Galilei, Galileo, Discourse concerning the natation of bodies, 1663

Page concordance

< >
Scan Original
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
< >
page |< < of 77 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb pagenum="417"/>
              ment or ebbing of the water A C, hath to the riſe or elevation of
                <lb/>
              the ſaid Solid M. Therefore, by Perturbation of proportion, in the
                <lb/>
              aſcent of the ſaid Solid M, the abaſement of the water A B C D, to
                <lb/>
              the abaſement of the water E N S F, hath the ſame proportion, that the
                <lb/>
              Surface of the water E F, hath to the Surface of the water A D;
                <lb/>
              that is, that the whole Maſs of the water E N S F, hath to the whole
                <lb/>
              Maſs A B C D, being equally high: It is manifeſt, therefore, that
                <lb/>
              in the expulſion and elevation of the Solid M, the water E N S F
                <lb/>
              ſhall exceed in Velocity of
                <emph type="italics"/>
              M
                <emph.end type="italics"/>
              otion the water A B C D, aſmuch as it
                <lb/>
              on the other ſide is exceeded by that in quantity: whereupon their
                <lb/>
              Moments in ſuch operations, are mutually equall.</s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              And, for ampler confirmation, and clearer explication of this, let us
                <lb/>
              conſider the preſent Figure, (which if I be not deceived, may ſerve to
                <lb/>
              detect the errors of ſome Practick Mechanitians, who upon a falſe
                <lb/>
              tion ſome times attempt impoſſible enterprizes,) in which, unto the large
                <lb/>
              Veſſell E I D F, the narrow Funnell or Pipe I C A B is continued, and
                <lb/>
              poſe water infuſed into them, unto the Levell L G H, which water ſhall
                <lb/>
              reſt in this poſition, not without admiration in ſome, who cannot conceive
                <emph.end type="italics"/>
                <lb/>
                <figure id="fig268" number="7"/>
                <lb/>
                <emph type="italics"/>
              how it can be, that the heavie charge of the great
                <lb/>
              Maſs of water G D, preſſing downwards, ſhould
                <lb/>
              not elevate and repulſe the little quantity of the
                <lb/>
              other, contained in the Funnell or Pipe C L, by
                <lb/>
              which the deſcent of it is reſisted and hindered:
                <lb/>
              But ſuch wonder ſhall ceaſe, if we begin to ſuppoſe
                <lb/>
              the water G D to be abaſed only to Q D, and
                <lb/>
              ſhall afterwards conſider, what the water C L
                <lb/>
              hath done, which to give place to the other, which
                <lb/>
              is deſcended from the Levell G H, to the Levell
                <lb/>
              Q O, ſhall of neceſſity have aſcended in the ſame
                <lb/>
              time, from the Levell Lunto A B. </s>
              <s>And the
                <lb/>
              aſcent L B, ſhall be ſo much greater than the
                <lb/>
              ſcent G Q, by how much the breadth of the Veſſell
                <lb/>
              G D, is greater than that of the Funnell I C;
                <lb/>
              which, in ſumme, is as much as the water G D,
                <lb/>
              is more than the water L C: but in regard that the Moment of the Velocity
                <lb/>
              of the Motion, in one Moveable, compenſates that of the Gravity of
                <lb/>
              ther, what wonder is it, if the ſwift aſcent of the leſſer Water C L, ſhall
                <lb/>
              reſiſt the ſlow deſcent of the greater G D
                <emph.end type="italics"/>
              ?</s>
            </p>
            <p type="main">
              <s>The ſame, therefore, happens in this operation, as in the Stilliard,
                <lb/>
              in which a weight of two pounds counterpoyſeth an other of 200,
                <lb/>
              asoften as that ſhall move in the ſame time, a ſpace 100 times
                <lb/>
              er than this: which falleth out when one Arme of the Beam is an </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>