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# Title: Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo (shelfmark Leibn. Marg. 182)
# Folio 202, page id 1066518432:0230
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202 DE VLRIBUS FF MOTIBUS CORPORUM. L1B. II.
C OR OL L A R X U M IV.
363. SinUNCn SIE F, adeoque Curra C FC2C hyperbola conica cen.
erum habens in O, quadrilinea aequalia ALC, IAZC, Sc. habebunE
abscisaS OA, OTA, OZA, ec. Continue proportionales, et vice
verla, si hae abscissae fuerint in progressione geometrica, quadrili-
nea praedicta erunt aequalia, ac consequenter densitates AB, TALB,
2A2B, ec. erunt continue proportionales, plane ut habet PrOp. 21.
Lib. II. Princ. PB. Nat. Math. Cel. Nertoni, quam Peortim démon.
Aravit.
C OR OLL A R L U M V.
364. Si n IE 2, atque adeo curra C C 2C hyperbola quadrati
ca; id est, si graritates corporum sint in reciproca duplicata ratio.
ne distantiarum a CentrO, _ OA ==, OTA = =, O2A = , _EC. in prO.
crellione arithmetica, atque adeo Ccrici hujus reciproca OA, OTA,
O2A, in progressione harmonica, (5. 361. 362.) ordinatae AB, TAIB,
2A2B, eC. erunt in progrestione Geometrica. Hloc iplum demon.
Atratum dedic alia ratione C el. Newtonus Prop. 22. L ib. II.
COR OL L A R Y U M VI.
365. Si n = - 2, hoc cA, si graritas est ut distantia corporis à
CCNErO O, curra C +C2C mutabitur in lineam rectam transcuntem
Per centrum O, Ceriesque, quae juxta 5. 362. debet esse in arittime
cica progressione OA1 =n, OLAI =n, O2AI =n, eC. nunc AC OA,
OTAE, O2A2, ec. adeoque, si quadrata distantiarum OA, OTA,
O2A, exc. Fuerint in progrestione arithmetica, trapezia rectilinca,
ATC, EA2C, _C. erunt aequalia, atque adeo (5. 36r.) Ordinatae
scalae densitatum AB, TAFB, 2A2B, CrunE ContinuE PrOPOrtIONA
les. Ur alseruit, sed absque ulla demonstratione, laudatissimus
Nertonus in Scholio Post ProP. XXII. Lib. II. Princ. Phil. Nat.
Math.
C O R OL L A R Y u M VII.
366. Oin Vecon iueeo la cu, l slanitas Coperum nnos
Ceu constans fuerir, qualis communiter considerari Colet, tunc scala
SIa