Salusbury, Thomas, Mathematical collections and translations (Tome I), 1667

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="040/01/224.jpg" pagenum="206"/>
              of the accelerated degrees of velocity, anſwering to the triangle
                <lb/>
              A B C, hath paſſed in ſuch a time ſuch a ſpace, it is very reaſonable
                <lb/>
              and probable, that making uſe of the uniform velocities anſwering
                <lb/>
              to the parallelogram, it ſhall paſſe with an even motion in the
                <lb/>
              ſame time a ſpace double to that paſſed by the accelerate
                <lb/>
              tion.</s>
            </p>
            <p type="main">
              <s>SAGR. </s>
              <s>I am entirely ſatisfied. </s>
              <s>And if you call this a probable
                <lb/>
              Diſcourſe, what ſhall the neceſſary demonſtrations be? </s>
              <s>I wiſh
                <lb/>
              that in the whole body of common Philoſophy, I could find one
                <lb/>
              that was but thus
                <lb/>
                <arrow.to.target n="marg408"/>
              </s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg408"/>
                <emph type="italics"/>
              In natural
                <lb/>
              ences it is not
                <lb/>
              ceſſary to ſeek
                <lb/>
              thematicall
                <lb/>
              dence.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>SIMP. </s>
              <s>It is not neceſſary in natural Philoſophy to ſeek
                <lb/>
              ſite Mathematical evidence.</s>
            </p>
            <p type="main">
              <s>SAGR. </s>
              <s>But this point of motion, is it not a natural queſtion?
                <lb/>
              </s>
              <s>and yet I cannot find that
                <emph type="italics"/>
              Ariſtotle
                <emph.end type="italics"/>
              hath demonſtrated any the
                <lb/>
              leaſt accident of it. </s>
              <s>But let us no longer divert our intended
                <lb/>
              Theme, nor do you fail, I pray you
                <emph type="italics"/>
              Salviatus,
                <emph.end type="italics"/>
              to tell me that
                <lb/>
              which you hinted to me to be the cauſe of the
                <emph type="italics"/>
              Pendulum's
                <emph.end type="italics"/>
                <lb/>
              eſcence, beſides the reſiſtance of the
                <emph type="italics"/>
              Medium
                <emph.end type="italics"/>
              ro penetration.</s>
            </p>
            <p type="main">
              <s>SALV. </s>
              <s>Tell me; of two
                <emph type="italics"/>
              penduli
                <emph.end type="italics"/>
              hanging at unequal
                <lb/>
              ces, doth not that which is faſtned to the longer threed make its
                <lb/>
              vibrations more ſeldome?</s>
            </p>
            <p type="main">
              <s>
                <arrow.to.target n="marg409"/>
              </s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="marg409"/>
                <emph type="italics"/>
              The
                <emph.end type="italics"/>
              pendulum
                <lb/>
                <emph type="italics"/>
              hanging at a
                <lb/>
              er threed, maketh
                <lb/>
              its vibrations more
                <lb/>
              ſeldome than the
                <emph.end type="italics"/>
                <lb/>
              pendulum
                <emph type="italics"/>
              hanging
                <lb/>
              at a ſhorter threed.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>SAGR. Yes, if they be moved to equall diſtances from their
                <lb/>
              perpendicularity.</s>
            </p>
            <p type="main">
              <s>SALV. </s>
              <s>This greater or leſſe elongation importeth nothing at
                <lb/>
              all, for the ſame
                <emph type="italics"/>
              pendulum
                <emph.end type="italics"/>
              alwayes maketh its reciprocations in
                <lb/>
              quall times, be they longer or ſhorter, that is, though the
                <emph type="italics"/>
              pendulum
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>
                <arrow.to.target n="marg410"/>
                <lb/>
              be little or much removed from its perpendicularity, and if they
                <lb/>
              are not abſolutely equal, they are inſenſibly different, as
                <lb/>
              rience may ſhew you: and though they were very unequal, yet
                <lb/>
              would they not diſcountenance, but favour our cauſe. </s>
              <s>
                <lb/>
              fore let us draw the perpendicular A B [
                <emph type="italics"/>
              in Fig.
                <emph.end type="italics"/>
              9.] and hang from
                <lb/>
              the point A, upon the threed A C, a plummet C, and another
                <lb/>
              on the ſame threed alſo, which let be E, and the threed A C, being
                <lb/>
              removed from its perpendicularity, and then letting go the
                <lb/>
              mets C and E, they ſhall move by the arches C B D, E G F, and
                <lb/>
              the plummet E, as hanging at a leſſer diſtance, and withall, as
                <lb/>
              (by what you ſaid) leſſe removed, will return back again faſter,
                <lb/>
              and make its vibrations more frequent than the plummet C, and
                <lb/>
              therefore ſhall hinder the ſaid plummet C, from running ſo much
                <lb/>
              farther towards the term D, as it would do, if it were free: and
                <lb/>
              thus the plummet E bringing unto it in every vibration continuall
                <lb/>
                <arrow.to.target n="marg411"/>
                <lb/>
              impediment, it ſhall finally reduce it to quieſcence. </s>
              <s>Now the
                <lb/>
              ſame threed, (taking away the middle plummet) is a compoſition
                <lb/>
              of many grave
                <emph type="italics"/>
              penduli,
                <emph.end type="italics"/>
              that is, each of its parts is ſuch a
                <emph type="italics"/>
                <lb/>
              lum
                <emph.end type="italics"/>
              faſtned neerer and neerer to the point A, and therefore </s>
            </p>
          </chap>
        </body>
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    </archimedes>
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