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# Title: Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo (shelfmark Leibn. Marg. 182)
# Folio 260, page id 1066518432:0288
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260 DF VFRTBVS FY NIOTTBOS CORPORDM. LID. II.
atque haec est analogia, quam Celeb. Tac. Bernoullius. in ACtis L ipC.
1696. Pa5. 336. Sine ulla analysi de demonstratione exhibuit, ec in
quam haud dubie ria multo breriore incidit. Nam licet hunc ca-
cum particularem non parum brerius, quam hoc loco a nobis factum
siE, Colri porse non ignoro, non absre tamen Fore arbitratus Tum, si
methodum nostram generalem talia tractandi eriam in aliquo casu
Fusius illustrarem, de cujus reritate aliunde constare possit.
456. Praelens exemplum particulare sic brerius etiam expedic.
TuT: Per angulos rectanguli B et 2B aGantur BC, 2B2C aequidi-
Santes ipsi AT, e per punctum A. eidem perpendicularis C2C, ac
denique ex punctis C, 2C demittantur ad latera rectansuli per-
vendiculares CD2C2D, ac astumta unitate pro designanda celeri-
tate, qua rectangulum in Auido incodit, rel quod idem cAt, pro velo-
citate, qua Auidum lateribus rectanguli AB, A2B allabituE, et
(5. 429.) A2D exponet impressionem Ruidi, quam latus A2B in di-
rectione ipsi normali excipiet, ex AD exponet imprestionem, quam
latus AB excipiet juxta directionem lateri A2B parallelam, Peu AB
Derpendicularem. Onde cum media directio AN impressionum Rui-
di in laceribus AB et A2B nascatur a potentiis lateralibus AL Sc
LNT, necCNC CA UE HabCAEUE, AL: L N = A2D: AD; atqui A2D:
A2B = (A2B): (A2C)  = AI 2: AT2, ee A2B: 2A2B vel AB = ZI:
AL. = AL. ZL: AL, E, CrGOCX aquO A2D: AB = AL. ZL: ATZ; eAt-
que pOrro AB: AD = AB: AO = ATE: TI, adeoque itCrUM Cx
aQUO A2D: AD = AI. ZL: TI. AEqui (secundum hypothesin)
AL: L. N = AED: AD, CrgO AL: L. N =AI. ZI: TI., et quia TI:
AL. = TI2: AL. TL, crit denigue CX aequo TI: NI = AL. ZL:
AL. TL = ZL: TL, atque adeo TL est media proportionalis inter
tansentes ansulorum datorum Z AL. vel A2A2B e NAI., ut supra
invenimus. Ouod erat demonstrandum.
RiB. XY3, 457. F X F M DL. TI. Relimatur bilincum BA2B, quod pOnatUE
e r4 eNe parabolicum, cujus aequatio 2ax = yy; existentibus coordinatis ad
aXCM AFI, ∞ X TIB. vel 2IT2B, y ac parametro 2a. A quatio bi
linei differentiata praebet adx = pdy, vel substitutis loco elemento-
rum da _ dy lineis. proportionalibus m ex a; am = ay atque adco
m == Y; hinc nn = aa = yY. IdCIrCOOR =KL = TII (= e; + 2bem: nn;
+ eff: nn) = e; + 2bey: aa + yy; + eff: aa + 7y. FLinc (5. 454.) rec lum
L. = edy; + 2beydy: aa + 77; + effdy: ac + 77.
Atqui omnia edy seu summa edy = ey; ac omnia ydy: aa L yy X quan-
cs loS morationis ac + yy adac qui lo3 us dicatur z: a; respicirque
1c