Galilei, Galileo, Mechanics, 1665

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                <pb xlink:href="070/01/023.jpg" pagenum="293"/>
              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.</s>
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              * Or along.</s>
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              <s>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. </s>
              <s>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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                <figure id="id.070.01.023.1.jpg" xlink:href="070/01/023/1.jpg" number="20"/>
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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. </s>
              <s>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. </s>
              <s>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.</s>
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              <s>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.</s>
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