Philosophiae naturalis principia mathematica . tSPg*^.xgTgW. inverfe. Q__E. D. Corol. Hinc fi detur figura quaevis, & in ea pun&um ad quodvis centripeta dirigitur; inveniri poteft lex vis centripetae quajcorpus infigurae illius perimetro gyrari faciet. Nimirum compu- tandum eft folidum ——?—— —_i-JL__* huic vi reciproce pro- portionale. Ejus rei dabimus exempla in problematis fequenti-bus. w: Prop. VII. Prob. II. Gyretur corpus incircumferentia circuli^ requiritur lex fis centripe-t£ tendentis adpunSium aliquod in circumferentia circuli oircumferentia S QP A> centrum vis centripet
Philosophiae naturalis principia mathematica . tSPg*^.xgTgW. inverfe. Q__E. D. Corol. Hinc fi detur figura quaevis, & in ea pun&um ad quodvis centripeta dirigitur; inveniri poteft lex vis centripetae quajcorpus infigurae illius perimetro gyrari faciet. Nimirum compu- tandum eft folidum ——?—— —_i-JL__* huic vi reciproce pro- portionale. Ejus rei dabimus exempla in problematis fequenti-bus. w: Prop. VII. Prob. II. Gyretur corpus incircumferentia circuli^ requiritur lex fis centripe-t£ tendentis adpunSium aliquod in circumferentia circuli oircumferentia S QP A> centrum vis centripetaj S,corpus in circumferentia latum P, locus proximus in quem mo- vebitur Q__ Ad diametrum SA Sc rectam S P demitte perpendi- cuh PK,£T,.8cpergjpfiSP pirallelam age L R occurrentem circulo in L & tangenti P R m R, & cocantTgJ, ?K m Z. Ob iimilitudinem triangulorum ZQR, ZTP, SP^eritivP quad. ( hoe eft Q_RL ) ad QfX quad. ut S A quad. ad SP quad. Ergo ^- X, i-—- xquatur QJf quad.~D\ictuv .hac aquar- S/f quad. Iia. [4*] Ka inspg;/ffj:3&pun&is P &£coeuntibus,fcribatur SP proKL03- S\z fiet^JV *quale QllgtZl. Ergo ( per Corol. Theor. V.) SAq VIS QK cenfripetareciproceeftut ^2L, id eft ( ob datum S^ ^W ) O /3 Cj ut quadrato-cubus diftantise S P. Quod erat invenienduni. Prop. VIII. Prob. III. Moveatur corpm in circulo P Q_A : ad hunc effeSium requiritur lexvh centripet<x tendentk adpunSium adeo longinquum, ut linetf om-nesPSj KS adid duSide, pro paraUelis haberi circuli centroC agaturfeuiidiameterC^ parallelas iftas per- pendiculariter fecans in M &: N, & jungantur CP. Ob fimilia trian^ula CPM, & TPZ, vel ( per Lem. ^eftCP^. ad P Mq. ut P Qj%. vel ( per Lcm. VII. )?Kq. ad Qjq. &exnatu- ra circuli re&angulum QKxKN •{-QN sequale eft PK quadra- to. Coeuntibus autem pun&is P, Qfit KN + QN aqualissPM. Ergo eft CP quad. ad PM quad- ut QK x i PMadQjqnad. ade- OTauad. , iPMcub. c OT quad. xSP quad. , oq; ~~-2 aequale - ? , ,&t^n^ —i aequale 4
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