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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 81, page id 1041163592:0115
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RINCTPTA MATHIEMAEIC
Dico praeterea quod si recta aliqua tansat lineam curram in R- L 1DER
sura prima; haec recta eodem modo cum curra in fguram novam a
cranslata canset lineam illam curvam in Aigura nora: et contra. NNam
si Currae puncta quaeris duo accedunt ad invicem et cocunt in A.
sura prima, puncta eadem translata accedene ad inricem ec coibune
in fixura nora, atque adeo rectae, quibus haec puncta junguntur, si-
mul cradene currarum tansentes in Agura urraque. Componi pot-
sene harum astertionum Demonstrationes more magis Geometrico.
Sed breritati consulo
situr s figura rectilinca in aliam transmutanda est, sufticit rec.
tarum a quibus consatur interfectiones transferre, ex per caldem
in tioura nova lineas rectas ducere. Sin curvilincam cransmutare
oportet, transterenda sunt puncta, tangentes ex alix rectae quarum
oDe curva linea dehnitur. Inserrie aucem hoc Lemma Colucioni
difficiliorum Problematum, tran (inutando RguTAS PTODONCaS in lim-
Pliciores. Nam rectae quaeris convergentes transmutantur in pa-
rallelas, adhibendo pro radio ordinaco primo, lineam quam-
vis rectam quae per concursum convergentium transit: id adco quia
concurtus ille hoc pacto abic in infinitum, linca autem parallelae
Tunc quae ad punctum infinite distans tendunt. Postquam autem
Problema solritur in ligura nora, si per invertas opcrationes trans-
mucetur haec Egura in figuram primam, habebitur solutio quaelita.
Orile eA etiam hoc Lemma in solutione Solidorum Problema-
cum. Nam quoties dux sectiones Conicae obrenerine, quarum in-
terfectione Problema solri potest, transmutare licet carum alter-
utram, E AIyperbola sic vel Parabola, in Ellipsin: deinde Allipsis
tacile mutatur in Circulum. Recta irem ex sectio Conica, in COn-
structione Planorum Problematum, vertuncur in Rectam et Cir-
CCUm.
PROBLEMA XVII
PRO
S+L
XXV.
Trajcuotum describere quae per data duo puncta transibit es rectas
tres continget positione datas.
Per concursum eangentium quarumris duarum cum se inricem, de
concursum tangentis tertix cum recta illa, quae per puncta duo data
cransie, asc rectam infinitam; eaque achibita pro radio ordinaco pri-
moscransmuretur tisura per Lemma superius, in tisuramnoram. In
HaC
11I
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