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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 256, page id 1041163592:0290
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256
PFTTLOSOPTILAE NATDRALIS
D Moro tam in eodem loco ut 3OSad O F. Nam rires illae sune ad invi-
vicem ut iRr e F Q sve W 8X
2PG
8c
Shocect, uc: V e
et F Q, seu 2OS et OF. Dara igitur Spirali datur proportio re-
Sistentiae ad rim centripetam, e vicerersa ex data illa proxortione
datur Spiralis.
Corol. 4. Corpus itaque orrari nequie in hac Spirali, nisi ubi ris
relistenciae minor est quam dimidium vis centripece. Fiat resisten-
tia equalis dimidio ris cencripetx ex Spiralis conveniee cum linea
recta F S, inque hac recta corpus descendet ad centrum, ea cum
velocitate quae sit ad velocitacem qua probarimus in suxerioribus
in casu Parabola (TheOr. Z, L Ib. T,) delcensum in Mledio non resi-
Aente heri, in subduplicata ratione unitatis ad numerum binarium.
Ec tempora descensus hic crunt reciproce ut relocitates, atque
adeo dantur.
Corol. 5. EE quoniam in aqualibus a centro distantiis velocitas
eadem est in Spirali F OR acque in recta SF, ex longicudo Spi-
ralis ad longitudinem rectae PS est in data ratione, nempe in
ratione OF ad OS; tempus descentus in Spirali erit ad tem-
Dus descensus in recta SP in eadem illa data ratione, proinde.
que daeur.
Corol. 6. Si centro S’interrallis duobus quibuscunque datis descri-
bantur duo Circuli; e manencibus hisce Circulis, mutetur utcun-
que angulus quem Spiralis continet cum radio PS: numerus revo-
lutionum quas corpus inera Circulorum circumterentias, peroendo
in Spirali a circumterentia ad circumterentiam, complere porcst, est
uE = sire ut Tangens anguli illius quem Spiralis continet cum
radio FS; tempus vero revolurionum carundem uc  id cAt, ut
Secans anguli ejusdem, vel etiam reciproce ut Medii densicaS.
Corol. 7. Si corpus, in Medio cujus densitas eAt reciproce ut di-
stantia locorum a cenero, rerolutionem in Curra quacunque AL B
circa cenerum illud Fecerit, ex Radium primum AS in eodem an-
sulo secuerie in B quo prius in _, idque cum velocitare oua fue-
ric ad relocitatem Tuam primam in A reciproce in (ubduplica-
ea ratione distanciarum a centro (id eAt, ut AS ad mediam pro-
portionalem inter AS e B 5) corpus illud perger innume-
ras consimiles revolutiones BFC, C. (D ec. Facere, d incerse-
ctionibus
CORPORVM