Philosophiae naturalis principia mathematica . , per longitudinum rationes compli-catas, determinari poflunt j caeterafq; ( ut Spirales, Quadratrices,Trochoides) Geometrice irrationales. Nam Iongitudines quaefunt vel non funt ut numerus ad numerum ( quemadmodum indecimo Elementorum ) funt Arithmetice rationales vel irratio-nales. Aream igitur Ellipfeostemporiproportionalem ablcindoper Curvam Geometrice irrationalem ut fequitur. Prop. XXXI. Prob. XXIII. Corporis in dataTrajeStoria Elliptica nwventis invenire kcnmadtem- pm ajpgnatum. Ellipfeos APBfit Avertex principalis, Sumbilicus,0centrum,fitq
Philosophiae naturalis principia mathematica . , per longitudinum rationes compli-catas, determinari poflunt j caeterafq; ( ut Spirales, Quadratrices,Trochoides) Geometrice irrationales. Nam Iongitudines quaefunt vel non funt ut numerus ad numerum ( quemadmodum indecimo Elementorum ) funt Arithmetice rationales vel irratio-nales. Aream igitur Ellipfeostemporiproportionalem ablcindoper Curvam Geometrice irrationalem ut fequitur. Prop. XXXI. Prob. XXIII. Corporis in dataTrajeStoria Elliptica nwventis invenire kcnmadtem- pm ajpgnatum. Ellipfeos APBfit Avertex principalis, Sumbilicus,0centrum,fitq; F corporis locus inveniendus. Produc 0 A ad G ut fit OG p 2 ad [ .o8 ]ad 0 A ut 0 A ad 0 S. Erige p erpendiculum G H, centroq^ 0 &intervallo 0 G defcribe circulum £ LG, & fuper regula G H, ceufundo, progrediatur rota GEF revolvendo circa axem fuum, &interea pun&o fuo A defcribendo Trochoidem y^L/.Quo fa&o,cape GK in ratione ad rot# perimeirum GEFG^ ut eft tempusquo corpus progrediendo aby^ defcripfit arcum A?y ad tempus. revolutionis unius in Ellipfi. Erigatur perpendiculum K L oc-currens Trochoidi in L, & a£ra L P ipfi if G parallela occurretEllipfi in corporis locoquadito P. Nam centro 0,intervallo 0^defcribatur fcmicirculus AQB, Scarcui y^ £?_occurrat LP producla in £?__;, jjuBganturq; SQ^ , 0_2__Arcui E FG occurrat 0 _2jn F, & in eandtni 0 ___demirtatur per-pendiculum SR. Area APS eft ut area A QS^ id eft,ut diffe-rentia inter feclorem 0 Q_A & trian^ulum 0_x y^ QJk 0 Qjl SK, hoc eft, ob datam _0_7_, ut differentia inter arcum A ___& reclam SR., adeoq;( ob aqualitatem rationum Siiad finum arcus AQ^^ OSadOA, OAzd OG, AQjdGF, & divlfim AQ-SR ad GF-fin. arc. AQj) utGK differentia inter arcum G l & finum ar-cus A_7_,OE. D. &/w- L iop j Scholinm. Caeterum ob difficultatem defcribendi hanc curvam prseftatconftru&iones vero proximas in praxi Mechanica adhibere. El-lipfeos cujufvis fit AB axis major, 0 centrum, S um
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