Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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FED. COMMANDINI
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            <s xml:space="preserve">ABSCINDATVR à portione conoidis rectanguli
              <lb/>
            a b c alia portio e b f, plano baſi æquidiſtante: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">eadem
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            portio ſecetur alio plano per axem; </s>
            <s xml:space="preserve">ut ſuperficiei ſectio ſit
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            parabole a b c: </s>
            <s xml:space="preserve">planorũ portiones abſcindentium rectæ
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            lineæ a c, e f: </s>
            <s xml:space="preserve">axis autem portionis, & </s>
            <s xml:space="preserve">ſectionis diameter
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            b d; </s>
            <s xml:space="preserve">quam linea e fin puncto g ſecet. </s>
            <s xml:space="preserve">Dico portionem co-
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            noidis a b c ad portionem e b f duplam proportionem ha-
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            bere eius, quæ eſt baſis a c ad baſim e f; </s>
            <s xml:space="preserve">uel axis d b ad b g
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            axem. </s>
            <s xml:space="preserve">Intelligantur enim duo coni, ſeu coni portiones
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            a b c, e b f, eãdem baſim, quam portiones conoidis, & </s>
            <s xml:space="preserve">æqua
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            lem habentes altitudinem. </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">quoniam a b c portio conoi
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            dis ſeſquialtera eſt coni, ſeu portionis coni a b c; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">portio
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            e b f coniſeu portionis coni e b feſt ſeſquialtera, quod de-
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              <anchor type="figure" xlink:label="fig-0202-01a" xlink:href="fig-0202-01"/>
            monſtrauit Archimedes in propoſitionibus 23, & </s>
            <s xml:space="preserve">24 libri
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            de conoidibus, & </s>
            <s xml:space="preserve">ſphæroidibus: </s>
            <s xml:space="preserve">erit conoidis portio ad
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            conoidis portionem, ut conus ad conum, uel ut coni por-
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            tio ad coni portionem. </s>
            <s xml:space="preserve">Sed conus, uel coni portio a b c ad
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            conum, uel coni portionem e b f compoſitam proportio-
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            nem habet ex proportione baſis a c ad baſim e f, & </s>
            <s xml:space="preserve">ex pro-
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            portione altitudinis coni, uel coni portionis a b c ad alti-
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            tudinem ipſius e b f, ut nos demonſtrauimus in com men-
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            tariis in undecimam propoſitionem eiuſdem libri A rchi-
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            medis: </s>
            <s xml:space="preserve">altitudo autem ad altitudinem eſt, ut axis ad axem.
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            </s>
            <s xml:space="preserve">quod quidem in conis rectis perſpicuum eſt, in ſcalenis ue</s>
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