Astrotiomia mechamca. 239 ' 



d.QCOSS = ~ ^g^^^''"*0-*-gcos5)' 4gdt(Qcos(p—Psin<p)Vp 



P T'2gL 



Porro autem ob -^= qdVsms -^ Fd.qsms, erit 



' V Vpp , ^ ' ^ y 



ex qulbus duabus aequationibus concluditur 



— Yqdtsir\scoss(\ -\-qcoss)^ Agdt coss(Q costp — P sintp^Vp 



dq 



P V^gL 



qdV sin'^ s " jgLqdt sins coss ^^ ., 'i gdt sin s{P cos(p -t- Q sin<p) 



V "^ v^ {l-^qcossy , 



Vpp 



quae expressio evanescere debet casu P == et (2 = 0, >ubi simul T fieret constans, ex qua con- 

 ditione prodit 



, VF=^-^ et r=^ et d. = qdtsmsy^. 



Praeterea ob 



Vp 



dV —dp 'igdt^QcoSf — Psiaip^Vp 



V 2j) {i-t-qcoss^V^gL ' 



gj.^ ^ qpQgg_. -g^^sin5(l-f-gcos5)V2g£ Agdt {Q cosf- P sia(p)Vp 



'^ pVp V^gL 



■w ' . qdtcoss^V-^qcoss^^V^gL '^ gdt {P coscp-^- Q iin(p)Vp 



(*»Q sin s — 7 • —- T- 



■-. pVp V^gL 



V ^gqats\ns{Qcos(p-~Ps\a<p)Vp 



m Btm;; (1 -t- ? cos«) V2gL ' 



unde colligimus 



j —'igdtVp/^,^ n • \ /r» >-»•%• g(Ocos©— Psinfip^sin^^sN 



^^= y^gL (^2((2cosy — Psiny)cos^-4-(Pcosy-i-(2siny)sm^-^- ^^'^ in-gcoss )' 



, od<(l-+-5'cos»)2"/2gl 2srdfVp/_ ,^ _, . , . ,„ /-» . \ g(Q cosfl!)—Psinffl)sinscos4\ 



^^^= p/p '~y2^C^(^^^'y"~^^'"y)'^°^""(^^^'9p-*-Qs'py)cos^-- i.^gcos5 / 



ita ut hinc sit 



, df (l-i-gcosa^^^y^j/L Sjfd^Vp /^(Ocos^!) — Psin^^^sins (Pco8f-*-0sin 99)005« {Qcosf — Psin^j^sinscossN. 



pVp V2gL \ ff 9 l-»-gco8* J 



Inde autem variatio excentricitatis q definitur, aeque ac semiparametri p, quibus inventis pro ipso 

 motu erit ' wpj^itjoiqqi. 



p M. j dt{l -t-qcoss)^V^gL 



^ = i-Hgcos* ^^ ^f = Wp "'•* .1 ooiioiioa 



Cum deiode w — 8 designct longitudinem absidis imae, et baec erit variabilis, babebiturque 



:io'j 0(iiitM ."ntf)f;!T!f.;^ v.\' -.WvMO 3K! Tm)1;j' :'.\'\v , ,<i;rtiinv. 



d.i^P -s) = jy^ [{Pcoscp -fr Qsmcp) coss - 2 {Qcostp — Psm^) sms h ^^^,,,, ) 



sicque omnia, quae ad motus determinationcm attinent, sunt determinata. 



