•^-' Asironomia mechamca. 281 



Cum jam sit dp = — 2 nuv^ dcp sin /u f— -\ erit 



iiuiiijao uJiJjiit/; 



g (d?) — d$) sin s nuv^df siajuicoss-i-^q-t-qq coss) / l 1\ n^dfcost 



\Mj3 ttSy 



nuvdfsiuficoss/l i\ nu di> cosAcoss / i 



l nolfoiti»et :d^i 



/1 1 "\ MM dt' COS /i cos « / 1 1 \ 



Q 

 q(dq> — ds) nuv^ df sin s aia fi ^^ \^^ ^\ nv^^dfcoss nuvvdfcosscosX/i 



seu 



p pp 



fct. \ / 1 ^N nf^d» cos* njtwdffl cos*cos/i / 1 1\ 



(2 -I- g cos 5) ( -r 5 )h S ^^ ( -^ — - V 



cstque w=y(w-i-Ha — 2accosA), unde patet ^ denotare angulum MLN. Cum ergo sit 

 do = dcp — dip cos (Oj erit 



, , nMc^dffl sinacoso sin(v — ^) / 1 1\ 



do=:d(p ^-^ 'l — -) et 



, , nt^^dffl cos* nMf3dffii sin« sinif /_. \/l 1\ nwwda) coss cos>l / 1 1\ 



ds = dcp \ 1 ^(2-f-gcos5)(— -)-\ — (-^ -); 



•^ qw^ pq \ a / \^,3 j^ay q \^3 „3/ ' 



, , gw'dm sins n, 



tam vero ob rfp = — ■ — — lit 

 ' p 



■t/-\ qv^dtpsins -, / , of coS/i sin*\ / 1 1\ 



unde per integrationem valor ipsius Q colligi debet. Denique pro ratione temporis habemus 



I 



)• iniant 2)id dO Ji82oq 



Quodsi jam motus corporis N sit regularis ponaturque « = r— > erit 



1 /r^ /-r j«T\ MMd^ ^ , eMudtT^sinr 



dt^^2g{h-\-N) = -y^ et du = —^ ; 



'tnm 



fL-k-M 1 p, J_ vvd<pVh ,, ,^ wtwdyV 



L-t-N m , m Mwd^ "/p mm Vp 



quare pos.to V = , fit - = -— -^, hmc d^ = — -^- et 



, mevvdcpsiarVb mevvdcp sinr . , jq^ 



"*" = tV~~= y>^ '' dr = d,?. 



193. Coroll* 1. Cum termini littera n affecti sint minimi, primo his terminis penitus ncglectis 

 habebimus p = f, q = k, ds = d^y p = ^_^[^^,, ? da = d<p et dyj = Q, ^(»^^^,5 , juibus^ y4orj^W5 

 corpori N motus regularis inducitur. ,r,Jldio m\\ ui nu;J 



194-. Coroll. 2. Deinde hi ipsi valores in terminis littera n affcclis adhibcaniiir, ei quibiis 

 per integrationem primo quantitates P et Q, tum vero anguli s, o, ip ct co invesligcntur, quibus 

 inventis erit accuratius p = f—2nP et </ = T/(y-+-^— 2/i (?/))» hincque ^ = ,^^^08/ 



L. Euleri Op. postbiuna T. II. 36 



