Galilei, Galileo, Mechanics, 1665

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              <s>
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              Artificers had, and ſtill have, that they are able with a ſmall force
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              to move and raiſe great weights; (in a certain manner with their
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              Machines cozening nature, whoſe Inſtinct, yea moſt poſitive con­
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              ſtitution it is, that no Reſiſtance can be overcome, but by a Force
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              more potent then it:) which conjecture how falſe it is, I hope by
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              the enſuing true and neceſſary Demonſtrations to evince.</s>
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              <s>In the mean time, ſince I have hinted, that the benefit and help
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              derived from Machines is not, to be able with leſſe Force, by help
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              of the Machine to move thoſe weights, which, without it, could
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              not be moved by the ſame Force: it would not be beſides the
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              purpoſe to declare what the Commodities be which are derived to
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              us from ſuch like faculties, for if no profit were to be hoped for,
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              all endeavours employed in the acquiſt thereof will be but loſt
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              labour.</s>
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            <p type="main">
              <s>Proceeding therefore according to the nature of theſe Studies,
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              let us firſt propoſe four things to be conſidered. </s>
              <s>Firſt, the weight
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              to be transferred from place to place; and ſecondly, the Force
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              and Power which ſhould move it; thirdly, the Diſtance between
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              the one and the other Term of the Motion; Fourthly, the Time
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              in which that mutation is to be made: which Time becometh the
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              ſame thing with the Dexterity, and Velocity of the Motion; we
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              determining that Motion to be more ſwift then another, which in
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              leſſe Time paſſeth an equal Diſtance.</s>
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            <p type="main">
              <s>Now, any determinate Reſiſtance and limited Force whatſoever
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              being aſſigned, and any Diſtance given, there is no doubt to be
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              made, but that the given Force may carry the given Weight to the
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              determinate Diſtance; for, although the Force were extream
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              ſmall, yet, by dividing the Weight into many ſmall parts, none
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              of which remain ſuperiour to the Force, and by transferring them
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              one by one, it ſhall at laſt have carried the whole Weight to the
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              aſſigned Term: and yet one cannot at the end of the Work with
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              Reaſon ſay, that that great Weight hath been moved, and tranſ­
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              ported by a Force leſſe then it ſelf, howbeit indeed it was done
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              by a Force, that many times reiterated that Motion, and that
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              Space, which ſhall have been meaſured but only once by the whole
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              Weight. </s>
              <s>From whence it appears, that the Velocity of the Force
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              hath been as many times Superiour to the Reſiſtance of the weight,
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              as the ſaid Weight was ſuperiour to the Force; for that in the
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              ſame Time that the moving Force hath many times meaſured the
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              intervall between the Terms of the Motion, the ſaid Moveable
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              happens to have paſt it onely once: nor therefore ought we to
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              affirm a great Reſiſtance to have been overcome by a ſmall Force,
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              contrary to the conſtitution of Nature. </s>
              <s>Then onely may we ſay
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              the Natural Conſtitution is overcome, when the leſſer Force tranſ­
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              fers the greater Reſiſtance, with a Velocity of Motion like to that </s>
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          </chap>
        </body>
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    </archimedes>
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