Valerio, Luca, De centro gravitatis solidorum, 1604

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    <archimedes>
      <text>
        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="043/01/093.jpg" pagenum="6"/>
              quàm A: ergo & F maior quàm
                <lb/>
              E, minor maiori, quod eſt ab­
                <lb/>
              ſurdum. </s>
              <s>Non igitur maior eſt
                <lb/>
              proportio A ad B quàm C ad
                <lb/>
              D: eadem autem ratione non
                <lb/>
              maior erit proportio B ad A
                <expan abbr="quã">quam</expan>
                <lb/>
              D ad C, hoc eſt non minor A
                <lb/>
              ad B, quàm C ad D; eſt igitur
                <lb/>
              A ad B, vt C ad D. </s>
            </p>
            <figure id="id.043.01.093.1.jpg" xlink:href="043/01/093/1.jpg" number="66"/>
            <p type="main">
              <s>Rurſus in ſecunda parte hypotheſis, quæ attinet ad mi­
                <lb/>
              norem defectum: ſi non eſt A ad B vt C ad D; eſto, ſi fie­
                <lb/>
              ri poteſt, minor proportio A ad B quàm C ad D. igitur A
                <lb/>
              ad aliam quam B minorem eandem habebit
                <expan abbr="proportionẽ">proportionem</expan>
              ,
                <lb/>
              quam C ad D, eſto illa E: ſintque
                <lb/>
              aliæ duæ magnitudines, G minor
                <lb/>
              quàm A minori defectu magnitudi­
                <lb/>
              ne eiuſdem generis cum A, quam
                <lb/>
              quis voluerit, & F minor quàm B,
                <lb/>
              & maior quàm E: ſit autem G ad
                <lb/>
              F, vt C ad D, hoc eſt vt A ad E.
                <lb/>
              </s>
              <s>Quoniam igitur permutando eſt vt
                <lb/>
              G ad A, ita F ad E, & G eſt mi­
                <lb/>
                <figure id="id.043.01.093.2.jpg" xlink:href="043/01/093/2.jpg" number="67"/>
                <lb/>
              nor quàm A; erit & F minor quàm E, maior mino­
                <lb/>
              ri, quod eſt abſurdum; non igitur minor eſt proportio
                <lb/>
              A ad B quàm C ad D: eadem autem ratione non minor
                <lb/>
              erit proportio B ad A, quàm D ad C, hoc eſt non maior
                <lb/>
              A ad B, quàm C ad D; eſt igitur A ad B vt C ad D.
                <lb/>
              </s>
              <s>Quod demonſtrandum erat. </s>
            </p>
            <p type="head">
              <s>
                <emph type="italics"/>
              PROPOSITIO III.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>Si maior, vel minor prima ad vnà maiorem, vel
                <lb/>
              minorem ſecunda, minori exceſſu, vel defectu </s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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