Philosophiae naturalis principia mathematica . ^-^X^^1: erit vis TEqq qua corpufculum a tota Sphaera attrahitur ut arca ABNA. Corol. 4. Et univerfaliter fi vis centripeta ad fingulas Sphasrae particulas tendens ponatur efie reciproce ut quanticas V , fiat au- D E ay-JP Stem T)Nut -y4. y ; erit vis qua corpufculum a Sphaera t©- ta attrahitur ut area ^iSiV^. Aa \ PROPO- Db Motu m, PHILOSOPHIiE NATURALIS PROPOSITIO LXXXI. PROBLEM A XLL Stantihusjam pofitts, menfuranda eji Area A B N A. Apunfto T ducatur redla T H SphsEram tangens in H, & acfeaxem !P^^ demilTa normali HI, bifecetur ?* / in L ; & e
Philosophiae naturalis principia mathematica . ^-^X^^1: erit vis TEqq qua corpufculum a tota Sphaera attrahitur ut arca ABNA. Corol. 4. Et univerfaliter fi vis centripeta ad fingulas Sphasrae particulas tendens ponatur efie reciproce ut quanticas V , fiat au- D E ay-JP Stem T)Nut -y4. y ; erit vis qua corpufculum a Sphaera t©- ta attrahitur ut area ^iSiV^. Aa \ PROPO- Db Motu m, PHILOSOPHIiE NATURALIS PROPOSITIO LXXXI. PROBLEM A XLL Stantihusjam pofitts, menfuranda eji Area A B N A. Apunfto T ducatur redla T H SphsEram tangens in H, & acfeaxem !P^^ demilTa normali HI, bifecetur ?* / in L ; & erit(per Prop. ix. Lib- x. Elem.) T E q aequale T S q -^- S E q-^-1. P ST). Efl autem S Eq feu SHq (ob fimilitudinem triangu-lorum^P//, SHI) a?qua]e reaangulo ?>^/. Ergo TEq aequa-le ell contento fub 5° 5 & P ^ ^ J/-i- i STi, hoc eft, fub T S &^xST), id eft, fub yj& z Z!). Porro T> E quad. sequaleefl»y^^/_^*D^, feu SEq — LSq-^ zSLTi — LT)q, id eih,X SLT>—LT>q—ALB. Nam Z/^^ — J£^ feu L^f ~ SJf. (per Prop. ^. Lib-. t. ElemO aequatur redangula ALB. Scriba-^tur itaque t SLT>—LT> q — A L Br^ro T>Eq; &l quantitas BJbqy^F^^ qu3B fecundum Corollarium quartum PrOpofitionis prsecedentis eft ut longitudo ordinatim applicatse T> N, refolvet.\., . , tS S LTq^TS ALBxTS-fefe m tres partes —^-g^,^^.^ t/^ixV TEkST: ubi fi pro V fcribatur ratio inverfa vis centripetae, & pro T E me-dium proportionale inter TS & x LT>; tres illae partes evadent or-dinatim applicatse linearum totidem curvarum , quarum areaeper-Meihpdos vu! ^E^F.*: PRINCIPIA MATHEMATICA. 187 Exmpl. 1. Si vis centripeta ad fingulas Sphaerae particulasten-Liejrdens fit reciproce ut diftantia; pro V fcribe diftantiam TE\ dein P^» «*- -L TSy^LT) pro TEq, & fiet T>N. ut SL~ LT>-^-Alt^- 2 L D Pone ©iV aequalem duplo e]us z »yZ/—Z,© L^D & ordi- natae pars data 1. S L duda in longitudriiem A B defcribet areafnredtangulam t , & pars indefinita LT&
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