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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 348, page id 1041163592:0382
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348
PFITLOSODMILLE NATVRALIS
n Moro distinguatur Fluidum in Orbes innumeros concentricos ejusdem
onxonom crassicudinis. Finge autem Orbes illos esse Colidos; ee quoniam
homogeneum est Fluidum, imprectiones conciguorum Orbium in
se mutuo Factae, crune (per FIypothesin) ue eorum transtationes
ab inricem et superticies contisux in quibus imprestiones HUnE.
Si imprestio in Orbem aliquem major elt vel minor ex parre COn
cava quam ex parte convexa; praevalebit impessio Fortior, ee velo-
citatem Orbis vel accelerabie vel recardabie, prout in candem regi
onem cum ipsius motu vel in concrariam dirigitur. Proinde ut
Orbis unusquisque in motu suo persereret unitormiter, debebune
imprestiones ex parte utraque sibi invicem aequari, de fieri in re-
siones contrarias. Inde cum imprestiones sint ut contiguae su-
perticies ee harum translationes ab invicem; crunt tranlationes
inverse ut superticies, hoc est, inverse ue quadrata dictantiarum (y-
perticierum a cenero. Sunt autem differentia mocuum angularium
circa axem ue hae cranstationes applicatae ad distantias, sive ut
cranslationes directe ec dictantia inverse; hoc eAt (conjunctis ra-
tionibus) uc cubi distanciarum inverse. Ouare A ad rectae infn
nica SABCD F Q partes singulas crisantur perpendicula Aa.
Bb, C6, Dd, F. es _C. ipParum S A, SB, SC, SD, SF, _C.
cubis reciproce proportionalias crune summae differentiarum, hoc
elt, motus coci angulares, uc respondentes Cummae lincarum as
Bb, Cc, Da F C: id est (R ad constituendum Medium unitormi-
ter Auidum, numerus Orbium ausentur ec lacicudo minuatur in in-
Finitum) ut arex FIyperbolicae his Cummis analoga Aad, Bb8.
C69, Dd2. F CQ _C. Et tempora periodica motibus anou-
laribus reciproce proportionalia, erunt etiam his areis reciproce
proportionalia. Est isitur tempus periodicum Orbis cujulris
DIO reciproce ut arca D d Q, hoc cAt, (per nocas Currarum
quadracuraS) directe ut quadracum dictantix SD. Id quod vo-
lui primo demonstrare.
Ca5. 2. A centro Sphaerae ducantur intinitae rectae quam pluri-
mae, quae cum axc datos contincane angulos, aequalibus ditteren-
eiis se muruo superantes; et his rectis circa axem revoluris concipe
Orbes in annulos innumeros secari; et annulus unusquisque habe-
Bic annulos quatuor sibi contiguos, unum inceriorem, alterum ex
ceriorem ex duos laterales. Acrritu interioris e exterioris non
Dotest annulus unusquisque, nili in moru juxta legem casus primi
facto, aequaliter ex in partes contrarias urgeri. l’atet hoc ex de-
monstratione casus primi. Et propterea annulorum series quaelibee
à Cl0b0