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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
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PRINCIPLA MATHEMATICA.
secundum) composicx, similes habebune determinationes, perin- LIVen
de 2c si centra inter parriculas similiter sITa reSPICCTENE; _E CrUINESECORDOS.
vires illae eorae ad invicem ut vires singulae componentes, hoc elt,
ut correspondentium particularum diametri inverse, et quadrata
velocitarum directe: ee propterea cfficient ut correspondentes par-
ticulae figuras similes describere persane. HIaec ita se habebunt per
Corol. 1, _ 8 ProP. IV, Lib. 1. si modo centra illa quiclcant.
Sin moreantur, quoniam ob transtationum similicudinem, similes
manene eorum licus inter Syctematum particulas; similes indu-
centur mucationes in fguris quas particulae describunt. Similes isi-
tur erunt correlpondentium ec similium particularum morus ul
que ad occurtus uos primos, et propterea limiles occursus, ec M-
miles redlexiones, ec subinde (per jam otten(a) similes motus in-
ter se donec iterum in se mutuo inciderine, et sic deinceps in in-
Anitum. 2. F. D.
Corol. 2. Elinc A corpora duo quaeris, quae similia sInE e 2d
Srctematum particulas correspondences similiter sca, inter ipsas
cemporibus proportionalibus similiter moveri incipiane, sintque
eorum magnitudines ac densicates ad invicem ut magnitudines ac
densitates correspondentium parricularum: haec pergent cempori-
bus proporcionalibus limiliter moreri. F.C enim eadem ratio par-
cium majorum opllematis ucriulque acque particularum.
Corol. 2. FF A similes et similiter poliex Systematum parees Om-
nes quieseant inter sc: e carum duxe, quae exeteris majores sInE, et
Ebi mucuo in atroque Systemate correspondeant, secundum lineas.
similicer Ccas simili cum mocu uccunque moveri incipiane: hae (1-
miles in reliquis Systematum partibus excitabunt motus, ec pergent
incer iplas temporibus proporcionalibus similiter moveri; aeque
adeo spatia diametris suis proportionalia delcribere.
PROPOSITIO XXXIII. THEOREMA XXVII.
Iisdem positis, dico quod Systematum partes majores resistituntur
in ratione composita ex duplicata ratione velocitatum suarum es
duplicata ratione diametrorum es ratione densitatis partium
Systematum.
Nam rehltentia orirur partim ex viribus centripetis vel centri-
Fugis quibus parriculae Systematum se mutuo agItANE, Partim eX
Occursibus ec rehexionibus parricularum et Partium majorum.
Prioris
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