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# Title: Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo (shelfmark Leibn. Marg. 182)
# Folio 65, page id 1066518432:0093
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a
1
DE VTRFDUS ET NIOTFDUS CORPORUM. LIB. I. 65
tum, quod usu formularum ex praecedentibus mutuo sumendarum
quilibet pocerit experiri. Craritas urlibet rariabilis dicatur 8, (pa-
tium perpendiculariter a corpore cadente describendum. a, tempus
quo percurri debet i, relocitas in fine hujus temporis acquisita W;
elementa spatii, temporis, ec relocitatis da, dt ex du, quibus po-
sITIS (5, 132.) crit prima Formula edx = udu, _ (5. T3F.) habetur
dt =mdu: e, ubi m tigniticat mallam mobilis e e ejus pondus: quo-
niam vero mobile cum nullo alio CompATATUE, SCdL ejUS FANEUM MOtUS
exquiruntur, loco ipsius m unitas poni potest, eritque dt. =du: 8.
Sccunda Formula.
T46. Sint nunc celeritates acquisitx, ut spatia confecta, ut rult
Balianus, id cA W =∞, _ W =XX aC udu = XdX, eFIEqUC PFOPEEF
edx = udu, etiam e da = xdae id eA e =X, ergo existente X =0 exit
etiam e =0, ergo in principio delcentus graritas mobilis nulla Fo-
ret, atque adeo iptum per Epatium ae nunquam delabi PoNet. POr-
ro, quia secunda Formula dt == du: e e e = ∞, praebent dt =dX: X,
unde + = lo9. x, jam existente a =0, e l0g. iplius o intinito, quod
Per c significabimus, erit + = co, hoc eA, infinitum tempus requi
ritur ad percurrendum ab initio nullum spatium, adeoque grare
ibi perpetuo quielcet, et consequenter Baliani hrpothesis impossibi-
lis de imaginaria est. Ihoc ipsum alia adhuc ratione octendi in Actis
Lipl. 1709. Pa5. 404. Sc9.
247. Si celeritates acquisIt W sUnE ut an, ubi m est quilibet nu-
merus integer ex politirus index potestatis spatii, cui celeritas pro-
POTTIONaEUT, P~E Un =X e udu = mX d = 5dX, atque adco
=m-, atqui existente ∞ =0, exit etiam ma m -1 = 8 = O, ergO
ejusmodi hypochesis impossibilis et imasinaria cA.
POrrO dt (= du: 5 = man-: ma m - 1) = da: a. Verum juxta arti-
culum 92. Cummationem incundo, invenietur + = (∞ m -
M = + = ∞ : m = +. TIOC CA, tempUS desCenTUS DEF MiniMaM
quamcunque altitudinem est in hac hypochesi, uc potectas infiniti co-
Cujus exponens est numerus integer m = T. Ergo haec hrpothesis, mul
co maris quam praecedens, imaginaria est et impossibilis.
Flactenus generalia motuum acceleratorum habuimus, dispicien-
dum restat, quid ex una alteraque sraritatis hypotheli sequi de-
bcat.