Ceva, Giovanni, Geometria motus, 1692

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              <s id="s.000280">
                <pb pagenum="26" xlink:href="022/01/032.jpg"/>
              ad verticem parabolarum, vel trilineorum; erit rectangu­
                <lb/>
              lum ad parabolam ſibi inſcriptam vt aggregatum
                <expan abbr="exponẽ-tium">exponen­
                  <lb/>
                tium</expan>
              vtriuſque poteſtatis ad exponentem altioris ipſarum
                <lb/>
              poteſtatum parabolæ; & ad trilineum vt aggregatum ex­
                <lb/>
              ponentium poteſtatum trilinei ad exponentem inferioris
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              poteſtatis eiuſdemmet trilinei. </s>
              <s id="s.000281">Sic enim in expoſita figu­
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              ra prædicta, ſi eſſet quadratum ex FG ad quadratum ex
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              IH, ſicut cubus ex FK ad cubum ex IH, eſſet rectangulum
                <lb/>
              GF in FK ad figuram GFK (quæ tunc foret trilineum, vt
                <lb/>
              5 ad 2; nam vbi poteſtas abſciſſarum maior eſt illa applica.
                <lb/>
              </s>
              <s id="s.000282">tarum eſt ſemper GF trilineum. </s>
              <s id="s.000283">Simili modo, ſi ſit vt qua­
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              dratum ex FK ad quadratum ex KI ita cubocubus ex FG
                <lb/>
              ad cubocubum ex IH; hoc eſt ſi ſit cubus ex FG ad
                <expan abbr="cubũ">cubum</expan>
                <lb/>
              ex IH, vt linea FK ad KI (tolluntur enim vtrinque ex ſimi­
                <lb/>
              libus ſimiles rationes) erit ſigura GFK parabola, ad quam
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              ſibi circumſcriptum rectangulum eandem habebit
                <expan abbr="rationẽ">rationem</expan>
              ,
                <lb/>
              quam 4 ad 3, & ſic dicendum erit de omnibus alijs para­
                <lb/>
              bolis atque trilineis. </s>
            </p>
            <p type="main">
              <s id="s.000284">
                <emph type="center"/>
              DEMONSTRATIO.
                <emph.end type="center"/>
              </s>
            </p>
            <p type="main">
              <s id="s.000285">VErùm vt propoſitum oſtendamus, eſto quælibet ex
                <lb/>
              parabolis GFK, nimirum quadratocubus ex FG ad
                <lb/>
              quadratocubum ex IH habeat eandem rationem, quam̨
                <lb/>
              cubus ex FK ad cubum ex IK. Demonſtro, rectangulum
                <lb/>
              GF in FK habere eandem rationem ad parabolam GFK,
                <lb/>
              quam aggregatum exponentium 8 ad maiorem exponen­
                <lb/>
              tem 5. Primùm, quam rationem habet rectangulum GF in
                <lb/>
              FK ad parabolam GFK, eandem habebit rectangulum HI
                <lb/>
              in IK ad parabolam HIK (hoc enim demonſtrabimus in­
                <lb/>
              frà) permutandoque, erit rectangulum GF in FK ad re­
                <lb/>
              ctangulum HI in IK, vt parabola GFK ad parabolam HIK;
                <lb/>
              componuntur verò illa rectangula ex rationibus GF ad
                <lb/>
              IH, & FK ad IK, ergo etiam parabola ad parabolam com-</s>
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          </chap>
        </body>
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