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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 255, page id 1041163592:0289
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PRINOIDTA MATHEMATICA.
duplicata ratione ipsius S Q reciprOCC. Sunt autem arcus illi F Q LIDEK
ec QR ut relocitates descriperices ad invicem, id est in subdupli- SEcvnDD.
Cata rationC SG ad S P, Sve uE SG ad V SP ZSB; e ob aequa-
les angulos SF
Se
r et aequales areas PS _ QSr, eAt ar-
cus P Q ad arcum Qr ut S) ad SP. Sumantur proportionalium
consequentium diferentix, _ HCF arcUS P Q ad arcum Rr uE SL
ad SF = VSPXSC
seu
EYe
 nam punctis P ec Q) cocunti-
bus, ratio ultima SP = V SF XS  ad =V  SC aequalitatis.
Ouoniam decrementum arcus F9, ex relictentia oriundum, live
hujus duplum Ar, eA ut relistentia ec quadratum temporis con-
junctim; crit resistentia ut p
ut S Q ad :V Q. et inde
Ut
05
Q9Z5Z. Frat autem P Q ad RP,
+ _4X S. F EC VE Z
IVG
sre
OFX5F9. Namque punctis P de Qcocuntibus, SF de S
coincidunt, et angulus FV  Et rectus; ec ob similia criangula
PV 9, FSO, AC F Q ad EV a ut OF ad EOS. FR igitUE
OP X SPqut relstentia, id cst,. in ratione densitaris Medii in Z
ex ratione duplicata relocitatis conjunctim. Ruferatur duplicata
ratio relocitaris, nempe racio, et manebie Medii densicas in
D ut.
D.
O∞X 5. F. Decur Spiraliss e ob datam rationem OS ad
OF, densitas Medii in P erit ue . In Medio isitur cujus
densitas eAt reciproce ur distantia 2 CenErO SP, corpus syrari PO-
rest in hac Spirali. Q. F. D.
Corol. 1. Velocitas in loco quovis P ea semper est quacum cor-
Dus in Medio non relstente srrari porest in Circulo, ad candem a
centro distantiam SP.
∞3. Et
distancia illa non daturs ut D. F X S.F. Et inde Spiralis ad quam.
dibet Medii densicarem aptari potest.
Corol. 3. Vis relistentia in loco quovis P, est ad vim ceneripe.
Far
235