Galilei, Galileo, Mechanics, 1665

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              <s>
                <pb xlink:href="070/01/010.jpg" pagenum="280"/>
              D hath the ſame proportion to the Reſiſtance made by the Weight
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              A, in the point C: as the Diſtance
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              B
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              C hath to the Diſtance C D,
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              whereby it's clear, that the nearer the Fulciment E ſhall approach
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              to the Term B, encreaſing the proportion of the Diſtance D C to
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              the Diſtance C
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              B,
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              the more may one diminiſh the Force in D which
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              is to raiſe the Weight A. </s>
              <s>And here it is to be noted, which I ſhall
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              alſo in its place remember you of, that the benefit drawn from all
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              Mechanical Inſtruments, is not that which the vulgar Mechanitians
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              do perſwade us, to wit, ſuch, that there by Nature is overcome, and
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              in a certain manner deluded, a ſmall Force over-powring a very
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              great Reſiſtance with help of the Leaver; for we ſhall demonſtrate,
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              that without the help of the length of the Leaver, the ſame Force,
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              in the ſame Time, ſhall work the ſame effect. </s>
              <s>For taking the ſame
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              Leaver B C D, whoſe reſt or Fulci­
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              ment is in C, let the Diſtance C D
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                <figure id="id.070.01.010.1.jpg" xlink:href="070/01/010/1.jpg" number="6"/>
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              be ſuppoſed, for example, to be
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              in quintuple proportion to the
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              Diſtance C
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              B,
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              & the ſaid Leaver to
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              be moved till it come to I C G: In
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              the Time that the Force ſhall have
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              paſſed the Space D I, the Weight
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              ſhall have been moved from B
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              to G: and becauſe the Diſtance
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              D C, was ſuppoſed quintuple to the other C B, it is manifeſt from
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              the things demonſtrated, that the Weight placed in B may be five
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              times greater then the moving Force ſuppoſed to be in D: but now,
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                <arrow.to.target n="marg1108"/>
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              if on the contrary, we take notice of the ^{*} Way paſſed by
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              the Force from D unto I, whilſt the Weight is moved from B unto
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              G, we ſhall find likewiſe the Way D I, to be quintuple to the Space
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              B G. </s>
              <s>Moreover if we take the Diſtance C L, equal to the Diſtance
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              C B, and place the ſame Force that was in D, in the point L, and
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              in the point B the fifth part onely of the Weight that was put there
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              at firſt, there is no queſtion, but that the Force in L being now
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              equal to this Weight in B, and the Diſtances L C and C B being
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              equall, the ſaid Force ſhall be able, being moved along the Space LM
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              to transfer the Weight equall to it ſelf, thorow the other equall
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              Space B G: which five times reiterating this ſame action, ſhall tranſ­
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              port all the parts of the ſaid Weight to the ſame Term G: But
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              the repeating of the Space L M, is certainly nothing more nor leſſe
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              then the onely once meaſuring the Space D I, quintuple to the
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              ſaid L M. </s>
              <s>Therefore the transferring of the Weight from B to G,
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              requireth no leſſe Force, nor leſſe Time, nor a ſhorter Way if it
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              wee placed in D, than it would need if the ſame were applied
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              in L: And, in ſhort, the benefit that is derived from the length of
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              the Leaver C D, is no other, ſave the enabling us to move that </s>
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    </archimedes>
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