Philosophiae naturalis principia mathematica . Problema in Hyperbola, Sitfjus Centrum O, Vertex t^, Umbilicus iJ & AfymptotosO A. Cog. nofcatur PRINCIPIA MATHEMATICA. 103 nofcatur quantitas areae abfcindendae tempori proportionalis. Sit ea Li A, &fiat conjefturadepofitione reftaei?, quae nrcnmJTSzbidn-^^^ dat verae proximam. Jungatur 0T,8< J8c T&d Afympto- ton agantur y^/j^Pi^ Aiympto- to alteri parallelffi, & perTabu- lam Logarithmorum dabitur A- rea AIKT^ eique asqualis area OT A i quae fubdufta de trian- gulo O T S relinquet aream ab- {dS^vaATS. Applicando areae abfcindendse A & abfc
Philosophiae naturalis principia mathematica . Problema in Hyperbola, Sitfjus Centrum O, Vertex t^, Umbilicus iJ & AfymptotosO A. Cog. nofcatur PRINCIPIA MATHEMATICA. 103 nofcatur quantitas areae abfcindendae tempori proportionalis. Sit ea Li A, &fiat conjefturadepofitione reftaei?, quae nrcnmJTSzbidn-^^^ dat verae proximam. Jungatur 0T,8< J8c T&d Afympto- ton agantur y^/j^Pi^ Aiympto- to alteri parallelffi, & perTabu- lam Logarithmorum dabitur A- rea AIKT^ eique asqualis area OT A i quae fubdufta de trian- gulo O T S relinquet aream ab- {dS^vaATS. Applicando areae abfcindendse A & abfciffae ATS difFerentiam duplam % AT S—i, A vel X A — 1 ATS zd lineam SN, quas ab umbilico Sm tangen- tem T Z^perpendicularis eft, orietur longitudo chordae !P^. Inlcri- batur autem chorda i!Ia ?*^inter^& ?*, fi area abfcifla ATS major fit area abfcindenda A, fecus ad punfti 7* contrarias partes: & punftum ^erit locus corporis accuratior. Et computatione re- petita invenietur idem accurattor in perpetuum. BBRMU*.. Atque his calculis Problema generaliter confit Analytice. Verumulibus Aftronomicis accommodatior eft calculus particularis qui fe-quitur. Exiltentibus AO, O B , OT> femiaxibus EUipfeos, ,& Lipfius latere redo, ac D differentia inter femiaxem minorem 02>& lateris refti femiflTem i L ; quaere tum angulum Y , cujus finusfitadRadium ut eftreftangulum ^ fub differentia illa D , & femi- * fumma axium A O -^ OT) adquadratum axis majoris A B; tumangulum ^,cujus fmusfitadRa-dium ut eflduplumreftangulumfub umbilicorum diftantia*y//&difterentia illa D ad triplum quadratum femiaxis majoris AO. His angulis femel inventis;locus corporis fic deinceps determinabitur. Sume angulum Tproportionalem tempori quo arcus B T defcriptus efl, feu mo-tui medio (ut loquuntur) aequalem ; & angulum V (pri-mam medii motus aequationem) ad angulum Y (aequationemmaximam primam) ut efi: finus dupli anguli T ad Radium-: atque
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Keywords: ., bookauthornewtonisaacsir16421727, booksubj, booksubjectmechanics
