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# Title: Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo (shelfmark Leibn. Marg. 182)
# Folio 44, page id 1066518432:0072
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4 DE VEREBOS EF NIOTTBDS: CORPORDM. L. IB. L.
sBE: B = BMI: BMI. POrro, quia ordinata ae vertici A proxima in
iplam curram Aa desinit, e B. gencraliter constantem potentiam
juxta ordinatarum directiones denotans, etiam eam, quae juxta dirc.
ctionem ea vel Aa agit, exPOneL, Sed potentia jixta Aa es cenaci.
tas CurrX in vertice A, ergO A = B, atque adeo sBE: B = sBF:
A = BM: bN.
S C FT O L 1 O N.
20O. Ex Corollariis theoremati nostro adjectis satis constare po.
test quam late pateat ejus ulus, rerera enim infinitorum id proble.
matum Polutionem continet, quorum Problemata Catenariae, Vela
riae, et fgurx lintei ab incumbente liquore inflexi nonnisi casus
Tunt specialissimi nostri theorematis. Scd priusquam ad applicacio.
nem ejus nonnullis specialibus. ejusmodi casibus accedam, monen-
dum est atque notandum, potentias applicatas BFL, BFI; Ctsi Sim
plicibus ex tinitxe magnituctinis lineis exprestas, nonnunquam li.
neolas tantum infinite parras, quandoque etiam rectangula infini-
celima significare; ex tenacitates fiti in singulis punctis ejusdem
Temper generis magnitudines existere quidem cum potentiis applica
tis, sed prae hisce infinitas; ut id ex ipla applicatione clarius clur
celcet.
FOF. SinE ergO AC = ~, CB = y, BM = dx, DM = dy, BD =d5,
AO = a AP = m _. PO = n = V (aa mm). FIINC PO =dn, ec
DD =dm. Ilisce Positis, triangula similia BBMI, d OAP prxbent
ds =adx: n, e dy= max: n. Idcirco substitutis his raloribus in ana-
losia BO: T = PO: AP, 5. 94. TCDCKTa, Crit BO: I = dn: M; pri
IUS Canon. EF T = A + sOHI, altera Formula gencralis.
102. Sint Potentix applicatae BHI curraque perpendiculares =
bas, ubi b est magnitudo data, critque hoc catu (5. 96.) T = A,
_ R. (5. 200.) ejusdem generis magnitudo cum potentia applicata,
atque adco dicatur = ab. TIinc ex BCE: T Aet bds: ab, vel ds: a ac-
que adco as: a = dn: m = BC: T, vel quia (5. FOF.) ds= adX: n,
crit (adx: n): a = dn: m; atque adeo dx: n = dn: m erso max =ndn
=mam, ex da = - am, ec. intcorandto X = a = m vel m = a = X, CF-
3On = V (aa =mm) = V (2a∞ = ∞∞) hinc dy (= mdx: n) = adX - aed x:
Y (2a∞ = XX), CrCO y = Y (2aN = XN) qua cA aequatio ad circu-
lum.
203. Si potentia currae perpendicularis BD vel BC aut BF I (hx
eres in hoc catu unum idemque signifiCANE) (INE = ds: ds, qui eA
d ddit