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# Title: [Philosophiae Naturalis Principia Mathematica] Philosophiæ Naturalis Principia Mathematica (shelfmark Leibn. Marg. 166)
# Folio 257, page id 1041163592:0291
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DRINCIPTA MATETEMAEEI
continue provortionales.
Rerolutionum rerO FEMDOTA CrUNE UE SECVRvOSI
ctionibus distinouer Radium AS in partes AS, BS, CS, DS, _C. LIBEM
perimetri Orbitarum AF. B, BFC, C G D, _cc. directe, de reloci
caces in principiis , B, C, inverse; id CA, ut S2, BS2, CS2. AL
que cempus eorum, quo corpus perreniet ad centrum, erit ad tem-
Dus rerolutionis primae, uc lumma omnium continue proportiona-
lium ASE, BSE, CS2 persencium in infinitum, ad terminum pri-
mum A52; id eAt, ne terminus ille primus A5+ 2d differenciam du-
orum primorum AS2 =BSE, sive uc Z AS ad AB quam proxime.
IInde tempus illud torum expedite invenitur.
Corol. 8. Ex his eriam praeter propter colligere licet motus cor-
Porum in Mediis, quorum densitas aue unitormis est, aut aliam
quamcunque legem astignatam observat. Cenero si intervallis con-
tinue provortionalibus SA, SB, SC, ecc. describe Circulos quot-
cunques ex Ratue tempus rerolutionum inter perimetros duorum
quorumris exhis Circulis, in Medio de quo csimus, esle ad tempus
rerolutionum inter eordem in Medio propolico, ue Medii proxo-
liti densitas medioeris inter hos Circulos ad Mediis de quo egimus,
densicarem medioerem inter eoldem quam proxime: Sed ec in ca-
dem quoque ratione ese Sccancem anguli quo Spiralis pexetinita,
in Medio de quo csimus, sccat radium A5, ad Sccancem ansuli
quo
IIIIABPIAIIIMIIIMMIIIII MIHIIMMIII