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# Title: Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo (shelfmark Leibn. Marg. 182)
# Folio 251, page id 1066518432:0279
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DE VTREBOSET MLOTFBOS GORPORDM. LIB. II. 251
in hac recta positione data tertium punctum C, ut linea ex eo ad data
puncta ducta AC, CB cum rectis AD, BF rectae CI ejusque paral-
lelae DF normalibus, ficuram rectilineam DACBF forment, qu’ae circa
auem DF in errum acta produeat solidum, cujus superficies exclusis cir-
culis a lineis AD, BF descriptis, minimam in fuido resistentiam pa-
tiatur, incedente solido juxta directionem axis FD.
Analys. Puneta data A, B a recta C l aequaliter distare ponan-
tUT, UE SInE aequales C( e BI. FX puncto I medio datx linex LMI
quadratum celeritatis exponentis, qua Auidum solido patienti alli-
ditur) tanquam centro descriptus lit semicirculus L PM, quem linca
NO alECri DE in directum posita contingat in M, criique adeo
L.MI parallela ipsIS AD eE BF. PeT L AGANEUF LO, LN parallelae
lineis AC, BC, sccantes semicirculum in P et 9, per quae puncta
FrANSCANE PR, OS ParallelA MN; reCLX MP et MO ipsS PL _OI
perpendiculares erune. Puncto C, aliuds indefinite ricinum intellis
TUF, tum etiam reCtX CA, CB duCEX SInE, et hisce paraIIClX LD, Ln
semicirculum secantes in punctis g et p, per quae Dariter cranseant
ordinatae g5 ex pr, ductisque Pr et Oo Parallelis diameter L. MI, px
et qu’erunt elementa ordinatarum PK eF OS. SIFITerUM p CXDOHCNS
rationis circumterentix circuli ad radium, bisectisque CC in a, et
BI in B, denotabunt p. Pa circumferentiam radii Fa, ec p. FB cir-
cumterentiam radii PB, adeoque annuli a lineis CC, Bi CIrCA DF
rerolrentibus geniti, erunt p. La. C G, eE p. FB. BI.
II. Jam per ea, quae in prxecedentibus (5. 435.) Tunt ostenla, resisten-
tia, quam in Auido Cubibit annulus conicus a recta AC circa DF in
orbem acta deseriptus, exponitur per p. L. ∞. CC5. L. S ex resictentia annu-
li ex BC CirCa DF per p. FB. BI. LR, adeoque resistent. annuli
AC + resistent. annuli BC = p. Fa. CC. LS + p. FB. BI. L.R. Simili-
ter relistent. annuli ex AC + resistent. annuli BC = p. F. a. C 6. L. S +
p. FB. BI. Lr. Jam, quia ex natura minimi relistentia annuli AC + rC
sistent. annuli BC = resistent. annuli AC + resistent. annuli BC,
erit etiam p. F a. CC. LS L p. FB. BI. LR = p. E a. C6. L,S + p. FB. BI.
LS, vel quia (secundum hypothesin) CC e BI aequales sunt, di
videndo per p. CC aut p. BI; erit P a. L S F FB. LR = F a. L. 5 + F B. L1
atque adcd La. 55 = FB. Rr, vel Ss: Rr = FB: P a.
III. OB parallelas LO, AC, e L0, AC; erit OO: LMI =∞: CO
vel Oo:C0 = L. M: COe Nn: C0 = LM: BI vel CO, Cr3OOO=Nn.
Acqui An: PP ut triangulum NEn ad 2. triansula PYp, quorum sci
licet balis ep, alcirudo rero pP; nam crianguli hujus PIp duplum