Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

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[71.] THEOREMA VI. PROPOSITIO VI.
[72.] THE OREMA VII. PROPOSITIO VII.
[73.] THE OREMA VIII. PROPOSITIO VIII.
[74.] THE OREMA IX. PROPOSITIO IX.
[75.] PROBLEMA I. PROPOSITIO X.
[76.] PROBLEMA II. PROPOSITIO XI.
[77.] PROBLEMA III. PROPOSITIO XII.
[78.] PROBLEMA IIII. PROPOSITIO XIII.
[79.] THEOREMA X. PROPOSITIO XIIII.
[80.] THE OREMA XI. PROPOSITIO XV.
[81.] THE OREMA XII. PROPOSITIO XVI.
[82.] THE OREMA XIII. PROPOSITIO XVII.
[83.] THEOREMA XIIII. PROPOSITIO XVIII.
[84.] THEOREMA XV. PROPOSITIO XIX.
[85.] THE OREMA XVI. PROPOSITIO XX.
[86.] THEOREMA XVII. PROPOSITIO XXI.
[87.] THE OREMA XVIII. PROPOSITIO XXII.
[88.] THEOREMA XIX. PROPOSITIO XXIII.
[89.] PROBLEMA V. PROPOSITIO XXIIII.
[90.] THEOREMA XX. PROPOSITIO XXV.
[91.] THEOREMA XXI. PROPOSITIO XXVI.
[92.] THEOREMA XXII. PROPOSITIO XXVII.
[93.] PROBLEMA VI. PROPOSITIO XX VIII.
[94.] THE OREMA XXIII. PROPOSITIO XXIX.
[95.] THEOREMA XXIIII. PROPOSITIO XXX.
[96.] THEOREMA XXV. PROPOSITIO XXXI.
[97.] FINIS LIBRI DE CENTRO GRAVITATIS SOLIDORVM.
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            <s xml:id="echoid-s5060" xml:space="preserve">ABSCINDATVR à portione conoidis rectanguli
              <lb/>
            a b c alia portio e b f, plano baſi æquidiſtante: </s>
            <s xml:id="echoid-s5061" xml:space="preserve">& </s>
            <s xml:id="echoid-s5062" xml:space="preserve">eadem
              <lb/>
            portio ſecetur alio plano per axem; </s>
            <s xml:id="echoid-s5063" xml:space="preserve">ut ſuperficiei ſectio ſit
              <lb/>
            parabole a b c: </s>
            <s xml:id="echoid-s5064" xml:space="preserve">planorũ portiones abſcindentium rectæ
              <lb/>
            lineæ a c, e f: </s>
            <s xml:id="echoid-s5065" xml:space="preserve">axis autem portionis, & </s>
            <s xml:id="echoid-s5066" xml:space="preserve">ſectionis diameter
              <lb/>
            b d; </s>
            <s xml:id="echoid-s5067" xml:space="preserve">quam linea e fin puncto g ſecet. </s>
            <s xml:id="echoid-s5068" xml:space="preserve">Dico portionem co-
              <lb/>
            noidis a b c ad portionem e b f duplam proportionem ha-
              <lb/>
            bere eius, quæ eſt baſis a c ad baſim e f; </s>
            <s xml:id="echoid-s5069" xml:space="preserve">uel axis d b ad b g
              <lb/>
            axem. </s>
            <s xml:id="echoid-s5070" 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:id="echoid-s5071" xml:space="preserve">æqua
              <lb/>
            lem habentes altitudinem. </s>
            <s xml:id="echoid-s5072" xml:space="preserve">& </s>
            <s xml:id="echoid-s5073" xml:space="preserve">quoniam a b c portio conoi
              <lb/>
            dis ſeſquialtera eſt coni, ſeu portionis coni a b c; </s>
            <s xml:id="echoid-s5074" xml:space="preserve">& </s>
            <s xml:id="echoid-s5075" xml:space="preserve">portio
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            e b f coniſeu portionis coni e b feſt ſeſquialtera, quod de-
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              <figure xlink:label="fig-0202-01" xlink:href="fig-0202-01a" number="149">
                <image file="0202-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0202-01"/>
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            monſtrauit Archimedes in propoſitionibus 23, & </s>
            <s xml:id="echoid-s5076" xml:space="preserve">24 libri
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            de conoidibus, & </s>
            <s xml:id="echoid-s5077" xml:space="preserve">ſphæroidibus: </s>
            <s xml:id="echoid-s5078" xml:space="preserve">erit conoidis portio ad
              <lb/>
            conoidis portionem, ut conus ad conum, uel ut coni por-
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            tio ad coni portionem. </s>
            <s xml:id="echoid-s5079" 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:id="echoid-s5080" 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-
              <lb/>
            tariis in undecimam propoſitionem eiuſdem libri A rchi-
              <lb/>
            medis: </s>
            <s xml:id="echoid-s5081" xml:space="preserve">altitudo autem ad altitudinem eſt, ut axis ad axem.
              <lb/>
            </s>
            <s xml:id="echoid-s5082" xml:space="preserve">quod quidem in conis rectis perſpicuum eſt, in ſcalenis </s>
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