Ceva, Giovanni, Geometria motus, 1692

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              <s id="s.000291">
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              eius HIK eße in octuplicata ratione eiuſdem A ad B; quod
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              idem omnino diceretur ſi figura GFK trilineum eſſet. </s>
              <s id="s.000292">Ratio
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              autem A ad B dicetur impoſterum logarithmica poteſtatum
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              parabolæ, ſeu trilinei, aut hyperbolæ.
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            <p type="main">
              <s id="s.000293">
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              ASSVMPTVM.
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            </p>
            <p type="main">
              <s id="s.000294">REliquum eſt vt oſtendamus, parabolam GFK ad
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              portionem HIK eſſe vt rectangulum GF ad rectan­
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              gulum HI in IK, ſcilicet eſſe in ratione compoſita baſium,
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              & altitudinum parabolarum, quod nempe ſic oſtendetur,
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              Sit vt ſupra FGK parabola, eiuſque portio IHK; exiſtenti­
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              bus verò applicatis FG, IH, fiat EG ad IE vt FK ad KI, ſit­
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                <arrow.to.target n="marg68"/>
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              que IE baſis, et K vertex parabolę IEK ſimilis ipſi GFK pa­
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              tet propter ſimilitudinem figurarum, eſſe parabolam GFK
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              ad parabolam IEK in eadem duplicata ratione FG ad IE,
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              in qua nempe eſt rectangulum GF in FK ad ſibi ſimile re­
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              ctangulum EI in IK, ob idque rectangulum GF in FK ad
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              rectangulum EI in IK, cum ſint interſe vt parabola GFK ad
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              parabolam EIK, hæc verò parabola ad ipſam IHK habeat
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              eandem rationem, ac IE ad IH; ſeu ob eandem altitudinem
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              IK vt rectangulum EI in IK ad rectangulum HI in IK, erit
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              ex æquali parabola GFK ad parabolam HIK vt rectangu­
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              lum GF in FK ad rectangulum HI in IK. </s>
              <s id="s.000295">Quod &c. </s>
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              Tab.
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              3.
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              Fig.
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              2.</s>
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              PROP. XIV. THEOR. XIV.
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            <p type="margin">
              <s id="s.000298">
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              Tab.
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              2.
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              fig.
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              3.</s>
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            <p type="main">
              <s id="s.000299">IN quacunque hyperbola (excepta ſemper conica) cu­
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              ius aſſymptoti EA, EM, ſi ſit poteſtas applicatarum DC
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              AB altior poteſtate abſciſſarum AE, ED (ſic enim finitą
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              erit magnitudine ſecundum eam aſſymptoton, quæ appli­
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              catis parallela eſt) ſpatium ipſum hyperbolæ & BAE &
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              ad ſui portionem & CDE & habebit eandem rationem, ac
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              rectangulum BAE ad rectangulum CDE, ſeu (aſſumpta </s>
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          </chap>
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