = — 20%'22" et 

 ^ Q = 2^Z%'\^" i reperietur particula illa c = — 2'53". Deinde, quia habemus 



a-H6 = 28'14", a — 6 = 24' 36", a — 6h- c = 21^43" et a — 6-c = 27'29" 

 reperietur - tang {2x — c) = 39776 ^.^g^^^,) > unde colligitur 



— (2a; — c) = 20« 10' 14" = — 2aj -f- c = — 2aj — 2'53" 

 ideoque 2£c = — ^O^^l^' 7" et aj = — 10° 6'34". Erat autem per tabulas 



a; = — 10 3 11 

 diflP. 3 23 



