To the extent possible under law, the Text Creation Partnership has waived all copyright and related or neighboring rights to this keyboarded and encoded edition of the work described above, according to the terms of the CC0 1.0 Public Domain Dedication (http://creativecommons.org/publicdomain/zero/1.0/). This waiver does not extend to any page images or other supplementary files associated with this work, which may be protected by copyright or other license restrictions. Please go to http://www.textcreationpartnership.org/ for more information.
Revolvatur corpus in Ellipsi: Requiritur lex vis centripetae tenden∣tis ad umbilicum Ellipseos.
Esto Ellipseos superioris umbilicus S. Agatur SP secans Ellip∣seos tum diametrum DK in E, tum ordinatim applicatam Qv in ×, & compleatur parallelogrammum Q×PR. Patet EP ae∣qualem esse semi∣axi
& GvP ad Qv ••uad. ut CP quad. ad CD quad; & (per Lem. VIII.) Qv quad. ad Qx quad. punctis Q & P coeuntibus, est ratio aequa∣litatis, & Qx quad. seu Qv quad. est ad QT quad. ut EP quad. ad PF quad, id est ut CA quad. ad PF quad. sive (per Lem. XII.) ut CD quad. ad CB quad. Et conjunctis his omnibus rationi∣bus, L×QR sit ad QT quad. ut AC ad PC+L ad Gv+CPq ad CDq+CDq. ad CBq. id est ut AC×L (seu 2 CBq.)×C∣Pq. ad PC×Gv×CBq. sive ut 2 PC ad Gv. Sed punctis Q & P coeuntibus, aequantur 2 PC & Gv. Ergo & his proportio∣nalia L×QR & QT quad. aequantur. Ducantur haec a qualia in SPq./QR & fiet L×SPq. aequale SPq.×QTq./QK Ergo (per Corol. Theor. V.) vis centripeta reciproce est ut L×SPq. id est recipro∣ce in ratione duplicata distantiae SP.Q.E.I
Eadem brevitate qua traduximus Problema quintum ad Parabo∣lam, & Hyperbolam, liceret idem hic facere: verum ob dignita∣tem Problematis & usum ejus in sequentibus, non pigebit casu∣caeteros demonstratione confirmare.