Gravesande, Willem Jacob 's
,
Physices elementa mathematica, experimentis confirmata sive introductio ad philosophiam Newtonianam; Tom. 1
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MATHEMATICA. LIB. I. CAP. XIX.
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quam per chordas vibratur corpus.</
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<
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<
s
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xml:space
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">Durationes vibrationum pendulorum inæqualium poſſunt
<
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<
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">290.</
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inter ſe comparari. </
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<
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xml:space
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">Quando arcus ſunt ſimiles, deviationes re-
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ſpectu chordarum ſunt etiam ſimiles & </
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<
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xml:space
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">tempora vibrationum
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per arcus ſunt ut tempora vibrationum per chordas; </
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<
s
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xml:space
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">hæc vero
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ut tempora deſcenſus per longitudines octuplas longitudinum
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pendulorum ; </
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<
s
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xml:space
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">& </
s
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<
s
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xml:space
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">ſic quadrata durationum ſunt ut iſtæ
<
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">279.</
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gitudines octuplæ ; </
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<
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<
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</
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<
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<
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2.</
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">Duo pendula CP, cp, quorum longitudines ſunt ut 4.
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</
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<
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">291.</
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ad 1.</
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">TAB XI.
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fig. 5.</
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vibrationbius arcus ſimiles deſcribant; </
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<
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mel vibratur, dum minus duas peragit vibrationes; </
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<
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<
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quadrata durationum vibrationum ſunt ut 4. </
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<
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">ad 1.</
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<
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pe ut longitudines pendulorum.</
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</
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<
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<
s
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">Quando vibrationes ſunt exiguæ, hæc ratio etiam locum
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habet, licèt pendula non vibrentur per arcus ſimiles .</
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<
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</
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">280.</
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<
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<
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">Velocitates pendulorum in puncto infimo, in vibrationibus
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">292.</
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inæqualibus, ſunt inter ſe, ut ſubtenſæ arcuum, quos corpus
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deſcendendo deſcribit. </
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<
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">Sic velocitas corporis P, cadentis per
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">TAB. XI.
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fig. 2.</
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arcum PB, eſt ad ejus velocitatem quando cadit per DB,
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ut chorda PB ad chordam DB. </
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<
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">Nam ductis lineis hori-
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">293.</
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zonti parallelis P f, D d & </
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<
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">A, triangula P f B,
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BPA ſunt ſimilia : </
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<
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">idèo B f, BP, BA ſunt in
<
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8: El. VI.</
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tinuâ proportione, & </
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ctum diametri per B f: </
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B d æquale eſt producto diametri per BD: </
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<
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chordarum ſunt inter ſe ut producta hæc, quæ ſunt ut li-
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neæ f B, dB. </
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<
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253.</
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iâm ut iſtæ lineæ f B, d B ; </
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<
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<
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<
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">Circa omnia, quæ hucuſque dependulis dicta ſunt, non in-
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tereſt quantum ponderet corpus quod agitatur, aut an corpora
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diver ſorum pendulorum inæqualiter ponderent, aut ex diverſa
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dentur materiæ. </
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<
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titati materiæ in omnibus corporibus , omnia corpora,
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iiſdem circumſtantiis, gravitate æque celeriter moventur.</
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