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

Table of figures

< >
[Figure 1]
Page: 11
[Figure 2]
Page: 12
[Figure 3]
Page: 13
[Figure 4]
Page: 14
[Figure 5]
Page: 15
[Figure 6]
Page: 17
[Figure 7]
Page: 18
[Figure 8]
Page: 36
[Figure 9]
Page: 46
[Figure 10]
Page: 47
[Figure 11]
Page: 48
[Figure 12]
Page: 51
[Figure 13]
Page: 52
[Figure 14]
Page: 54
[Figure 15]
Page: 54
[Figure 16]
Page: 56
[Figure 17]
Page: 57
[Figure 18]
Page: 58
[Figure 19]
Page: 76
< >
page |< < of 77 > >|
    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb pagenum="407"/>
              this Weight ſhould deſcend more than that, or that more than this;
                <lb/>
              and therefore they make an
                <emph type="italics"/>
              Equilibrium,
                <emph.end type="italics"/>
              and their Moments continue
                <lb/>
              of ſemblable and equall Vertue.</s>
            </p>
            <p type="main">
              <s>The ſecond Principle is; That</s>
            </p>
            <p type="head">
              <s>AXIOME II.</s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              The Moment and Force of the Gravity, is encreaſed by
                <lb/>
              the Velocity of the Motion.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>So that Weights abſolutely equall, but conjoyned with Velocity
                <lb/>
              unequall, are of Force, Moment and Vertue unequall: and the
                <lb/>
              more potent, the more ſwift, according to the proportion of the
                <lb/>
              locity of the one, to the Velocity of the other. </s>
              <s>Of this we have a
                <lb/>
              very pertinent example in the Balance or Stiliard of unequall Arms,
                <lb/>
              at which Weights abſolutely equall being ſuſpended, they do not
                <lb/>
              weigh down, and gravitate equally, but that which is at a greater
                <lb/>
              diſtance from the Centre, about which the Beam moves, deſcends,
                <lb/>
              raiſing the other, and the Motion of this which aſcends is ſlow, and
                <lb/>
              the other ſwift: and ſuch is the Force and Vertue, which from the
                <lb/>
              Velocity of the Mover, is conferred on the Moveable, which receives
                <lb/>
              it, that it can exquiſitely compenſate, as much more Weight added to
                <lb/>
              the other ſlower Moveable: ſo that if of the Arms of the Balance,
                <lb/>
              one were ten times as long as the other, whereupon in the Beames
                <lb/>
              moving about the Centre, the end of that would go ten times as far
                <lb/>
              as the end of this, a Weight ſuſpended at the greater diſtance, may
                <lb/>
              ſuſtain and poyſe another ten times more grave abſolutely than it:
                <lb/>
              and that becauſe the Stiliard moving, the leſſer Weight ſhall move
                <lb/>
              ten times faſter than the bigger. </s>
              <s>It ought alwayes therefore to be
                <lb/>
              underſtood, that Motions are according to the ſame Inclinations,
                <lb/>
              namely, that if one of the Moveables move perpendicularly to the
                <lb/>
              Horizon, then the other makes its Motion by the like Perpendicular;
                <lb/>
              and if the Motion of one were to be made Horizontally; that then
                <lb/>
              the other is made along the ſame Horizontall plain: and in ſumme,
                <lb/>
              alwayes both in like Inclinations. </s>
              <s>This proportion between the
                <lb/>
              Gravity and Velocity is found in all Mechanicall Inſtruments: and
                <lb/>
              is conſidered by
                <emph type="italics"/>
              Ariſtotle,
                <emph.end type="italics"/>
              as a Principle in his
                <emph type="italics"/>
              Mechanicall Queſtions
                <emph.end type="italics"/>
              ;
                <lb/>
              whereupon we alſo may take it for a true Aſſumption, That</s>
            </p>
            <p type="head">
              <s>AXIOME III.</s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              Weights abſolutely unequall, do alternately counterpoyſe
                <lb/>
              and become of equall Moments, as oft as their
                <lb/>
              ties, with contrary proportion, anſwer to the Velocity of
                <lb/>
              their Motions.
                <emph.end type="italics"/>
              </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
Impressum