Gravesande, Willem Jacob 's
,
Physices elementa mathematica, experimentis confirmata sive introductio ad philosophiam Newtonianam; Tom. 1
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MATHEMATICA. Lib. I. Cap. XXVII.
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xml:space
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">Dum elaſteria actionibus æqualibus in ſe mutuo premunt, utrumque agit
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quaſi obſtaculo immobili inſiſteret; </
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">& </
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xml:space
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">integram ſuam vim in partem oppoſitam
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exerit ; </
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<
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">id eſt elaſteria agunt in corpora A & </
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<
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xml:space
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">C ita, ut ſingulis, præter
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moratas vires, communicent vim C ff; </
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<
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">quare vis corpori A communicata va-
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let B ff + 2C ff, & </
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<
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">C movetur vi A ff + B ff + Cff, dum B ad par-
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tem Cpellitur actione quæ valet A ff-C ff.</
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<
s
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">Sed B non poteſt moveri, quin eâdem velocitate propellatur elaſterium
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inter B & </
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<
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<
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">ab elaſterio ita agitato accipit corpus C vim ftatim memo-
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ratam eodem modo ac in nave, in qua elaſterium obſtaculo cede-
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re neſcio inſiſteret, actione elaſterii moveretur; </
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<
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">id eſt velocitas qua
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corpus C a B recedit, aut B celerius movetur, illa eſt quæ competit impreſſio-
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ni ſtatim memoratæ, quæ velocitas eſt f {√A + B + C\x{0020}/C} . </
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<
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locitas dicatur x, erit x + f {√A + B + C\x{0020}/C} velocitas corporis C. </
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um horum corporum eſt A ff + B ff + C ff & </
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<
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">præterea A ff-C ff, ideſt
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valet ſumma hæc 2 A ff + B ff; </
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">Unde deducimus {B xx + C xx +
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2fx √AC + BC + CC\x{0020} + A ff + B ff + C ff = 2Aff + Bff ;</
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aut {x x + 2f x √AC + BC + CC\x{0020}/B + C = Aff-Cff/B + C}; </
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{x = f√AB + 2AC\x{0020}-f√AC + BC + CC\x{0020}/B + C}: </
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f√A + B + C\x{0020}/C} qua C recedit à B habemus ipſius C velocitatem
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{fC √AB + 2AC\x{0020} + fB √AC + BC + CC\x{0020}/BC + CC}</
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">Corporis autem A velocitas ex ipſius vi ante determinata detegitur eſtque
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velocitas hæc {f√AB + 2AC\x{0020}/A}.</
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">Velocitates hæ ex velocitate v ſunt ſubtrahendæ, aut ipſi ſunt addendæ,
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pro ut cum motu navis conſpirant aut contrariæ agunt.</
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">Si in primo motu A celerius B feratur, id eſt m ſuperet n, velocitas cor-
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poris A poſt ictum erit {v-f√AB + 2AC\x{0020}/A}; </
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<
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corporum B & </
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<
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æqualem eſſe A mm + B nn + C pp; </
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