Philosophiae naturalis principia mathematica . eta incentrifugam verfa, movebitur in HyperJDola conjugata. L E M M A XIII. Latus reBum Varahola ad vertkem quemvis pertinens, eflquadruplum diflantne verticis ilUus ah umhdko figura,Patet ex Conicis, L E M M A XIV. Perpendkulum quod ah umhtlko Varahola ad tangentem ejusdemittttur, medtum eji proportionale inter diftantias um^hilici a punBo contaBus &* a vertice princtpalt figura, Sit enim A T ^Parabola, S umbilicus ejus, A vertex principa-lis, T punftum ^ t> y contaftus, TO ^- - ordinatim ap-plicata ad dia- metrum prin- ^^ X/Sl cipalem, T Mtan
Philosophiae naturalis principia mathematica . eta incentrifugam verfa, movebitur in HyperJDola conjugata. L E M M A XIII. Latus reBum Varahola ad vertkem quemvis pertinens, eflquadruplum diflantne verticis ilUus ah umhdko figura,Patet ex Conicis, L E M M A XIV. Perpendkulum quod ah umhtlko Varahola ad tangentem ejusdemittttur, medtum eji proportionale inter diftantias um^hilici a punBo contaBus &* a vertice princtpalt figura, Sit enim A T ^Parabola, S umbilicus ejus, A vertex principa-lis, T punftum ^ t> y contaftus, TO ^- - ordinatim ap-plicata ad dia- metrum prin- ^^ X/Sl cipalem, T Mtangens diame--tro principali y occurrens inA/, y^ & S N y linea ^ perpendicularis ^ ^ ^ ^ . ^ ab umbilico in tangentem. Jungatur ^iV, & ob fequales M S &ST, MN8i NT, M A^ AO, parallelse erunt rea£e AN &OT, ik inde triangulum^y^iVreaangulum erit ^^ A ik fimile tri-angulis aequalibus S NM, SNT. Ergo P J eft ad J iV, ut ^ iNTadJ^. ^. CoroL x:TSq. efl ad SNq ut Piad SA. Corol. X. Et ob datam SAy eil SNq. \x\.TS. G X S% PHILOSOPHI^ NATURALIS DeMotu Corol. 3. Et concurfus tangentis cujufvis T M cum refta S NyCoRPORUM. quaeab umbilico in ipfam perpendicularis eft,incidit in reftamL^/\r,qu£e Parabolam tangit in vertice principali. PROPOSITIO XIII. PROBLEMA VIIL Moveatur corpus m perimeiro Farahola : requmtur Lefsvis centripet<£ tendentts ad umhiltcum hujus figura» Maneat conftruftio Lemmatis, fitque T corpus in perimetro Pa-rabolae, & a loco ^in quem corpus proxime movetur, age ipfi S^Pparallelam ^i? & perpendicularem ^2, nec non §lv tangenti pa-rallelam & occurrentem tum diametro TT Gmv, tum Jam ob fimilia triangula Txv^ STM 81 aqualia uniuslatera S M, ST, aequalia funt alterius latera^P^ iew ^, ex Conicis,quadratum ordinatEC ^v aequale eft redangulo fublatere refto&fegmento diametri ??:;, id eft () reftan-gulo 4 !P J X 2^ i, feu 4? .y X ^R; & punftis T & ^coeuntibus, ra-tio §lv ad ^x (per Corol. x. Lem. vii.) fit ratio sequal
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