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# Title: Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo (shelfmark Leibn. Marg. 182)
# Folio 234, page id 1066518432:0262
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234 DE V ZRTBUS EF MLOTIBUS CORPORUM. LIB. H
PROEOSTTIOZLL PROBLEMA.
B. 102. 420. Resistentiis aquae fuentis existentibus proportionalibus agnae ve-
locitatibus in sineulis sectionis punctis, invenire ipsas velocitates.
Sit Aumen BFTK, atque EG sectio ejus, AB Suxerticies manens
horizoncalis, seu initium canalis aut Ruminis. PrOdUCatUE ECG in 9
usque ad occursum ejus cum plano AB icidem producto; et deni-
que ex quibuslibet punctis F, F, C sectionis FC ad AO demis-
(a SInE perpendiculares FL, FMI, e GN, _C. atque ordinata P FI,
FI, GEE SEC. aliCUjUS CUIEra KTFT ipSI GF perpendiculares expO.
nanE relOCIEateS aquX per punCta R, F, G AuentIS. SInE jam LF,
a OF, b; ordinata P HI, quae aquae per punctum P Auentis quanti.
tatem designat =c; relistentia Fundi ex contactu = m, resistentia (pon-
dae =n; CF, x ec FL, y atque haec ordinata pariter quantitatem
aquae per punctum F Auentis indicat ejusque celeritas eA y: C, ac
MOtuS =Y: C. EC, quia (Secundum hypochelin) relistentia in F, hOC
est m, ad resistentiam in F se habeE UE F FI ad FI, erie resictentia
in F, quatenus haec participat relistentiam in Fundo, = my: C, et rC-
Sistentia in eodem loco proveniens a relictentia (pOndx =nV: C. De-
tractis nunc resistentiis à quantitate prestionis aqua puncto cuilibet
E incumbentis, quae GuanEIFAS pEF MF, (CU aN: b eXPONIEUE, _E re-
liquum (ax: b) = (MY = ny): C, exponet rim extrudentem aquam
per punctum phrlicum F, ec cum haec ris extrudens constanter
proportionalis sic motui aquae genito, crit (ax: b) - (my = ny):
6 =77: C, id CA acx = bmy =bBy = byy, quae est sequatio ad parabo-
lam, cujus axis principalis ab F distat, propius accedens ad B, in-
terrallo :m L in _ vertex in hoc axc a Fundo DFI distat interval.
10b +  Facta Scilicet p =m + n; ac denique parabolae hujus para-
meter exit . Quod erat inreniendum.
Fortasse alix possune excositari resistentix hypotheles, quae prae-
Tente reriores sine, hanc enim a nobis assumptam non pro certissi-
ma vendiro, sed duntaxat uno exemplo Facili ostendere placuit, quo
Dacto relocitates aquarum Auentium assignari debeant, non neglectis
relistentiis, quae a Frictionibus proveniunt.