De Motu Corporum in Orbibus mobilibus^ deqi motu Apfidum. Prop XLIII. Prob. XXX.
Efficiendum efi ut corpus in TrajeStoria quacunq; circa centrmi virìum
revolvente perinde moverì pojpt, atq^ corpus aliud in eadem
IInra OjerBboer ia quiefcente. V P K pofitione dato revolvatur corpus P pergendo a V verfus K. A centro C agatur femper Cp, qu* fit ipfi CP qualis, angulumq; *- VCp angulo V C P at area quam linea proportionalem conftitu- Cp defcribit erit ad aream VCP nea quam liC
ìocitasP ldinefec*r ibdiet,f curitb evne-- tis C p ne* deafcdr ivbeelnoctiista temi liC
P y eft, ut angulus hoc VCp angulum VCP,adeoq;aind data ratione, Serea tempori pro pproorptitoe-- pnaolrjsi ., prGppuomrt ioanreaal ist emfit
quam linea C p immobili deicribinit ,p lmanao- pnuifse,f cttoygne neteft juqfuto*d q ucaonr-
titatis vi centripeta, revolvi poffit una cum punfro p la linea quam punfrum idem in curva ilp
plano immobili. Fiat angulus Vra tione jam expofita defcribit in C v angulo PCp, & linea C v neli*ne*
l I 33 ] CV, atqi figura vCp figur* V C P *qualis, Se corpus in femper exiftens movebitur in perimetro figur*. revolventis p v Cpeodemq; tempore deferibet arcum ejus , vp quo corpus aliud arcum ipfi fimilem P Sc *qualem V P in figura quiefcente V P Kfcribere poteft. Qu*ratur igitur, per Corollarium Propofitio dneis- * VquIa, mv ips ucnefrnutmrip eta qua corpus revolvi poifit in curva illa linea p defcribit in plano immobili, Sema. <ÌE.F. folvetur ProbleProp.
XLIV. Theor. XIV.
Differentia virium, quibus corpus in Orbe quiefcente, corpus
aliud in eodem Orbe revolvent e ¿equaliter mover i poffuntj efi in
tPraiprltiicbautsa roartbioins eq cuoimefmeeunntiiss aVltPitu, dinis inverfe. P K funto fìmiles Seorbis revolventis partes *quales vp, pl{. A punita refrain pCmitte perpendiculum ^r,idemq; produc ad de- m,ut fit m r ad firangulus V ut Cp ad angulum VCP.dines Quoniam corporum altitu-, PC SepC, KC Se fiC femper *quantur, manifeftum eft quod fi corporum in locis y ' P Se ptus fingali exiftentium diftinguantur mo- ( centrum, fiv ep eferc Lunegduumm Clitoieraosl . PaC.), ipnC b; inaolst,e r(i quponrourmib uhsi vtrearfnufst vmeortfui fse cvuenrfduusm ce lninteruasm i pefrius nPtC *,pqCu apleersp,&en mdioctuulsa rteras ndfevteerrfmusì ncoarnptuorrijs) p erit ad motum tranfvèrfum corporis P, ut motus angularis lineas pC ad motum angularem line* PC, id eft ut angulus VCpangulum ad VCP.utroq; pervenir ad Ipgiutnufrr uemod iefm, tceomrppuosr e quo corpus Pmotu fuo ptu aquaìitei movebitur a P verfus C, ade o*qqiu caolim ipnl ecteon triluiom .tmemopore
rèperietur alicubi in linea mkjr, qu* per punctum fiìnneam li- p C pefpendicularis eft j Setantiam a linea pC, qu* fit ad dif tmànotitaum t raqnufavmer fcoo rapcuqsu iarletet rduimfi acquirit a linea P C, ut eft hu;us motus tranfvcrfi* sfd motum
tran ft