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>
            <pb pagenum="411"/>
            <p type="head">
              <s>THEOREME II.</s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              When in one of the above ſaid Veſſels, of what ever
                <emph.end type="italics"/>
                <lb/>
                <arrow.to.target n="marg1412"/>
                <lb/>
                <emph type="italics"/>
              breadth, whether wide or narrow, there is placed ſuch
                <lb/>
              a Priſme or Cylinder, inviron'd with Water, if we
                <lb/>
              vate that Solid perpendicularly, the Water
                <lb/>
              ſed ſhall abate, and the Abatement of the Water,
                <lb/>
              ſhall have the ſame proportion to the Elevation of the
                <lb/>
              Priſme, as one of the Baſes of the Priſme, hath to
                <lb/>
              the Surface of the Water Circumfuſed.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg1412"/>
              The proportion
                <lb/>
              of the water
                <lb/>
              ted, to the Solid
                <lb/>
              raiſed.</s>
            </p>
            <p type="main">
              <s>Imagine in the Veſſell, as is aforeſaid, the
                <lb/>
                <figure id="fig263" number="2"/>
                <lb/>
              Priſme A C D B to be placed, and in the
                <lb/>
              reſt of the Space the Water to be
                <lb/>
              fuſed as far as the Levell E A: and
                <lb/>
              ſing the Solid, let it be transferred to
                <lb/>
              G M, and let the Water be abaſed from
                <lb/>
              E A to N O: I ſay, that the deſcent of
                <lb/>
              the Water, meaſured by the Line A O,
                <lb/>
              hath the ſame proportion to the riſe of the
                <lb/>
              Priſme, meaſured by the Line G A, as the Baſe of the Solid G H
                <lb/>
              hath to the Surface of the Water N O. </s>
              <s>The which is manifeſt:
                <lb/>
              becauſe the Maſs of the Solid G A B H, raiſed above the firſt Levell
                <lb/>
              E A B, is equall to the Maſs of Water that is abaſed E N O A.
                <lb/>
              Therefore, E N O A and G A B H are two equall Priſmes; for of
                <lb/>
              equall Priſmes, the Baſes anſwer contrarily to their heights:
                <lb/>
              fore, as the Altitude A O is to the Altitude A G, ſo is the
                <lb/>
              cies or Baſe G H to the Surface of the Water N O. </s>
              <s>If therefore,
                <lb/>
              for example, a Pillar were erected in a waſte Pond full of Water,
                <lb/>
              or elſe in a Well, capable of little more then the Maſs of the ſaid
                <lb/>
              Pillar, in elevating the ſaid Pillar, and taking it out of the Water,
                <lb/>
              according as it riſeth, the Water that invirons it will gradually abate,
                <lb/>
              and the abaſement of the Water at the inſtant of lifting out the
                <lb/>
              Pillar, ſhall have the ſame proportion, that the thickneſs of the Pillar
                <lb/>
              hath to the exceſs of the breadth of the ſaid Pond or Well, above
                <lb/>
              the thickneſs of the ſaid Pillar: ſo that if the breadth of the Well
                <lb/>
              were an eighth part larger than the thickneſs of the Pillar, and the
                <lb/>
                <arrow.to.target n="marg1413"/>
                <lb/>
              breadth of the Pond twenty five times as great as the ſaid thickneſs,
                <lb/>
              in the Pillars aſcending one foot, the water in the Well ſhall deſcend
                <lb/>
              ſeven foot, and that in the Pond only 1/25 of a foot.</s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg1413"/>
              Why a Solid
                <lb/>
              leſs grave
                <emph type="italics"/>
              in
                <lb/>
              cie
                <emph.end type="italics"/>
              than water,
                <lb/>
              ſtayeth not
                <lb/>
              der water, in
                <lb/>
              ry ſmall depthst.</s>
            </p>
            <p type="main">
              <s>This Demonſtrated, it will not be difficult to ſhew the true
                <lb/>
              cauſe, how it comes to paſs, that,</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum