Gravesande, Willem Jacob 's
,
Physices elementa mathematica, experimentis confirmata sive introductio ad philosophiam Newtonianam; Tom. 1
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PHYSICES ELEMENTA
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runtur motu æquabili, momenta enim temporis adeo exigua coucipipo ſſunt,
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ut acceleratio aut retardatio inſenſibilis ſit; </
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<
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">celeritates ergo in punctis F & </
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G ſunt, ut F f & </
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<
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la ſimilia HBF, A h l, & </
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neæ AD; </
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<
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">& </
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<
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xml:space
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">Incrementa celeritatum momentis æqualibus minimis in punctis F & </
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prefſiones agentes in iſtis punctis , ſunt ut l h & </
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<
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ritatum in punctis F, f, & </
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& </
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corpus agentes ſunt inter ſe ut diſtantiæ a puncto medio B.</
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<
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">Quæ de incrementis celeritatum demonſtrantur in parte AB Hineæ AD,
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in parte BD de decrementis eodem modo demonſtrantur. </
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pus juxta legem corporis in cycloïde oſcillati.</
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<
s
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">Detur corpus motu æquabili ſemicir culum percurrens ALD, in tempore
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unius vibrationis in cycloide, id eſt in tempore, in quo corpus, in linea
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recta AD ut explicavimus motum, illam percurrit. </
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F f, & </
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ctiones ſint parallelæ in L & </
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corpus celeritate quam corpus pendulum habet in B, in tempore unius vibrationis
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deſcribit ſemicirculum, cujus diameter eſt arcus cycloidis a corpore percurſus.</
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<
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<
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">Si corpus integram percurrat cycloidem ABD, diameter hæc erit quadru-
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pla diametri FB , & </
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fig. 4.</
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ne FB acquirit , qua celeritate motu æquabili corpus in tempore caſus
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teſt percurrere lineam duplam ipſius FB Sed ſpatia æqualibus
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percurſa ſunt ut tempora , id circo tempus caſus per
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penduli eſt ad tempus unius vibrationis per integram cycloidem, aut arcum
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quemcumque , ut dupla FB, ad ſemicircumferentiam circuli, cujus
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ter eſt quadrupla lineæ FB, aut ad integram circumferentiam, cujus diame-
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ter eſt etiam dupla FB; </
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ferentiam; </
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lationis O, cujus hæc eſt proprietas, poſitâ virgâ AC rigidâ & </
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fig. 3.</
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dere, ut pondus Q, multiplicatum per BC, ad pondus P, multiplicatum per
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AC, ita AO ad OQ. </
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& </
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inclinatis; </
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pora virgâ rigidâ juncta forent, illis celeritates communicarent æquales .</
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Junctorum autem ponderum celeritates neceſſario ſunt inæquales, & </
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tas corporis P, actione ponderis Q, augetur, dum hocalterius actione retardatur;
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</
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<
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O, centrum nempe oſcillationis, movetur celeritate ex actione gravitatis ori-
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unda.</
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">Sit B b, O o, aut A a (has enim æquales ponimus lineas) ſpatium percur-
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ſum ex actione gravitatis juxta inclinationem quamcunque agentis in tem-
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pore quocunque minimo. </
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per BE transſertur Q, & </
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