Galilei, Galileo
,
Mechanics
,
1665
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riſing or aſcending: it of neceſſity remaineth manifeſt, that in the
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Superficies which is exactly equilibrated, the ſaid Ball remaineth in
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different and dubious between Motion and Reſt, ſo that every ſmall
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Force is ſufficient to move it, as on the contrary, every ſmall Reſi
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ſtance, and no greater than that of the meer Air that environs it, is
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able to hold it ſtill.</
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* Or along.</
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>From whence we may take this Concluſion for indubitable, That
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Crave Bodies, all Extern and Adventitious Impediments being re
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moved, may be moved along the Plane of the Horizon by any ne
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ver ſo ſmall Force: but when the ſame Grave is to be thrown along
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an Aſcending Plane, then, it beginning to ſtrive againſt that aſcent,
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having an inclination to the contrary Motion, there ſhall be requi
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red greater Violence, and ſtill greater the more Elevation that ſame
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Plane ſhall have. </
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>As for example, the Moveable G, being poſited
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upon the Line A B parallel to the Horizon, it ſhall, as hath been
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ſaid, be indifferent on it either to Motion or Reſt, ſo that it may
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be moved by a very ſmall Force: But if we ſhall have the Planes
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Elevated, they ſhall not be driven along without Violence; which
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Violence will be required to be
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greater to move it along the Line
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A D, than along A C; and ſtill
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greater along A E than along A D:
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The which hapneth, becauſe it hath
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greater
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Impetus
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of going down
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wards along A E than along A D,
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and along A D than along A C. </
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<
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>So
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that we may likewiſe conclude
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Grave Bodies to have greater Reſiſtance upon Planes differently
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Elevared, to their being moved along the ſame, according as one
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ſhall be more or leſs elevated than the other; and, in fine, that the
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greateſt Reſiſtance of the ſame Grave to its being raiſed is in the
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Perpendicular A F. </
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>But it will be neceſſary to declare exactly what
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proportion the Force muſt have to the Weight, that it may be able
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to carry it along ſeveral elevated Planes, before we proceed any
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farther, to the end that we may perfectly underſtand all that which
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remains to be ſpoken.</
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>Letting, therefore, Perpendiculars fall from the points C, D,
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and E unto the Horizontal Line A B, which let be C H, D I, and
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E K: it ſhall be demonſtrated that the ſame Weight ſhall be mo
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ved along the Plane A C with leſſer Force than along the Perpendi
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cular A F, (where it is raiſed by a Force equal to it ſelf) accor
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ding to the proportion by which the Perpendicular C H is leſs than
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A C: and that along the Plane A D, the Force hath the ſame pro
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portion to the Weight, that the Perpendicular I D hath to D A:
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and, laſtly, that in the Plane A E the
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F
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orce to the Weight obſer
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veth the proportion of E K and E A.</
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