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# Title: Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo (shelfmark Leibn. Marg. 182)
# Folio 45, page id 1066518432:0073
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DE VEREDUS EY NIOTTBUS CORPORUM. LIB. I. 45
calus Velariae, ut suo Joco plenius octendetur, crit, Factis debitis
Tubstitutionibus, BD =mndx: an, atque polica A (= Y.) = a, a1a-
logia (5. TOT.) BC: T = du: m, nunc tiet mmdx: aan = dn: m, hinc
aandu =m da et m dx = aamdm vel dx = - aadm: mm, hinc X =
aa: M, = a aEquC M = aa: a + N eC n = V (aa - MM) = a V (2a ∞ + XX):
a = X, er5O dy (=mdi: n) = adX: Y (2aX = X X). Pro sequatione Ve
lariae.
204. Si pocentia applicata currae itidem perpendicularis BD SIE
eds, ubi e denotat quantitatem utlibet datam in a ec constantibus,
ponatur juxta superiorem (5. 200.) notam T = A = Eaa; Factisque
Cx (S. FOT.) conrenientibus substicutionibus analogia BC: I = dn: m,
mutabitur in 2RdX: an = dn: M, hinc 2tedx =anan: m == - adre Vel
2d = adm. PONatuT X + u = Constanti b, ergo du = - dX, _ 21d ub
= = 2hd∞ = adm. Onde SI Rat 2ldu = adp,: Cxit dp = am, atque adeo
P =m et dy = pda: V (aa = pp). Ouxe ex aliis principiis reperta est di
Celeberrimis Bernoulliis. Si k =W, Ret dy = = undu: V (a = 21) DEO
aequatione fgurx lintei vel E lasticae Acurissimi Jac. Bernoullii.
205. Si applicatae POtentIi BHI sunt axi AC ParaHLelX, ut BF;
ducatur F. I perpendicularis ad BD; unde sI BF = ag, proPtextrian-
sulorum BPF, APO Similitudinem invenietur latuS FI = ndg: a,
_ BI = mdg: a. Idcirco loco BC nunc eAt Cumenda BI, in analo-
sia BO: T = dn: m, Hetque (mag: a): t =. dn: m, vel atdu =mmdg.
sed a +sIF = a + sndg: a = T = E, e differentiando nag: a = dt, vel
dq= adt: n, quod in aequatione atdn =mmaq Custectum, prxbet
atnan=ammat vel at: t = ndn: mm = -mdm: mm = - dm: m; hinc
t =aa: m, quod in superiori analogia substitutum, dat (mag: a):
(aa: m) = dn: m, Cx. qua elicitur dg = a dn: m (vel Propter: aa =
um + un =amman + annan: m=amman- amnam: m=amdn
andm: mm; unde, Facta Cummatione; invenietur q = an: m, id est.
mg =an, vel substitutis loco m et n iplarum proportionalibus dy,
da; reperietur dy == adx: q: Oux aequatio omnis generis Catenarias
COntIneT.
Ftli vero modo inventa aequatio jam continetur in Corollario
sexto, quod dat analogiam sBF: A = BM: bM, in qua SIsBF =
Sdg = 9, A = a, BM = dx, _ bM = dy, habebitur g: a = d∞: dy,
atque adco dy = adx: g. Non tamen absre mihi visum est, si utum
analogix BC: D = dn: m etiam hoc calu illustrarem.
106. Sitg = 5, per sintelligendo curram ABB, crit dy = adX: 5;
qui calus est. simplicissimus problematis Catenariae. F’oret enim
MS