Gravesande, Willem Jacob 's
,
Physices elementa mathematica, experimentis confirmata sive introductio ad philosophiam Newtonianam; Tom. 1
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MATHEMATICA. LIB. I. CAP XXI
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<
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<
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in quieſcentia agit.</
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<
s
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<
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">centrum C; </
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<
s
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">moveatur corpus in Ellipſi, in quare-
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tinetur vi, quæ ad centrum dirigitur; </
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<
s
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">vis hæc determinanda eſt.</
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<
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<
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<
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<
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fig. 6.</
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diameter ipſi conjugata tangenti parallela ; </
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ſect. con.
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Lib. 2.
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pro. 10.</
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conſtanti deſcriptus; </
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<
s
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">IL, parallela AC, ſpatium eodem momento vi cen-
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trali percurſum, quod ſpatium ipſius vis centralis rationem ſequitur .</
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<
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<
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ad ED normalis; </
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<
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<
s
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xml:space
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">Triangula rectangula LHG, AFC, ſunt ſimilia propter angulos æqua-
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les LGH, ACF . </
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<
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<
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">& </
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<
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xml:space
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<
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xml:space
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<
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li ALC , quæ momento conſtanti quo AL deſcribitur proportionalis eſt . </
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<
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xml:space
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<
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<
s
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<
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xml:space
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<
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eſt ad LH x AC aut LG x AF, id eſt, ED ad LG, ſemper in eadem
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ſect. con.
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lib. 5.
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prop. 21.</
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ratione ubicunque punctum ut A in Ellipſi ſumatur; </
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<
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eſt ratio inter ED
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& </
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<
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. </
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<
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, LG
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:</
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<
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, AG x
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GB , aut LI x AB, propter æquales AG & </
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<
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<
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Lib. 3.
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prop 3.</
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tè exiguam inter GB & </
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<
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& </
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<
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LI x AB, id eſt, inter AB & </
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<
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">LI, augetur ideò LI, id eſt, vis centra-
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lis in eadem ratione in qua augetur & </
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<
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AC, quod æquale eſt diſtantiæ corporis à centro; </
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<
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<
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</
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<
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<
s
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xml:space
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">Si vero dum corpus in Ellipſi movetur vis ad focum dirigatur, hæc rece-
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<
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dendo a centro virium decreſcit in ratione inverſa quadrati diſtantiæ, ut
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habetur in n. </
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<
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<
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<
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<
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<
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<
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fig. 7.</
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tur; </
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<
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<
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exiguus.</
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<
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<
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<
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<
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lela AC; </
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<
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<
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<
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<
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& </
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<
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<
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focum alium & </
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<
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æquales , & </
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<
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<
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ſect. con.
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Lib. 8.
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prop. 8.</
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propter æquales CF, Cf: </
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<
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<
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<
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eſt EA dimidium ſummæ linearum FA, Af, quæ ſimul ſumtæ æquales
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ſunt axi BD .</
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<
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<
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<
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ciens rectos; </
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<
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<
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">Propter angulos rectos ALb, LHA, puncta H, b, ſunt in circumfe-
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rentia ſemi circuli cujus diameter A eſt L ; </
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>
<
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">idcirco anguli bLH,
<
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">31 El. 117.</
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ſunt in eodem ſegmento & </
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<
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<
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<
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& </
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<
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">æquales anguli LHb & </
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<
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<
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">hic autem quia AL eſt inſinitè </
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