Astronomia mechamca. 261 



2 1 1 * j . j .-» r / \ 1.7. dfsina cosc sin' u cos' w 

 v^dq)^ato sin «mcos w =; 12^L (a« — cc) dt * — — , sou 



j j GgZ^aa — cc) dt^ sina cosa Binucoscj ., 



d^ dw = 5 ideoque 



j 3 (ao — cc) do) sino coso sinu cos^ (>> . , dusino S (aa — «c)da) sin^tf cos^w 



cUa = 1— — — ct dit/ = : — = — ^^ ~- . 



2EEv ^ cosasmw 'iEEv 



Initio Igitur ob aa — cc minimum, clementa ip ct co ut constantia spectantur, et ciim sit d(f = 

 dd -I- dtp cos 0) , liifferentialia dqy et d(J pro aequalibus habentur. Ponatur jara EE= Fcos^^co et 

 i- (^cc — aa) (\ — 3 sin^ o sin^ w) = G , ut habeamus 



Edv , ^/,y. 1 F G. 



— =z dcp cos cjyiD-i H -^ ) . 



wv ■' ^ V vv V' ' 



Pooatur nunc c = , — » Gatque D-4- ^ ~^^ — Ff— ') -4-G(i^y = 0, ut sit 



j^ ^ 1 F(l-4-gg) ^ G(lH-3gg) ^Q ^^ j . ^^ , g(3-*-?y) ^^^ 



P PP P^ P PP ' 



ubi com G sit valde parvum, sit F = - hhm, ut prodeal valor prope verus ^0 = /", erltque 



EE = -^ ^cos^ oj -i- u cos^ w = Constanti. 

 Sit i valor medius inclinationis et EE= ^fcos^e, erit 



/^(COS*£ — COS^w) , . /■ (C08*£ — C0S*Cj) G (S -*- hk) ^ ,. 



u=-^—5 — 5 * atque 1 — -^^ 2 ' -t ^— — ^= 0, et hmc 



2cos^ w ^ p cos-' W /f ' 



1 1 (cos^c — cos«o) G(3-»-*ft) 



p" f fCOS^U f3 



Tum vero prior aequatio erit 



n 1 Ai-^J?) (l-^M)( cos'f-cos«o) G (1 -»- 3/*) _ ^ 

 p 'ipp Sfcos-^o p 



Sit constans D = -^, eritque 



gg kk {j -t- tk) (coa^ e ^ cos^ o) 2G(l-*-3M) .. 



PP J ^cos''^ "^ f* ' ' 4 



. r(co9*f-cos*o) G (3 -♦-**) ^ ,, (l-W)(cos2«-co8»o) «26(1 -A^) 

 p = / -»- ^-^ 5 :^ et qq = kk 2 ' 1^ ' 



" ' COS^W f ^^ COi*W ff 



unde formula irrationalis abit in 



qnint ^/ f f{co8*t — cos*<j) G(3 -4-*cot«) \ 



~^y\-^~^ 2 co»2 u f ) 



. t r" costVf .^ 



at ob E^-y^ iit 



