Newton, Isaac
,
Philosophia naturalis principia mathematica
,
1713
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<
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>Dico præterea quod ſi recta aliqua tangat lineam curvam in fi
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gura prima; hæc recta eodem modo cum curva in figuram novam
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tranſlata tanget lineam illam curvam in figura nova: & contra. </
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<
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>Nam
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ſi Curvæ puncta quævis duo accedunt ad invicem & coeunt in fi
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gura prima, puncta eadem tranſlata accedent ad invicem & coibunt
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in figura nova, atque adeo rectæ, quibus hæc puncta junguntur, ſi
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mul evadent curvarum tangentes in figura utraque. </
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<
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>Componi poſ
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ſent harum aſſertionum Demonſtrationes more magis Geometrico. </
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Sed brevitati conſulo. </
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LIBER
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PRIMUS.</
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>Igitur ſi figura rectilinea in aliam tranſmutanda eſt, ſufficit rec
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tarum a quibus conflatur interſectiones transferre, & per eaſdem
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in figura nova lineas rectas ducere. </
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<
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>Sin curvilineam tranſmutare
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oportet, transferenda ſunt puncta, tangentes & aliæ rectæ quarum
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ope curva linea definitur. </
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>Inſervit autem hoc Lemma ſolutioni
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difficiliorum Problematum, tranſmutando figuras propoſitas in ſim
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pliciores. </
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<
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>Nam rectæ quævis convergentes tranſmutantur in pa
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rallelas, adhibendo pro radio ordinato primo, lineam quam
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vis rectam quæ per concurſum convergentium tranſit: id adeo quia
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concurſus ille hoc pacto abit in infinitum, lineæ autem parallelæ
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ſunt quæ ad punctum infinite diſtans tendunt. </
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<
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>Poſtquam autem
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Problema ſolvitur in figura nova, ſi per inverſas operationes tranſ
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mutetur hæc figura in figuram primam, habebitur ſolutio quæſita. </
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<
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>Utile eſt etiam hoc Lemma in ſolutione Solidorum Problema
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tum. </
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>Nam quoties duæ ſectiones Conicæ obvenerint, quarum in
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terſectione Problema ſolvi poteſt, tranſmutare licet earum alter
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utram, ſi Hyperbola ſit vel Parabola, in Ellipſin: deinde Ellipſis
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facile mutatur in Circulum. </
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>Recta item & ſectio Conica, in con
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ſtructione Planorum Problematum, vertuntur in Rectam & Cir
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culum. </
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PROPOSITIO XXV. PROBLEMA XVII.
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Trajectoriam deſcribere qua per data duo puncta tranſibit & rectas
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tres continget poſitione datas.
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<
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>Per concurſum tangentium quarumvis duarum cum ſe invicem, &
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concurſum tangentis tertiæ cum recta illa, quæ per puncta duo data
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tranſit, age rectam infinitam; eaque adhibita pro radio ordinato pri
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mo, tranſmutetur figura, per Lemma ſuperius, in figuram novam. </
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<
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