Newton, Isaac - Philosophia naturalis principia mathematica

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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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