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# Title: Phoronomia, Sive De Viribus Et Motibus Corporum Solidorum Et Fluidorum Libri Duo (shelfmark Leibn. Marg. 182)
# Folio 338, page id 1066518432:0366
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338DE VIRZBUS ET MOTIBUS COREORUM. L. IB. II.
S C H OL YON.
588. In aliis rehstentiae hypothesibus res eradic paullo alcioris
indarinis, quam in corollariis TII. X V. hujus; cum in omni alia
hypOTheSi CUrrA ATRTC adhuc inrenienda sIC. IIlustris NCWTO-
nus statim post propositionem in corollario IV. hujus citatam asse-
RiC, hanc curram AR C ad ellipsn proxime accedere, (I, Curra ABC
existente creloide, resistentia aëris fuerint celeritatibus proportio.
nales; vel ad parabolam, si relistentiae fuerint in duplicata pro-
Portione celeritatum. Sed, accurate ex mathematice rem lumen do,
Deaenominata ATR TC non est elliplis in prima, nec parabola in
altera reliltentiae hypochesi; sed, quantum conjicere licet, utroque
calu erit transcendens. Ptenim, si resistentix tunt ut celeritates ac-
quisitae, nondum constat, qua ratione curra ARC construi debcat,
ne quidem concessis quadraturis Agurarum currilinearum. Pro al.
tera vero hypothesi ac naturae magis consentanca nominata currX
constructio haberi porest per quadraturas ex rectificationes currarum.
Ex PrOpOSItIOnO XXIX. laudatissimi Nemtoni Lib. II. ejusmodi
constructio peti potest in casu particulari, quo curra descensus ABC
est crclois. Hloc loco rero generalem constructionem adducam pro
quacunque curra ABC, idque semino modo.
PROPOSITIOLZZIII. PHEOREMA.
589. Per quoalibet in linea AM producta punctum V, descripta lo-
sarithmica VZY subtancentem habente aequalem datae lineae AC, ex
asimptotam C, ac protensa NVD usque ad occursum P cum loc-mica
VX; si omnia elementa PD. DN. Da alicujus solidi duobus planis MAV
ex NDP interjecti erecto scilicet ad anculos rectos plano MABS super
plano VAB, aequalia fuerint par allelexipedo AO. DO, sub quadrato
subtaneentis loc micae e ordinata DO cujusdam curvae AOAC; Bo-
moloea ordinata DT scala resistentiarum ARC erit quarta proportio-
nalis ad ordinatas PD, DO e AO Subtancentem loc- mica V X.
T. PHo linea pn alteri PN indetinite ricina, atque per puncta Y,
O_E P Currarum AY, AO _ VP ducxe sint lincolae ID, G0, d
Px; ac denique, sit DY quarta proportionalis ad PD, DO e AC.
vel, quod eodem recidic, rec- lum PD. DT = AO. DO, e pd. dt -
AO. do, id eA, PD. dt + Pr. at = PD. DT + PD. 1B + dt. pr = PD. DT +