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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da in puncto A, poterit velocitas in puncto quocunque, ut C, determina-
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ri. </
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logarithmicæ, & </
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& </
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<
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">æquales;
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velocitates in punctis a & </
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e f; </
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">decrementa ergo velocitatum, dum ſpatia æqualia A a, C c percurrun-
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tur, ſunt G g & </
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<
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">demonſtrandum, ſi G g reſolvatur in duas partes quæ
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ſint ut AB ad BI, FL poſſe reſolvi in duas ita, ut partes primæ utriuſque
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decrementi ſint inverſè ut GI ad FE . </
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">& </
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tione GI aut BI, (quia hæc eſt parabolæ parameter †) ad FE : </
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debemus probare G g ſe habere ad FL, ut {AB/GI} + {BI/GI} ad {AB/FE} + {FE/GI}.
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Hæc eſt autem demonſtratio; </
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xml:space
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{AE/FE} = {AB/FE} + {BE/FE} .</
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<
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">Sed {BE/FE} = {BE x FE/FE x FE} = {BE x FE/BE x BI} = {FE/BI} = {FE/GI} propter æquales
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">la Hire
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ſect. con.
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lib. 3.
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prop. 2.</
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GI: </
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">Spatium in quo corpus totam amittit velocitatem eſt BP, aut AQ; </
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puncto enim Q velocitas nulla eſt .</
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ſentatum, determinandum eſt, ut & </
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ſine experimentis, circa ipſas retardationes inſtitutis, pervenire non poſſu-
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mus.</
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<
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">Ponimus ergo experimento detectum fuiſſe ſpatium AQ, in quo corpus
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totam amittit velocitatem, quo ſpatio dato, ratio inter AB & </
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<
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ratio retardationum in puncto A, detegi poteſt.</
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<
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">Velocitas in A lineâ GI, aut BI ipſi æquali, repræſentatur, & </
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tio dum ſpatium A a percurritur eſt G g, ut vidimus, quæ (propter ſubtan-
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gentem duplam abſciſſæ BI , ideoque duplam GI) dimidium eſt
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ſect. con.
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lib. 2.
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prop. 20.</
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g H, aut i k.</
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<
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que IM, quæ ſecat k i in m, erit k i dupla m i, quæ ergo G g æqualis eſt,
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retardationemque repræſentat.</
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<
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les ſint AB, MN, ut & </
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erit AB, ad BI, id eſt prima retardatio ad ſecundam in puncto A, ut m n,
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ad n i; </
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ſumma retardationes conjunctim deſignat.</
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