Newton, Isaac - Philosophia naturalis principia mathematica

DE MOTU
CORPORUM

SECTIO IV.

LIBER
SECUNDUS.

De Corporum Circulari Motu in Mediis reſiſtentibus.

LEMMA III.

SitPQRr Spiralis quæ ſecet radios omnesSP, SQ, SR, &c.
in æqualibus angulis. Agatur rectaPT quæ tangat eandem in
puncto quovisP, ſecetque radiumSQ inT; & ad Spiralem
erectis perpendiculisPO, QO concurrentibus inO, jungatur
SO. Dico quod ſi punctaP &Q accedant ad invicem & co
eant, angulusPSO evadet rectus, & ultima ratio rectanguli
TQX2PS adPQquad. erit ratio æqualitatis.

Etenim de angulis rectis OPQ, OQRſubducantur anguli
æquales SPQ, SQR,& manebunt anguli æquales OPS, OQS.
Ergo Circulus qui tranſit

165[Figure 165]
per puncta O, S, Ptranſ
ibit etiam per punctum que
Coeant puncta P& Q,
& hic Circulus in loco co
itus PQtanget Spiralem,
adeoque perpendiculariter
ſecabit rectam OP.Fiet
igitur OPdiameter Cir
culi hujus, & angulus
OSPin ſemicirculo re
ctus. que E. D.

Ad OPdemittantur perpendicula QD, SE,& linearum ratio
nes ultimæ erunt hujuſmodi: TQad PDut TSvel PSad PE,
ſeu 2POad 2PS.Item PDad PQut PQad 2PO.Et ex
æquo perturbate TQad PQut PQad 2PS.Unde fit PQq
æquale TQX2PS. que E. D.

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