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# Title: Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo (shelfmark Leibn. Marg. 182)
# Folio 200, page id 1066518432:0228
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200 DE VERIBUS ET MOTIDUS CORPORUM. LIB. II.
= (ATO. TOTE = AO. OE): M = F = (AO. OR = ATO, TOFF
T =M. ErGO (OA. AC =OTA. IALC): R = L = (AO. OF = ANV
TOTF): F = m. Jam, quia ipla AC e OE nullius lunt determina-
tae magnitudinis, fat AC: FO =n = L: F = m, eritque rec- lum OA.
AC ad rec- lum AO. OF, in hac eadem ratione ac consequenter etiam
rec- lUM OTA. TATC ad rec. lum ALO. FOFF in eadem erit ratione
n = F ad T =m ICU AC ad OF. AC vero in ByperbOla C TC2C eAt
rec - lum OA. AC: OTA. TALC =OFAn = 2:OA. = 2, erGO CX XquO
EE Der COIPOSITIONeM FATIONUM CxIE OA. AC: AIO. TOTF = AC.
OTA = 2: OF. OAn = = item in hyperbola LsFZB, eA ATO. TOFF:
AO. OE = AOm = 2. AFOm = + (hOC CA PrOPter ParabOlaM A2DFD)
ODm = +: m. FOFDm = : : m Cr5O denUO CX X quO habetUE O A. AC:
AO. OE = AC. OTA. = r. ODm - 1: m: OF. OAn = 1. TOFDm = 1:m P. X
hac vero deducitur OFA = r, ODm - 2: m =O An - 1. 1O FDm - 2: m e
rejectis quancicatibus datis, seu constantibus, quXe proportiones non
alterant, Ccilicet ODm = 1: m, _CO An = F, exIEO TA = L UE FOFDm = 2: m
rel diridendo exponentes per m =T: m, resultabit sequens TOID
Ut OFAmn = m: m = 5. TTINC
20. Si cubus ris comprimentis proportionetur quadrato- quadra-
todensitatis, e graritas sit reciproce ut quadratum distantix a cen-
trO grarium, CrunE m = 2, eEn = 2, ad coque mn =M: m - L = - 3.
erSOTOFD erit hoc caluI, ut OT A =3, hoc est, densitaseritreciprO-
ce ut cubus distantix.
2. Si cubus vis comprimentis sit ut quadrato- cubus densitatis,
ee graritas reciproce ut quadratum dictantix, Aent m = , dC n = 2,
ersOmn =m: m = L = = 3, id CA, densItaS TOFD erit in rCCIPFOCA
Telquiplicata ratione distantiae OTA.
30. Si ris comprimens sit ut quadratum densitatis, ec gravitas in
reciproca duplicata ratione distantiae, Hent m = ; eE n = 2, ergo
mn =m: m = + = - 2, quod indicat densitatem hoc calu ese in re-
ciproca ratione distantix.
Ex hisce ersoliquet veritas assertionum nonnullarum sine ulla de
monstratione prolatarum ab TIIBIEr. Newiono in Scholio post PFOV. 22.
LIb. TI. Pr. Phil. Nat. Math. FC, quanquam hoc corollarium taneum
calus sit particularis propositionis nostra generalissimae, idem tamen
intinities intinitos casus direrlos in se continet.