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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<
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3.</
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præſentatur, applicatis huic Machinæ tribus globis ebur-
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<
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fig. 4.5.</
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neis in deſcriptione memoratis. </
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momento dimittantur ab æqualibus altitudinibus, & </
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tur parallelogrammum abcf cujus latera ab, ac, ſunt dire-
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ctiones corporum Q, Q, continuatæ, & </
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<
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">æqualia ſubtenſis
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arcuum per quos corpora Q, Q, deſcendunt; </
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<
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ſi angulus QPQ ſit acutus minori adſcendit velocitate, quàm
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qua adſcendendo poſſet percurrere arcum cujus ſubtenſa me-
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morati parallelogrammi foret diagonalis.</
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<
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tudinem quam quæ diagonali parallelogrammi determina-
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tur.</
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<
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mi velocitate a, ſecundi b, tertii c, ſumma virium eſt A a a - B b b -
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C c c ; </
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n. </
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mam, ſi A a - B b = C c; </
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<
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quamcunque concipiamus auctam aut diminutam quantitate quacunque ut x,
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& </
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væ movetur B velocitate b - x; </
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virium eſt A aa + 2A a x + A xx + B bb + 2B bx + B xx + C cc - 2C cx
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+ C x x, quæ excedit primam quantitate A x x + B x x + C x x ſublatis 2A a x +
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2 B b x - C c x quæ ſeſe mutuo deſtruunt; </
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modocunque velocitates mutatas ſervatis velocitatibus reſpectivis, conci-
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piamus, ſequitur ſummam in caſu memorato fuiſſe minimam.</
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<
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A & </
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<
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b + c . </
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rium in hoc caſu, in quo ſumma hæc eſt minima , & </
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Vim hanc amiſſam diximus æqualem </
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