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# Title: Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo (shelfmark Leibn. Marg. 182)
# Folio 73, page id 1066518432:0101
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a1
A
Me
DE VERREOS ET MIOTEBOS COREORDH. LXB. L. 73
Ap: DN (nuM. L.) =O DP. Np: DN V(PF: =O), ergOPO
ESDP. O. Ap: DN V(P F: =OO). HIoc est, si intelligatur aliqua
curras cujus abscissa DN, ordinata DPZ. O: DN Y (R. F2 -OD) area,
hujus currae ordinatis abscisarum DA _ DF. interjecta ad datam
lineam DP applicata praebebit lineam, cui si aequalis ubique Factus
Tuerit arcus PO, recta DON per hujus arcus terminum O ducta
aequalis abscistae DE. sua extremitate N in curra quaesita crit. Jam
quia quadratum ordinatae F F aequatur duploarex (BFHI datae per
absciltam DF vel DN e constantes, sinon alcebraice, (altem trans-
cendenter, atque  es quarta proportionalis ad DF vel DN, &
datas DR, AI, ea pariter data crit in DF e constantibus, unde
Cum omnes quantitateS, quae ip lam DPE. O: DN V(RF -O~) Or-
dinatam scilicet figurx quadrandae ingrediuntur, dentur in DN _
constantibus, ex tigurarum quadratura concessae sint; Factum esse
liquet, quod erat taciendum.
COR OL L A R L U M.
103. Si nunc aCantur DR, B; AT, C; DE vel DB, 2, velo-
Citas in currx puncto N, PCu FF, W; arcus circuli PO, D; ejus
radius DP, r; at elementum arcus crescens OO, + do, elementum
vero decrelcens Np, indeterminatx ND, - d Z. Adeoque O = cb: 2
_E FOta Formula O0 =O. DP. NID: DN Y(P F: =O) mutabitur
Factis debitis substicutionibus in d0 = - berd z: ZV (un ZZ = bbCC), quxe
est aequatio differentialis currae quaesitae ALIn.
S CH O L I O N.
264. FTOC prevea Primum Colutionem accepit a Cel. Newtono
ProP. 4 F. Lib. Princ. Phil. NTat. Math. _ postea a Perspicacissimo
Geometra Joh. Bernoulli gemino modo, tum etiam a CI. VirOP.
Varignon dirersis modis, quo etiam referri posset ee nostra solutio
quam in Diario Veneto Tom. V. Pa5. 318. Seg. exhibui cum non-
nullisaliis, ex Tom. VII. Pa5. 194. Pralens nostra Colutio a NCWtO-
niana non differt, nisi in leribus nec essentialibus circumstantiis,
nam nostra P F significat latus quadratum areae apud Ncwconum
ABFD bis sumex, quam tamen ille lemel tantum accipie, ejusque
nobis est rectangulum sub datis DR ex AI in nostra tgura, re
ro nobis est idem quod illi : A sou 2..
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