Newton, Isaac - Philosophia naturalis principia mathematica

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DE MOTU
CORPORUM

Corol.1. Hinc ſi agatur BCſecans PQin r,& in PTcapiatur
Ptin ratione ad Prquam habet PTad PR:erit Bttangens
Conicæ ſectionis ad punctum B.Nam concipe punctum Dcoire
cum puncto Bita ut, chorda BDevaneſcente, BTtangens eva
dat; & CDac BTcoincident cum CB& Bt.

Corol.2. Et vice verſa ſi

46[Figure 46]
Btfit tangens, & ad quod
vis Conicæ ſectionis punc
tum Dconveniant BD,
CD; erit PRad PTut
ut Prad Pt.Et contra,
ſi ſit PRad PTut Prad
Pt:convenient BD, CD
ad Conicæ Sectionis punc
um aliquod D.

Corol.3. Conica ſectio
non ſecat Conicam ſectio
nem in punctis pluribus quam quatuor. Nam, ſi fieri poteſt, tranſ
eant duæ Conicæ ſectiones per quinque puncta A, B, C, P, O; eaſ
que ſecet recta BDin punctis D, d,& ipſam PQſecet recta Cd
in r. Ergo PReſt ad PTut Pr ad PT; unde PR& Pr ſibi
invicem æquantur, contra Hypotheſin.

LEMMA XXI.

Si rectæ duæ mobiles & infinitæBM, CM per data punctaB, C, ceu
polos ductæ, concurſu ſuoM deſcribant tertiam poſitione da
tam rectamMN; & aliæ duæ infinitæ rectæBD, CD cum
prioribus duabus ad puncta illa dataB, C datos angulos
MBD, MCD efficientes ducantur; dico quod hæ duæBD,
CD concurſu ſuoD deſcribent ſectionem Conicam per puncta
B, C tranſeuntem. Et vice verſa, ſi rectæBD, CD concurſu
ſuoD deſcribant Sectionem Conicam per data punctaB, C, A
tranſeuntem, & ſit angulusDBM ſemper æqualis angulo dato
ABC, anguluſqueDCM ſemper æqualis angulo datoACB:
punctumM continget rectam poſitione datam.

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