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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              <pb o="24" file="0159" n="159" rhead="DE CENTRO GRAVIT. SOLID."/>
            los contineant. </s>
            <s xml:id="echoid-s3955" xml:space="preserve">Dico ſolidum a b ad ſolidum a c eãdem ha
              <lb/>
            bere proportionem, quam axis d e ad axem e f. </s>
            <s xml:id="echoid-s3956" xml:space="preserve">Sienim
              <lb/>
            axes in eadem recta linea fuerint conſtituti, hæc duo ſoli-
              <lb/>
            da, in unum, atque i @m ſolidum conuenient. </s>
            <s xml:id="echoid-s3957" xml:space="preserve">quare ex
              <lb/>
            iis, quæ proxime tradita ſunt, habebit ſolidum a b ad ſo-
              <lb/>
            lidum a c eandem proportionem, quam axis d e ad e f
              <lb/>
            axem. </s>
            <s xml:id="echoid-s3958" xml:space="preserve">Siuero axes non ſint in eadem recta linea, demittan
              <lb/>
            tur a punctis d, f perpendiculares ad baſis planum, d g, fh:
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            </s>
            <s xml:id="echoid-s3959" xml:space="preserve">& </s>
            <s xml:id="echoid-s3960" xml:space="preserve">iungantur e g, e h. </s>
            <s xml:id="echoid-s3961" xml:space="preserve">Quoniam igitur axes cum baſibus
              <lb/>
            æquales angulos eontinent, erit d e g angulus æqualis an-
              <lb/>
            gulo f e h: </s>
            <s xml:id="echoid-s3962" xml:space="preserve">& </s>
            <s xml:id="echoid-s3963" xml:space="preserve">ſunt
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              <figure xlink:label="fig-0159-01" xlink:href="fig-0159-01a" number="114">
                <image file="0159-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0159-01"/>
              </figure>
            anguli ad g h re-
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            cti, quare & </s>
            <s xml:id="echoid-s3964" xml:space="preserve">re-
              <lb/>
            liquus e d g æqua
              <lb/>
            lis erit reliquo
              <lb/>
            e fh: </s>
            <s xml:id="echoid-s3965" xml:space="preserve">& </s>
            <s xml:id="echoid-s3966" xml:space="preserve">triangu-
              <lb/>
            lum d e g triãgu-
              <lb/>
            lo f e h ſimile. </s>
            <s xml:id="echoid-s3967" xml:space="preserve">er-
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            go g d ad d e eſt,
              <lb/>
            ut h f ad f e: </s>
            <s xml:id="echoid-s3968" xml:space="preserve">& </s>
            <s xml:id="echoid-s3969" xml:space="preserve">per
              <lb/>
            mutando g d ad
              <lb/>
            h f, ut d e ad e f.
              <lb/>
            </s>
            <s xml:id="echoid-s3970" xml:space="preserve">Sed ſolidum a b
              <lb/>
            ad ſolidum a c
              <lb/>
            eandem propor-
              <lb/>
            tionem habet,
              <lb/>
            quam d g altitu-
              <lb/>
            do ad altitudinẽ
              <lb/>
            f h. </s>
            <s xml:id="echoid-s3971" xml:space="preserve">ergo & </s>
            <s xml:id="echoid-s3972" xml:space="preserve">ean-
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            dẽ habebit, quã
              <lb/>
            axis d e a l e f axẽ</s>
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          <p>
            <s xml:id="echoid-s3973" xml:space="preserve">Poſtremo ſint
              <lb/>
            ſolida parallelepi
              <lb/>
            peda a b, c d </s>
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