Philosophiae naturalis principia mathematica . pnn&oquovk VjfecetqueradinmSQ^inTj &• ad Spiralem ereSik perperi-jdiculk PO, QQ concurrentibus in O, quod fipun&a P & Q_accedant ad invicem & coeant, angnlus PSO evadetreSiHsy & ultima ratio reSianguli T Q_x P S ad P CL quad. erit ra-tio dcqualitatk. Etcnim de angulis re&is 0P£_., 00 R fubducantiM ariguli«quales SP ^, SQJL, & manebunt anguli a?quales OPS^ circulus qui tranfit perpun&a 0, Sy P tranfibit eti- /am perpun&um Q^ Coeantpun&a P8tQ_, & hic cir-culus in loco coitus PQtzn-get Spiralem, adeoque per-pendicuJa riter fec
Philosophiae naturalis principia mathematica . pnn&oquovk VjfecetqueradinmSQ^inTj &• ad Spiralem ereSik perperi-jdiculk PO, QQ concurrentibus in O, quod fipun&a P & Q_accedant ad invicem & coeant, angnlus PSO evadetreSiHsy & ultima ratio reSianguli T Q_x P S ad P CL quad. erit ra-tio dcqualitatk. Etcnim de angulis re&is 0P£_., 00 R fubducantiM ariguli«quales SP ^, SQJL, & manebunt anguli a?quales OPS^ circulus qui tranfit perpun&a 0, Sy P tranfibit eti- /am perpun&um Q^ Coeantpun&a P8tQ_, & hic cir-culus in loco coitus PQtzn-get Spiralem, adeoque per-pendicuJa riter fecabit reSam ?:V4;Cr0 P. Fiet igitur 0 P diame- XO ter circuli hujus, & angulus0 S P in femicirculo re&^E. T>. Ad 0 P demittantur perpendicula Q_D,SE, & linearum ra-tioncs ultimae erunt hujufmodi: T _9_ad P D ut 7 S vel P S adP £, feu P 0 ad P S. Item P D ad P ___ut F £_ad F 0. Etex«quo perturbate T g ad F £_ut P 0 ad f S, Unde fit F 6> ^iialis F£__xF5,. Q^ N n i Prop. XV. [ 3*4 ]; Prop. XV. Theor. XI. Si Meiii denftas w locis fingulk ft reciproce ut dijiantia locoruma centro immobili, fitque zris centripeta in duplicata ratione dcnfita-tk: dico quod corptts gyrari potejh in Spirali, qu<£ radios omnes acentro illo duBos interfecat in angulo dato. Ponantur quse in fuperiore Lemrnate, 8_ producatur SO^adV, ut fit S V .equalis SP. Temporibus aequalibus defcribat cor?pus arcus quam minimos PQJk. QR, fintque areae P SQ^ QSr_equales. Et quoniam vis centi ipeta, qua corpUs urgetur in Peft reciproce ut S P q. &( per Lem. X. Lib. I. ) line- /ola TQ, quae vi illa gene-ratur3 eft in ratione compp-fita ex ratione hujus*vis&_ratione duplicata temporisquo arcus P (2_ defcribitur,(Nam refiftentiam in hoccafu, ut infinite minoremquam vis centripeta negligo)erit T QjxSPq. ideft (perLemma noviii-mum ) PQq. x SP7 in ratione duplicata tem-poris, adeoque tempus eft ut PQxySP, & corporis velocitas P O qua arcus P Q\\\o tempore defcribitur ut _
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