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# Title: Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo (shelfmark Leibn. Marg. 182)
# Folio 323, page id 1066518432:0351
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DE VIRIBVS ET MIOTIBOS CORDORDM. LIB. II. 323
Lectoris ex praecedentibus eliciendam relinquo. PAo RO linca FIB. 13I
indetinita lonsitudinis, cui perpendicularis insiltat TMF. ad Partes
a indetinita, in hac perpendiculari portio IM exponat graritatem
uniformem, _E AM = AY semissem tenacitatis medii, duetaque AI
factisque AC = AIE = AI, centro A et latore transrerlo RC de
scripta sit hyperbola aequilatera CLP, in qua, si MO accipiatur PrO
celeritate initiali projectionis, ex MIS pro relocitate mobili post ali-
quod tempus relidua, agantur ordinatae OP ec SI hyperbola Oc.
currentes in P ec L, per quae puncta ducantur denique ex RE recte
IEP, IEL.G. Spatium ME; in cujus termino P mobilirelinquiturce
leritas MIS vel FD, erit = 108. (PO: L5) -
AM
15 108. (PO: O)
dE tempus per spatium MIF = l09. (PO: I.S): TMI. Omnes hi l092-
richmi sunt ex l0g-mica, cujus subtangens eMt equalis IMI. F.X hac
constructione jam latis apparet, scalam celeritatum ODa aCumpto
tam habere Ca, atque adeo mobilis celeritatem quidem continuo
decrelcere, nunquam rero ad celeritatem MC reduci posse.
PROPOSITIOLXVTTI. PHEORENA
559. Si gravitas exponatur per secantem alicujus arcus dati, ex cor-
pus grave verticaliter in altum projiciatur in aere praesentis resistentiae
hypotheseos, ac celeritate, quae exponitur excessu tancentis arcus cujus-
dam variabilis supra tancentem dati arcus; assumatur que maenitudo
quaedam, quae sit ad differentiam arcuum variabilis es dati, ut rec- lum
ex secante e tancente dati arsus ad quadratum radii.
Frit X. Spatium, quod mobile, ascendendo quousque potest, conficiet
ut loc- us rationis, quam secans arcus variabilis habet ad secantem dati
arcus, dempta maenitudine assumta.
20. Tempus, quo mobile hanc alcitudinem absol vet, erit ut magnitur
do assumta applicata ad tancentem dati arcus.
SInE ABKC quadrans circuli, BIL hyperbola aequilatera Cx cen- FI8. 2323
tro A et semilatere AB descripta. F xponat IM Icu AW sccanS dla-
ti arcus Ba graritatem uniformem, ac mobile ex R in altum proji-
ei intelligatur celeritate RP vel WO, qua est differentia tangen-
tium BO, BWV arcuum rariabilis BR eE dati B0. Descriptaque cir.
caarem AT l08. mica BON, cujus subtansens sicCFIvel IM; agan-
tur LC, LN Parallelae AS, ac per puncta (, IV, QEC. FFANSCANE OE-
dinatae l0s. micx GHI et NO; in NO producta siC OV certia Pron
8
POF-