Philosophiae naturalis principia mathematica . F, feuGifxAOg. ad^ASxODxCF, & ex aequo Ap ad G/*ut 2 AK ad GK + AOq. ad aASxOPxCF,ideft, utAKxAO^.ad^SxODxCF, hoc eft, obaequalia AKxAO & ODq. ut AOxOD ad ^SxCF. Proin-de^x T^SeftadG/xiGC ut^OxODxAS ad ASxC-FxGC, feu AOxODad CG^. id eft, fector nafcens ASf adfectorem nafcentem G Cfut AOxOD propterea utarea Ellipfeos totius ad aream circuli totius. Q^E. D. Argu-mento prolixiore probari poteft analogia ultima in Se&oribus e-vanefcentibus B S F, OCF: ideoq; locus puncri P prope y^pildesfatis accura- te inventus , h f eft. In qua- dratur
Philosophiae naturalis principia mathematica . F, feuGifxAOg. ad^ASxODxCF, & ex aequo Ap ad G/*ut 2 AK ad GK + AOq. ad aASxOPxCF,ideft, utAKxAO^.ad^SxODxCF, hoc eft, obaequalia AKxAO & ODq. ut AOxOD ad ^SxCF. Proin-de^x T^SeftadG/xiGC ut^OxODxAS ad ASxC-FxGC, feu AOxODad CG^. id eft, fector nafcens ASf adfectorem nafcentem G Cfut AOxOD propterea utarea Ellipfeos totius ad aream circuli totius. Q^E. D. Argu-mento prolixiore probari poteft analogia ultima in Se&oribus e-vanefcentibus B S F, OCF: ideoq; locus puncri P prope y^pildesfatis accura- te inventus , h f eft. In qua- draturis er- ror quafi quingentefi- mx partis ar- eas Ellipfeos totius vel pa«Io major obvenire fo- x ]et: qui tamcn propemodum evanefcet per ulteriorem Conftrue- tionem fequentem. Per pun&a G, 0, duc arcnm circularem GTO juftae magrntu- dinis-, dein prbduc E F hinc inde ad T & N ut fit E N ad FT ut l LadCF; centroqj N & intervallo ^N defcribe circulum qui fecet Ellipfin in P, nt fupra. Arcus autem G TO determinabitur quae-. [II.] quxrenda ejus pun&um aliquod T; quod conftructionem in illocafu accuratam redder. Si Ellipfeos latus tranfverfum multo majus fit quamlatus rec-tum, & motus corporis prope verticem Ellipfeos defideretur,(qui cafus in Theoria Comctarum incidit, ) cducere licctepundlo G recram GI axi AB perpendicularem, & in ea rationead GK quamhabetarea AV P S ad reftangulum AKxAS^ de-in centro I &. intervallo A I circulum defcribere. Hic enim fe-cabit Ellipfim in corporis Ioco quaefito P quamproxime. Eteademconftru&ione (mutatis mutandis) conficitur Problema inHyperbola. Hx autem conftru&iones demonftrantur ut fupra,& fi Figura ( vertice ulteriore B in inflnitum abennte ) verta-tur in Parabolam, migrant in accuratam illam conftrudionemProblematis. XXII. Si quando locus ille P accuratius determinandus fit, invenia-tur tum angulusquidam f>, qui fitadangulum graduum 57,29578quem arcus radio gequalis fubtendit, ut eft umbilicorum diftan-tia SH ad Ellipfeos diametrum AB\
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