Philosophiae naturalis principia mathematica . lagas op-pofitas progredientia. Et lineae omnes tertii Ordinisduohabent ejus-modi crura in plagas oppofitas progredientia in quas nuUa alia earumrcrura infinita (prasterquam in Parabola Cartejiana) tendunt., C A ^. I. Si crura illa fint Hyperbolici generis, fit GAS eorum AfymptotoSsr,& huic parallela agatur redta qucBvis CBcad Curvam utrinque (fi fieripotell) termi-nata, eademque bifecetur in pundloX, &locus pundi illius X erit Hyperbola Coni-ca (puta X ) cujus una Afymptotos eit ejus altera Afymptotos AB, & aqua-t!« qua relatio interOrdina
Philosophiae naturalis principia mathematica . lagas op-pofitas progredientia. Et lineae omnes tertii Ordinisduohabent ejus-modi crura in plagas oppofitas progredientia in quas nuUa alia earumrcrura infinita (prasterquam in Parabola Cartejiana) tendunt., C A ^. I. Si crura illa fint Hyperbolici generis, fit GAS eorum AfymptotoSsr,& huic parallela agatur redta qucBvis CBcad Curvam utrinque (fi fieripotell) termi-nata, eademque bifecetur in pundloX, &locus pundi illius X erit Hyperbola Coni-ca (puta X ) cujus una Afymptotos eit ejus altera Afymptotos AB, & aqua-t!« qua relatio interOrdinatam BC & Ab-fciiTam AB definitur, fi AB dicaturA*, &BCjy, femper induet hanc formam xyy + eyZlax-^bxx-^cx-¥d. Ubitermini,e,a,b,ir,«a^jdefignant quantitatesdatasfignisfuis4-&?—affedas, quarum quaelibetdeefTepoiruntmodo ex earum defedu figura in fedfonem Conicam non autem Hyperbola illa Conica cumAfymptotis fuis coincidere,id eft punftum X in reda AB locari: & tunc terminus-i-o deeft,.. TERTII ORDINIS. 7l. C A S, II. At fi redailk CBc non poteft utrinque ad Curvam terminari, fedCurvae in unico tantum pundo occurrit: agequamvis pofitione datam redam AB Afymp-toto AS occurrentem in A, ut & aliam quam-vis BC Afymptoto illi parallelam Curva^que oc-currentem in punfto C, & aequatio qua rela-tio inter Ordinatam BC & AblbifTam AB de-finitur, femper induet hanc formam, C A S, III. Quod fi crura illa oppofita Parabolici fint generis, reda CBcad Curvam utrinque, fifieripotefl, termina-ta in plagam crurum ducaiur & bifecetur inB, & locus punfti B erit Linea reda. Sit illaAB , terminata ad datum quodvis punftumA, & aequatio qua relatio inter OrdinatamBC & AbfciiTam AB definitur, femper in-duet hanc formam,
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