Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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page |< < (24) of 213 > >|
DE CENTRO GRAVIT. SOLID.
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            <s xml:space="preserve">
              <pb o="24" file="0159" n="159" rhead="DE CENTRO GRAVIT. SOLID."/>
            los contineant. </s>
            <s 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: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: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:space="preserve">Siuero axes non ſint in eadem recta linea, demittan
              <lb/>
            tur a punctis d, f perpendiculares ad baſis planum, d g, fh:
              <lb/>
            </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">iungantur e g, e h. </s>
            <s 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:space="preserve">& </s>
            <s xml:space="preserve">ſunt
              <lb/>
              <anchor type="figure" xlink:label="fig-0159-01a" xlink:href="fig-0159-01"/>
            anguli ad g h re-
              <lb/>
            cti, quare & </s>
            <s xml:space="preserve">re-
              <lb/>
            liquus e d g æqua
              <lb/>
            lis erit reliquo
              <lb/>
            e fh: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">triangu-
              <lb/>
            lum d e g triãgu-
              <lb/>
            lo f e h ſimile. </s>
            <s xml:space="preserve">er-
              <lb/>
            go g d ad d e eſt,
              <lb/>
            ut h f ad f e: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">per
              <lb/>
            mutando g d ad
              <lb/>
            h f, ut d e ad e f.
              <lb/>
            </s>
            <s xml:space="preserve">Sed ſolidum a b
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            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:space="preserve">ergo & </s>
            <s xml:space="preserve">ean-
              <lb/>
            dẽ habebit, quã
              <lb/>
            axis d e a l e f axẽ</s>
          </p>
          <div type="float" level="2" n="3">
            <figure xlink:label="fig-0159-01" xlink:href="fig-0159-01a">
              <image file="0159-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0159-01"/>
            </figure>
          </div>
          <p>
            <s xml:space="preserve">Poſtremo ſint
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            ſolida parallelepi
              <lb/>
            peda a b, c d in</s>
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