Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

< >
[51.] V.
[52.] DEMONSTRATIO SECVNDAE PARTIS.
[53.] COMMENTARIVS.
[54.] DEMONSTRATIO TERTIAE PARTIS.
[55.] COMMENTARIVS.
[56.] DEMONSTRATIO QVARTAE PARTIS.
[57.] DEMONSTRATIO QVINT AE PARTIS.
[58.] FINIS LIBRORVM ARCHIMEDIS DE IIS, QVAE IN AQVA VEHVNTVR.
[59.] FEDERICI COMMANDINI VRBINATIS LIBER DE CENTRO GRAVITATIS SOLIDORV M.
[60.] CVM PRIVILEGIO IN ANNOS X. BONONIAE, Ex Officina Alexandri Benacii. M D LXV.
[61.] ALEXANDRO FARNESIO CARDINALI AMPLISSIMO ET OPTIMO.
[62.] FEDERICI COMMANDINI VRBINATIS LIBER DE CENTRO GRAVITATIS SOLIDORVM. DIFFINITIONES.
[63.] PETITIONES.
[64.] THEOREMA I. PROPOSITIO I.
[65.] THEOREMA II. PROPOSITIO II.
[66.] THE OREMA III. PROPOSITIO III.
[67.] THE OREMA IIII. PROPOSITIO IIII.
[68.] ALITER.
[69.] THEOREMA V. PROPOSITIO V.
[70.] COROLLARIVM.
[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.
< >
page |< < (24) of 213 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div242" type="section" level="1" n="84">
          <p>
            <s xml:id="echoid-s3954" xml:space="preserve">
              <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:
              <lb/>
            </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
              <lb/>
              <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-
              <lb/>
            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-
              <lb/>
            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-
              <lb/>
            dẽ habebit, quã
              <lb/>
            axis d e a l e f axẽ</s>
          </p>
          <p>
            <s xml:id="echoid-s3973" xml:space="preserve">Poſtremo ſint
              <lb/>
            ſolida parallelepi
              <lb/>
            peda a b, c d </s>
          </p>
        </div>
      </text>
    </echo>