Galilei, Galileo, Mechanics, 1665

List of thumbnails

< >
1
1
2
2
3
3
4
4
5
5
6
6
7
7
8
8
9
9
10
10
< >
page |< < of 40 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="070/01/010.jpg" pagenum="280"/>
              D hath the ſame proportion to the Reſiſtance made by the Weight
                <lb/>
              A, in the point C: as the Diſtance
                <emph type="italics"/>
              B
                <emph.end type="italics"/>
              C hath to the Diſtance C D,
                <lb/>
              whereby it's clear, that the nearer the Fulciment E ſhall approach
                <lb/>
              to the Term B, encreaſing the proportion of the Diſtance D C to
                <lb/>
              the Diſtance C
                <emph type="italics"/>
              B,
                <emph.end type="italics"/>
              the more may one diminiſh the Force in D which
                <lb/>
              is to raiſe the Weight A. </s>
              <s>And here it is to be noted, which I ſhall
                <lb/>
              alſo in its place remember you of, that the benefit drawn from all
                <lb/>
              Mechanical Inſtruments, is not that which the vulgar Mechanitians
                <lb/>
              do perſwade us, to wit, ſuch, that there by Nature is overcome, and
                <lb/>
              in a certain manner deluded, a ſmall Force over-powring a very
                <lb/>
              great Reſiſtance with help of the Leaver; for we ſhall demonſtrate,
                <lb/>
              that without the help of the length of the Leaver, the ſame Force,
                <lb/>
              in the ſame Time, ſhall work the ſame effect. </s>
              <s>For taking the ſame
                <lb/>
              Leaver B C D, whoſe reſt or Fulci­
                <lb/>
              ment is in C, let the Diſtance C D
                <lb/>
                <figure id="id.070.01.010.1.jpg" xlink:href="070/01/010/1.jpg" number="6"/>
                <lb/>
              be ſuppoſed, for example, to be
                <lb/>
              in quintuple proportion to the
                <lb/>
              Diſtance C
                <emph type="italics"/>
              B,
                <emph.end type="italics"/>
              & the ſaid Leaver to
                <lb/>
              be moved till it come to I C G: In
                <lb/>
              the Time that the Force ſhall have
                <lb/>
              paſſed the Space D I, the Weight
                <lb/>
              ſhall have been moved from B
                <lb/>
              to G: and becauſe the Diſtance
                <lb/>
              D C, was ſuppoſed quintuple to the other C B, it is manifeſt from
                <lb/>
              the things demonſtrated, that the Weight placed in B may be five
                <lb/>
              times greater then the moving Force ſuppoſed to be in D: but now,
                <lb/>
                <arrow.to.target n="marg1108"/>
                <lb/>
              if on the contrary, we take notice of the ^{*} Way paſſed by
                <lb/>
              the Force from D unto I, whilſt the Weight is moved from B unto
                <lb/>
              G, we ſhall find likewiſe the Way D I, to be quintuple to the Space
                <lb/>
              B G. </s>
              <s>Moreover if we take the Diſtance C L, equal to the Diſtance
                <lb/>
              C B, and place the ſame Force that was in D, in the point L, and
                <lb/>
              in the point B the fifth part onely of the Weight that was put there
                <lb/>
              at firſt, there is no queſtion, but that the Force in L being now
                <lb/>
              equal to this Weight in B, and the Diſtances L C and C B being
                <lb/>
              equall, the ſaid Force ſhall be able, being moved along the Space LM
                <lb/>
              to transfer the Weight equall to it ſelf, thorow the other equall
                <lb/>
              Space B G: which five times reiterating this ſame action, ſhall tranſ­
                <lb/>
              port all the parts of the ſaid Weight to the ſame Term G: But
                <lb/>
              the repeating of the Space L M, is certainly nothing more nor leſſe
                <lb/>
              then the onely once meaſuring the Space D I, quintuple to the
                <lb/>
              ſaid L M. </s>
              <s>Therefore the transferring of the Weight from B to G,
                <lb/>
              requireth no leſſe Force, nor leſſe Time, nor a ſhorter Way if it
                <lb/>
              wee placed in D, than it would need if the ſame were applied
                <lb/>
              in L: And, in ſhort, the benefit that is derived from the length of
                <lb/>
              the Leaver C D, is no other, ſave the enabling us to move that </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>