ad C g | ] ' Fq., valet -ff.fi p. : eftq; hæc vis ( i. per hujus Corol. ) differentia virium quibus corpus P in Ellipfi immota V P K & corpus , p in Ellipfi mobili vp k.banc Prop. revolvuntur. Unde cum ('per ) differentia illa in alia quavis altitudine Aipfam in altitudine fit ad fe- C V ut—1 . ad . 1 eadem differentia A cub.CV cub. in omne altitudine A valebit-^. ^ —5^-ÌL. Igitur ad vira ^
qua corpus revolvi poteft in EllipAfi ciumb.m obili b A(\. VP K,ceffus ^ addatur ex- 8c componetur vis tota q_ KGq. KFq.
qua corpuAs. cuinb . Ellipfi mobili A q. Ac ub. vpl^poflìt. iifdem temporibus revolvi Corol.bilis g. Ad eundem modum còlligetur quod, fi orbis immo- V P K fimilis, aeq uEallilsip &fis cfoint cceennttrriucam p hoanbaetnusr iEnl lvipirfiius mm ocbeilnist ro C; eiq; vpk_,q; 2 fit- K Ellipfeos hujus latus redum,& 2 Tangulus latus tranfverfum, atq; VCp Temper fit ad angulum VCP ut G ad Fy,bus corpora in Ellipfi immobili & mobili temporibu sv isreqsu,qaulii-bus
revolvi poffunt, eruntut &— LlA 4. KGg. — . 1 ; RF q . TAAb. T cub. . refpectivc. ••....;; : ■A cub. ~ Corol.mine tur T4,. &E rta udinuisv ecrufarlvitaetru, rfai cqourapmor Oisr baiitsi tudo maxima C F noV
P K habet in Veft radius circuii azqualiter curvi, nominetur K vis centripe, tiad qua corpus in Trajedoria quacunq; immobili VP K teft, in loco F dicatur-Îj^ revolvi poV.
atq; aliis in locis P indefinite dicatur
Xr, a,l ti•t udi•n e M C f nominata A, & capiatur Gratione anguli ad Fin data VCp ad angulum V C P :corpus, idem eofdem motus in eadem Tr aejqridt ovriias centripeta qua <1'p fi circruiltae-r
riter mota temporibus iifde£m *p3e7ra g3ere poteft, ut fumma virium VRGq.-VRFq.
bili,Acub.
*vqiuriibuums Corol. aug cino e5ri.rrpaotrioan vDela neo mtoin dvaist iugii av,tupro i ri&bu tmefott isn dceen uc jcuosr itnrvipeentiirsi mpoortius si gnyorvein na nOgrublaerqisu tourrb.es occirucnaq immobiles ce inmtrmumo
in Igitur fi ad redam pofirione dataria eriga tur per- Corol. agatur caqualis 6.CVpendìeulum P longitudinis indeterminata, jungaturq; P C, ipfi VCPgyrar ii np odtaetfat V irna conftituens angulum qui fit ad angulum &Cp,Ctiounrvea ;, vililsa q ua ^corpus quam VCp,ut pproce cu Vppundum corpus F, per pbeursp vira aetltuitou dtainnigsi tC, erit reci- uinr rgee dntae , uniformiter inerti*,progredì nulla p.poteft aNliaa mvi C, cubo vis in centrum proportionalis,Cpproce V alti P.tuAddindiast uCr &P (vel ìnonftrata) detorquebitur per motus jam r edcei-- Eft autem haec Curva ille eadem redilineus cum in Curva Iineam illa curvam Vpk..imn oCdoi rvoirli.b 3u.s Partotpra. dXaL oIb ilniqvuene taai,Vpk.e ienn dquerae i.bi diximus corpora hVu Pju s-
Prop. XLV. Prob. XXXI.
iOnr bEPiurllomipb qlfeiu mim fiau onfbto ilClvii,ir tcuuurti tAisn rm itPahrxmoimpeoeti ffciiteni oiftnaimicsi ei frnuedpqone riuriomt rtiousr rb Cimso,o rtqouusl.e mA2p .fc iovderuplm u3.s. rceuvjuosiv Aenpsi,ì ddees fereriqbuiti riunn ptularn, o& i mqumaorbenilid, oa Accpefdidaets aodr bfoisr mquaemm o crobris
pquusir ielnlutd f oirnm palman, o fii mvimreos bcielin dtreifpeeritbai tq. uibOursb dees facuritbeumn teuarn, dienmte ra cfe- T eoi