datum, adeoq; facit illud in* hoc plano perinde moveri ac fi vis S T tolleretur, Sc corpus vi fola T V revolveretur circa centrum C in fpatio libero. Data autem vi centripeta in fpatio libero circa centrum datum T V qua corpus £)_ CXLII. tum Traje&oria revolvitur, datur per Prop. P Q jl quam corpus defcribit, tum locus Qjnniq; vqeulooc ictoarsp cuosr paodr idsa itnu mlo cqou ioldiov is tempus verfabitur, tum de- Q_± Sc contra. Q, E.I.
Prop. XLVII. Theor. XV.
Pofito qtiod vii centripeta proportionale fit difiantia corporis a centrai
corpora omnia in plants quibufcunq^ revolventia peragent defcribent
; EUipfes, revoiutiones temporibus aqualibus quaq\
pusNr moventur eadmem fdtai npteirbiuods in liwis oqsu iaiefd reSlis ienm f nitro utepmeprioorribeu citroqi Ps difcurrendo,raobpfoolfvietinotn.e fingulas ; vis SFqua eundi corQ
&
eft ut ìn diftantiä plano quovis revolvens trahitur verfüg centrum aotnqail easd eo ob propoSrQti-i PQ R -p S SVSc trahitur Vcorpus vis T S Q ,pun&Sc C Q,um datu min ve eOftr rqfuuas T V
z diftantia quibu Cpiano ,buist in plano trahuntur Cigitur,s corVpioreras cieoqrupaolreas rfuasti opnuen btudmif Rfantia P vuinridbiuqsu tCa,Q nfutinatr vveerr-aqquji butrsa purmo
corpora movebuntur iifdem huntur temporibus verfus centrum in iifdem figuri?& propterea in pqiuaon-o
quovis 1 147 3 P ORtrum S, adeo qci;r ca pun&um C,atq; in ipatiis liberis circa cen(
per Corol. 2. Prop. X. ScXXXVIII. Jtemporibus femper aequalibus, vel dCeofcrroilb. e2n.t EPrlloipp-. fes in piano illo circa centrum C , troq, in lineis re£ris per centrum vel periodos movendi ultro ci- Cbunt. Qj.E. D. in piano illo duftis, comple-
Scholium. busH cius ravfifsi.n es Cfuonntc iapfece lninfuesa sa cc udervfcaesn ifnu sp icaonrop odruemfcr iibni , fduepienr fciicricea- axes quofvis datos per centrum virium tranfeuntes revolví, Screvolütione íiiperficies curvas defcribere; tum corpora ita mov eerai ucot rpeoorrau mili ac eonbtlriqa uien ahficse nfdupenerdfoic iebus perpetuo reperiantur. Si Sctroq; peragentur eorum motus in p dlaenfcies npdeern adxoe mcu rtrraanntf euulntrtoib ucis-, aciteqs; gaedneitoa ei nf ulinnte. isI fctiusr vigisit uqur ainru cmaf irbeuvso lfüutfifoicniet mcuortvuams iilnia :h ifsu plienrefiis- curvis confiderare.
Prop. XLVIII. Theor.XVI.
Si rota globo extrinfecus ad ángulos re&los infijiat, & more rot arum re- volvendo progrediatur in circulo máximo \ longitudo itineris ctírvi-
linej quodpmSturn quodvis in rota perímetro datum, ex quo glo-
bum tetigit, confecit, erit ad duplicatum finum verfum arcus di-
midii qui globum ex eo tempore inter eundem tetigit^utfumma dia-
metrorum gbbi & rota ad femidiametrum globi. Prop. XLIX. Theor. XVII.
Si rota globo cóncava ad reStos ángulos intrinfecus infiflat revolven-
do progrediatur in circulo mVáx im2 o i longitudo itineris curvilinei V J quod