File:Philosophiae naturalis principia mathematica (1723) (14782204302).jpg

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Identifier: philosophiaenatu00newt (find matches)
Title: Philosophiae naturalis principia mathematica
Year: 1723 (1720s)
Authors: Newton, Isaac, Sir, 1642-1727 Cotes, Roger, 1682-1716, ed Adams, John, 1735-1826, former owner. BRL Adams, Thomas Boylston, 1772-1832, former owner. BRL John Adams Library (Boston Public Library) BRL
Subjects: Mechanics Celestial mechanics
Publisher: Amstaelodami : Sumptibus societatis
Contributing Library: John Adams Library at the Boston Public Library
Digitizing Sponsor: Internet Archive

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, TI, id eft (ob pa-rallelas IH, T R &: angulos aequales ITR, HTZ) ipfarum TS,?* f/, quarum differentia axem totum xy^Cadaequat. AA S T de-mittatur perpendicularis ^2. Et Hyperbote latere reclo princi- pali (feu ^—j^^difto L, erit Z. X^i? ad Z X?i; ut ^i? ad ^-r/, id eft , ut TE feu ^Cad ? C; Et L X P ^; ad G 1; ? ut /L ad G Gv\ ^o PHILOSOPHI^ NATURALIS BtMorvGv;-&: GvTad ^v quad. ut T C q. ad CTi t); & (per Corol. z. CoRPo&uM. Lem. VII.) ^v qtiad. ad ^x quad. punftis ^& T coeuntibus fitratio aequalitatis; & ^x quad. feu ^y quad. eil ad ^q. yit ETq.zdTFq, id eilut CJ^q, 2.6.T Fq, five (per Lem. xii.) ut CD^,zd C B q: & conjunftis his omnibus rationibus Z, X ^i? fit ad§Tq. ntJ CXLXT CqXCUq feu z C BqXTCqXCTfq adf C XGvy.CDqXC B quad. five ut x !P Cad Gi;. Sed punc-tis T & ^coeuntibus aequantur %T C dzG v. Ergo & his propor-tionalia L X ^R & ^J^ ^- aequantur. Ducantur haec £Equalia in ^;. & fiet L X J? f. ^quale ^^^^f^. Ergo (per Corol. i.
Text Appearing After Image:
& 5 Prop. VI.) vis centripeta reciproce eft ut L X «5* P^, id eft reci-proce in ratione duplicata diftantiae ST. ^E.I. Idem PRINGIPIA MATHEMATICA.Idem aliter. Si I BEB. Inveniatur vis quae tendit ab Hyperbolae centro C, Prodibit haecdiftantiae C^^proportionalis. Inde vero (per Corol. 3. Prop, vii.) vis ad umbilicum S tendens erit ut —ctb—j hoc efl, ob datam ST 1 TE, reciproce wx. STcj. ^E. I. Eodem modo demonftratur quod corpus , hac vi centripeta 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

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