Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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1
Idem aliter.
LIBER
PRIMUS.
E punctis datis junge tria quævis A, B, C; &, circum duo eorum
B, Cceu polos, rotando angulos magnitudine datos ABC,
ACB,applicentur cru­
49[Figure 49]
ra BA, CAprimo ad
punctum D,deinde
ad punctum P,& no­
tentur puncta M, Nin
quibus altera crura
BL, CLcaſu utroque
ſe decuſſant. Agatur
recta infinita MN,&
rotentur anguli illi mo­
biles circum polos ſuos
B, C,ea lege ut cru­
rum BL, CLvel
BM, CMinterſectio
quæ jam ſit mincidat
ſemper in rectam illam
infinitam MN& cru­
rum BA, CA,vel BD, CDinterſectio, quæ jam ſit d,Trajecto­
riam quæſitam PAD dBdelineabit. Nam punctum d,per Lem.
XXI, continget ſectionem Conicam per puncta B, Ctranſeuntem; &
ubi punctum maccedit ad puncta L, M, N,punctum d(per con­
ſtructionem) accedet ad puncta A, D, P.Deſcribetur itaque ſec­
tio Conica tranſiens per puncta quinque A, B, C, P, D. q.E.F.
Corol.1. Hinc recta expedite duci poteſt quæ Trajectoriam quæ­
ſitam, in puncto quovis dato B,continget. Accedat punctum dad
punctum B,& recta Bdevadet tangens quæſita.
Corol.2. Unde etiam Trajectoriarum Centra, Diametri & Latera
recta inveniri poſſunt, ut in Corollario ſecundo Lemmatis XIX.
Scholium.
Conſtructio prior evadet paulo ſimplicior jungendo BP,& in ea,
ſi opus eſt, producta capiendo Bpad BPut eſt PRad PT; &
per pagendo rectam infinitam pd ipſi SPTparallelam, inque ea
capiendo ſemper pd æqualem Pr; & agendo rectas Bd, Crcon­
currentes in d.Nam cum ſint Prad Pt, PRad PT, pBad PB,
pd ad Ptin eadem ratione; erunt pd & Prſemper æqua-

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