Philosophiae naturalis principia mathematica . irca centrum S gyrando, defcriberepoteft arcum O^. G) PROPOSITIO XXXVII. PROBLEMA XXVI. Corporjs de loco dato furfum vel deorfum projeuli defimreTempora afcenfus vel defcenfus. Exeat corpus de loco dato G fecundumlineam A S G cum velocitate duplicata ratione hujus velocitatis aduniformem in Circulo velocitatem, qua cor-pus ad intervallum datum SG circa centrumS revolvi poftet , cape G ^ ad ~ A ratio iila eft numeri binarii ad unita-tem , pundum A infinite diftat, quo ca-fu parabola vertice S^ axe SC^ latere quo-vis refto def
Philosophiae naturalis principia mathematica . irca centrum S gyrando, defcriberepoteft arcum O^. G) PROPOSITIO XXXVII. PROBLEMA XXVI. Corporjs de loco dato furfum vel deorfum projeuli defimreTempora afcenfus vel defcenfus. Exeat corpus de loco dato G fecundumlineam A S G cum velocitate duplicata ratione hujus velocitatis aduniformem in Circulo velocitatem, qua cor-pus ad intervallum datum SG circa centrumS revolvi poftet , cape G ^ ad ~ A ratio iila eft numeri binarii ad unita-tem , pundum A infinite diftat, quo ca-fu parabola vertice S^ axe SC^ latere quo-vis refto defcribenda eft. Patet hoc perProp. xxxiv, Sin ratio illa minor vel ma-jor eft quam x ad i, priore cafu Circulus,pofteriore Hyperbola redlangula fuper di-ametro S A defcribi debet. Patet perProp XXXIII. Tum centro S ^ intervalloaequante dimidium lateris refti, defcribaturCirculus HKk, & ad corporis afcenden-tis vel defcendentis loca duo qusevis G, C,erigantur perpendicula C/, CT) occurren--tia Conicffi Sedioni vel Circulo in / ac D. Dein 2/C. H & PRINCIPIA MATHEMATICA. irr Dein junftis-y/, STf, fiant fegmentis SEIS, SET>S, feaores Li«b*HSK, HSk asquiL^esy & per Prop. xxxv. corpus G defcribet fpa-^R*tium GC eodemTempore quo corpus K defcribere poteil arcumKk. ^ PROPOSITIO XXXVIII. THEOREMA XII. Fojito quod Vh centrtpeta proportionaln fit althudtm feudifianttce locorum a centro, dtco quod cadenttum TempOra, Velocttates Sf Spatta defcrtpta funt arcubus, arcuumque fimhus reBis ^ ftntbus verfts refpeStvs proportlo-nalta. Cadat corpus de loco quovis A fecun-dum reftam AS\ & centro virium S^\w-tervallo AS^ delcribaturCirculiquadransAE, fitque CT^ fmus reflus arcus cujuSv\%ATi\ & corpus (_x^, Tempore /fZ),cadendo defcribet Spatium AC , inqueloco C acquiret Velocitatem CD.
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