Astronomia mechamca. 255 



Qiiare cum in terminis his minimis sit (Zc = -^^^w, evidens est totam aequationem praecedentem 

 dividi posse per sin s; reperitur enim • 



1 1 «^•P/rr D(3h-Acos«) E(G-t-kk-+-4kcoss-i-kkcos'^s) FilO-t-^kk-t-kilO-i-kk^coss-t-^kkcos^^s-t-k^cos^s)^ 

 dy-* = j-^(G-.- ;; -H j _H-____ _ ^ 



^_^«»H^^1^^)^ .^_»_2ffi_3«_4|_5|_ s 



2ffk -^ \ vv v^ v^ v^ v^ J 



vvsms/jaf f fjat ^^\ (l+**)/^n ^^ ^^ „» \ (1-^-3**)/ jr ^F . v (\-^m-\-k*) ,j„ ^ .\ 



atque haec est methodus generalis hujusmodi problemata tractandi, quoties formula Tvdcp-^Vdv est 

 integrabilis. Deinde etiam pro formula fTv^d(py quam posuimus ^iS", sive sit integrabilis sive 

 minus, poni poterit -^y pro numero dimensionum, quas v in ea obtinet, unde solutio saepe commo- 

 dior reddi potest, ad quod haec solutio pariter extenditur. 



Tertia solutio probleinatis propositi. 



168. Instituantur omnia ut in solutione secunda § 159, sed ponatur 

 jaj^ = ^ erit , v^dcp- = 2gLdf {f-^ ^) , 

 ac porro per integrationem 



dy-i///. SnQ\ , V/**"* ^ ^ 2m-i-3ncos293-f-r)M(?\ 



vv \' V / ^ \ f V vv Iv^ ) 



Hinc posito v = - — - — , ut fiat 



'^ \ -i- q C0S5 



df -,///. 3n9\ ^ qdfsxns -t// n (3-t- jcos*) (2m-»-3ncos 295-t- 6n!p)\ 



-y\t V~)~~~r~ V 2^ \cA^ W) ^' ' 



seu quia Q est valde parvum, 



l/V j 6n0 (2m-*- 3n cos^f) (^-t-^cos*)^ 



dv qd(p sias 

 vv p 



statui debet 



•)«ui>I «^uni.i 



1 1 (3-i-fcA)(2m-H3nco8 29)-*-6n(?) qq kk (1 -f- 3M) (2m -i - 3 n cos 2y -i- 6nQ) 



unde fit • , . . 



(1 _ ;t4) (2m -f- 3n cos 2^3 -h 6n0 



„ — /• (3-^ft*)(2m-«-3nco82y-t-6nQ) na — kk -* 



P — T -^ ei ryr/ — KK-i ^^ 



Cum nunc sit vdQ — Qdv = vd(ps\n2(pf ideoque 



ly^ » ' r\ Qdv , . ^ AOi^d^sin* 



d(> = d(p sm 2r/? H = d^ sm 2^: h — * 



„„• . . . . ... ^ , kvvdrpiiat 



quia in termiois mmimis est dv = ^ — » ent 



