Philosophiae naturalis principia mathematica . duo. Sit H eoruminterfe&io communis, & um-bilicis S, H, axe illo datodefcribatur Traje&oria. Di-co faclum. Nam Tra)e&o-ria defcripta ( eo quod P H-f-SPinEllipfi, &PH-STin Hyperbola aequatur axi)tranfibitper punclum P, & ( per Lemma fuperius) tanget redlam TR. Et eodem argu-mento vel tranfibit eadem per pun&a duo P,£, vel tanget re&asduasTil, tr. F. Prop. XIX. Prob. XI. Circa datum nmbilicum TrajeSioriamTarabolicam defcribere^qnnetran-fibit per punSia data^ & reSias pofitione datas S umbilicus, P pun&um ScTR tangens traje&orke de
Philosophiae naturalis principia mathematica . duo. Sit H eoruminterfe&io communis, & um-bilicis S, H, axe illo datodefcribatur Traje&oria. Di-co faclum. Nam Tra)e&o-ria defcripta ( eo quod P H-f-SPinEllipfi, &PH-STin Hyperbola aequatur axi)tranfibitper punclum P, & ( per Lemma fuperius) tanget redlam TR. Et eodem argu-mento vel tranfibit eadem per pun&a duo P,£, vel tanget re&asduasTil, tr. F. Prop. XIX. Prob. XI. Circa datum nmbilicum TrajeSioriamTarabolicam defcribere^qnnetran-fibit per punSia data^ & reSias pofitione datas S umbilicus, P pun&um ScTR tangens traje&orke defcri- bendse. Centro P, intervallo P S defcribe circulum FG. Ab umbilico ad tangentem demitte perpendicularem S T, & produc e- am ad. V, ut flt T V sequalis S T. Eodem modo defcribendus eft altercirculus/£,fida- tur alterum pundtum p\ vel inveniendum aiterum punftum , fi datur altera tangens trj dein ducenda recla JF quae tangat du- os circulos FG, fg fi dantur duo pun&a P, h vel. p; vel tranfeat per duo pun&a V,v, fi dantur duse tangentes TRtr, vel tangat circulum FG & tranfeat per punclum ~y,fi da-tur punchim P & tangens TK. Ad FI demitte perpendicula-rera SI, eamq; bifeca in K; & axeS if, vertice principali /f de-fcribatur Parabola. Dico fa&um. Nam Parabola ob sequalcsSK 8cIK, SP& FP tranlibit per pun&um P; & (per Lemma-tis XIV. Corol. 3. ) ob aequalcs STfkTV & angulum re&uraS TR, tanget re&amTK.£KE. F. Prob. XII. Circa datum umbilicum TrajeBoriam auamvk fpecie datam defcribe-re, qu re&as tanget pofitione da-tas. Cas. 1. Dato umbilico S, defcribenda fit Trajecloria ABCper pun&a duo B, C. Quoniam Tra;e£toria datur fpecie, da-bitur ratio axis tranfverfi addiitantiam umbilicorum. In ea ratione cape KB ad BS, &LC U^TT^, adCS. Centrisf>, C, interval- \ip ?/& / lis BK, CL, defcribe circulos / duos, & ad reclam KL, quae q ~A~~t ~h—a. tangat
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