Ceva, Giovanni, Geometria motus, 1692

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              ponetur ex ijſdem rationibus; & quoniam ductis inuicem
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              exponentibus poſſunt conſiderari quindecim rationes in­
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              ter ſe ſimiles, ex quibus conſtet tam ratio dictorum cubo­
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              rum, quàm huic ſimilis altera quadratocuborum, & tunc
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              GF ad IH erit triplicata, et FK ad KI quintuplicata
                <expan abbr="eiuſdẽ">eiuſdem</expan>
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              ſubquindecuplæ rationis, quæ ſit A ad B; ergo ſimul ad­
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              ditis ijſdem rationibus, quintuplicata ſcilicet, & triplicata
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              exiliet ratio octuplicata ipſius A ad B; proptereaque pa­
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              rabola GFK ad HIK, ſeu ſi conſideremus figuram & BAEL
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              auuerſam parabolæ GFK, ita vt AE ad ED ſit vt para­
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                <arrow.to.target n="marg65"/>
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              bola GFK ad
                <expan abbr="parabolã">parabolam</expan>
              HIK; AE ad ED erit pariter octu­
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              plicata eiuſdem A ad B; & cum ſit ob naturam
                <expan abbr="auuerſarũ">auuerſarum</expan>
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              FG ad HI vt DC ad AB; erit DC ad AB triplicata
                <expan abbr="eiuſdẽ">eiuſdem</expan>
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              rationis A ad B, qnare vt cubus AE ad cubum DE, itą
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              quadratocubocubus DC ad quadratocubocubum ex
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              AB: rectangulum igitur ABME ad ſpatium hyperbolicum
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              infin
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              è longum & BM & erit vt quinque ad tria, & ad vni­
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              uerſum ſpatium & BAE & vt 5 ad 8, in qua nempe ratio­
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              ne debet eſſe parabola GF
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              K
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              ad rectangulum GF in FK.
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              Quod &c. </s>
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            <p type="margin">
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              Def.
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              8.
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              huius.
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            <p type="margin">
              <s id="s.000287">
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              Pr.
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              12
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              huius.
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              </s>
            </p>
            <p type="margin">
              <s id="s.000288">
                <margin.target id="marg67"/>
                <emph type="italics"/>
              Pr.
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              9.
                <emph type="italics"/>
              huius.
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            </p>
            <p type="main">
              <s id="s.000289">
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              Corollarium.
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                <emph.end type="center"/>
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            <p type="main">
              <s id="s.000290">
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              Conſtat ſi fuerit ratio A ad B eò ſubmultiplicata rationis
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              applicatarum, quoties eſt numerus exponentis poteſtatis ab­
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              ſciſſarum eiuſdem parabolæ, eſſe ipſam parabolam ad ſui por­
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              tionem in tam multiplicata ratione A ad B, ac eſt numerus
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              aggregati exponentium ambarum poteſtatum parabola. </s>
              <s id="s.000291">Nam
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              cum eſſet quadratocubus ex FG ad quadratocubum ex IH, ſi­
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              cut cubus ex FK ad cubum ex IK, propoſita inſuper eſſet A ad
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              B. ſubquindecupla alterius dictarum ſimilium rationum ex
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              poteſt atibus parabola, oſtenſum fuit rationem A ad B ſubtri­
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              plicatam ipſius GF ad IH, & ſubquintuplicatam alterius FK
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              ad KI, & tandem oſtendimus parabolam GFK ad portionem
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              </s>
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