De diametris apparenlibus motuque horario vero solis ac lunae, in eclipsibus lunarihus. 385 



4d quodvis igitur tempus hinc tam diameter solis apparens cum ejus parallaxi horizontali, quam 

 verus motus horarius assignari poterit. 



§ k. Diameter lunae apparens ejusque parallaxis horizontalis pendet ab ejus distantia a terra. 

 Scilicet si distantia media ponatur = c, et distantia vera =z, erit, uti supra vidimus, diameter 

 lunae apparens = — • 3i'l3 y'', *) et parallaxis lunae horizontalis =-^-56'39". Commodissime 

 jrgo primo quaeritur distantia lunae a terra z, ex qua cum sit c= 100000, levi calculo tam 

 iiameter apparens quam parallaxis lunae horizontales definitur. Interim tamen quoque formula — per 

 iivisionem evolvi poterit, sicque ex ea immediate tam diametrum apparentem, quam parallaxin hori- 

 zontalem definire licebit. Ponamus loco coefficientium numericorum litteras alphabeti, sitque 



1= l-t-/ccost'-r-acosr-i-fccos {y-v-V) — ccos {y — r)-Hb cos i] — ecos2>y — f cos(2^ — 2v) 

 —^cos[2rj-^v)-k-^cos{2r] — v)-\-\cos{2rj-^V)-^icos{2rj — V)—\cos{2r]—^-^V) — mcos(2;? — v — V). 



\ 5. Coefficientes ergo hi, quorum valores supra exhibuimus, sequenti modo per logarithmos 

 determinabuutur, ut sit 



it) = 6,^639186 



/e = 7,8W310 



if = 6,3091788 



7g = 6,5773131 



^fc= 8,7359900 

 Za = 6,1 5802 Ji.7 

 n = 6,2?t30230 

 k= 6,2803776 



«5 = 8,009261* 

 ii= 6,2771879 

 n= 6,3908075 

 n =6,2581595 

 Zm = 6,0152034 



Quibus notatis habebimus convertendo fractionem — • 



-=i — kcosv-\--^kkcos2v — 4 /«^ cos ^('-i-acosr— 16 cos (c-4-r)-i-c cos ((' — T) 



g * ■* < 



-^lkk — e^ -H/cb —a/c — a/c 



— f/c^ — ^I 



— f}m 

 — t) cos ?? -H e cos 2;/ -I- f cos (2;/ — 2v)-^q cos (2rj -t- ^) — f) cos {2yj — v) 

 ^kQ -f-/c§ — /ce — /ce 



-h/c^ — ^f 



— j cos (2;; -♦- r) — f cos (2^7 — r) -I- 1 cos (2^ — f -H r) -H m cos (2j7 — i» — r) 



— /cl — /cm -H/CJ -H/ce 



-t-6^ — c^ — a^ — a^ 



§ 6. Restitutis ergo loco harum litterarum valoribus erit 



= 1,00160 — 0,05kQk^ cos V -t- 0,00U8 cos 2f-f- 0,00012 cos V 



0,00069 8,73751 



7,17095 



6,07918 



*) Ad marginem: potius 31 H-j 

 L.Ealeri Op. posthoinaT.II. 



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