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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 253, page id 1041163592:0287
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LHINOIDIA MATHEMATLCA.
SF CTIO
De Corporum Circulari Motu in Mediis resistentibus.
E F MI M A III.
Sit PORL Spiralis quae secet radios omnes SP, SO SR, ec.
in aequalibus anculis. Acatur recta PT quae tangat eandem in
puncto quovis P, secetque radium S in Y; e ad Spiralem
erectis perpendiculis PO. O concurrentibus in O, juncatur
SO. Dico quod si puncta P es O accedant ad invicem e co-
eant, angulus PSO evadet rectus, e ultima ratio rectanculi
TOX 2PS ad P Oquad. erit ratio aequalitatis.
Etenim de angulis rectis O F Q, OQ R subducaneur anguli
aequales SP Q SQR, et manebune anguli aequales OF5, O95.
trso Circulus qui cransie
per puncta O, S,F erant.
ibic etiam per punctum .
Cocant puncta F et a
e hic Circulus in loco co-
itus F Q tanset Spiralem.
adeoqueperpendiculariter
secabic rectam OF. Fic
isitur O F diameter Cir-
culi hujus, ec angulus
dS F in Cemicirculo re-
etuS. d. P. D.
AdO P demittantur perpendicula 4D, SF, ec linearum ratio-
nes ultimae crunc hujusmodi: T9) 2d P D ut ZS vel FSad PF,
Tcu 2FO ad2P5. Item F D ad F  ut P e ad 2PO. LF CX
aequo perturbate T e
2d ~ G uc P _ 2d 2F5. Vnde Fc P 94
equale TQX2P5. & F D.
EIBeA
SECURVOS.
aaCt.