Ceva, Giovanni, Geometria motus, 1692

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              <s id="s.000271">
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              eiuſdem ſubduodecuplæ, erit figura GFK illius naturæ, vt
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              ſit ſemper cubus ex FK ad cubum ex KI ſicut GF ad IH, &
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              hoc modo eadem illa figura erit trilineum tertium, ſeu cu­
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              bicum, ex quo ergo ſequitur, GFK ad HIK ſit in eadem ra­
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              tione, in qua quadroquadratum ex FK ad quadroqua­
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              dratum ex KI, hoc eſt ſit vt AE ad ED; ſequiturque etiam
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                <arrow.to.target n="marg63"/>
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              ob hoc figuram GFK ſubquadruplam eſle circumſcripti
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              rectanguli GF in FK; eſt autem vt trilineum GFK ad
                <expan abbr="rectã-">rectan­
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                </expan>
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              gulum GF in FK circumſcriptum, ſic rectangulum ABME
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              ad auuerſam eidem trilineo figuram AB & EA, ergo re­
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              ctangulum ABME ſubquadruplum erit eiuſdem figuræ
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              AB & EA longitudinis infinitæ, quare ipſum rectangulum
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              erit ſubtriplum portionis & BM & longitudinis pariter im­
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              menſæ. </s>
              <s id="s.000272">Cum ita ſit, conſtat exemplo hoc quoque,
                <expan abbr="eandẽ">eandem</expan>
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              illam rationem eſſe exceſſum maioris exponentis ſuprą
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              minorem exponentem ad hoc ipſum, dictarum
                <expan abbr="poteſtatũ">poteſtatum</expan>
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              hyperbolæ. </s>
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            <p type="margin">
              <s id="s.000273">
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              Def.
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              8.
                <emph type="italics"/>
              huius.
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              </s>
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            <p type="margin">
              <s id="s.000274">
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                <emph type="italics"/>
              Pr.
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              10.
                <emph type="italics"/>
              huius.
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              </s>
            </p>
            <p type="margin">
              <s id="s.000275">
                <margin.target id="marg63"/>
                <emph type="italics"/>
              Pr.
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              10.
                <emph type="italics"/>
              huius.
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              </s>
            </p>
            <p type="margin">
              <s id="s.000276">
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                <emph type="italics"/>
              Pr.
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              9.
                <emph type="italics"/>
              huius
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              </s>
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            <p type="main">
              <s id="s.000277">
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              PROP. XIII. THEOR. XIII.
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              <s id="s.000278">SVperior demonſtratio effecta fuiſſet ampliſſima, ſi prę­
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              ponere voluiſſemus
                <expan abbr="quadraturã">quadraturam</expan>
              vt datam omnis ge­
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              neris parabolarum, & trilineorum, verùm cum iſta pars
                <expan abbr="nõ">non</expan>
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              ſit plenè tradita, vt videre eſt quinto libro infinitarum pa­
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              rabolarum eiuſdem de Angelis, ſatius ideo duximus qua­
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              draturam hyperbolarum à VValiſio, & Fermatio acutiſſi­
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              mis illis viris propoſitam omnino veram admittere, vt indè
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              eam parabolarum & trilineorum vniuerſalem, quam adhuc
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              ab alijs non habemus, facillimè, compendiosèque depro­
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              meremus. </s>
              <s id="s.000279">Hanc igitur ita proponimus vt ſubinde oſten­
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              damus. </s>
            </p>
            <p type="main">
              <s id="s.000280">Si ſimiles poteſtates applicatarum fuerint in eadem ra­
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              tione, ac ſunt interſe poteſtates quædam aliæ, & eiuſdem
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              gradus diametrorum ab ipſis applicatis abſciſſarum vſque </s>
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          </chap>
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