Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

< >
[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.]
< >
page |< < (25) of 213 > >|
DE CENTRO GRAVIT. SOLID.
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div type="section" level="1" n="85">
          <pb o="25" file="0161" n="161" rhead="DE CENTRO GRAVIT. SOLID."/>
          <p>
            <s xml:space="preserve">Sint duo priſmata a e, a f, quorum eadem baſis quadri-
              <lb/>
            latera a b c d: </s>
            <s xml:space="preserve">ſitq; </s>
            <s xml:space="preserve">priſmatis a e altitudo e g; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">priſmatis
              <lb/>
            a f altitudo f h. </s>
            <s xml:space="preserve">Dico priſma a e ad priſma a f eam habere
              <lb/>
            proportionem, quam e g ad f h. </s>
            <s xml:space="preserve">iungatur enim a c: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">in
              <lb/>
            unoquoque priſmate duo priſmata intelligantur, quorum
              <lb/>
            baſes ſint triangu
              <lb/>
              <anchor type="figure" xlink:label="fig-0161-01a" xlink:href="fig-0161-01"/>
            la a b c, a c d. </s>
            <s xml:space="preserve">habe
              <lb/>
            bunt duo priſma-
              <lb/>
            te in eadem baſi
              <lb/>
            a b c conſtituta,
              <lb/>
            proportionem eã
              <lb/>
            dem, quam ipſo-
              <lb/>
            rum altitudines e
              <lb/>
            g, f h, exiam de-
              <lb/>
            monſtratis. </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſi-
              <lb/>
            militer alia duo,
              <lb/>
            quæ ſunt in baſi a
              <lb/>
            c d. </s>
            <s xml:space="preserve">quare totum priſma a e ad priſma a f eandem propor
              <lb/>
              <anchor type="note" xlink:label="note-0161-01a" xlink:href="note-0161-01"/>
            tionem habebit, quam altitudo e g ad f h altitudinem.
              <lb/>
            </s>
            <s xml:space="preserve">Quòd cum priſmata ſint pyramidum tripla, & </s>
            <s xml:space="preserve">ipſæ pyrami
              <lb/>
            des, quarum eadem eſt baſis quadrilatera, & </s>
            <s xml:space="preserve">altitudo priſ-
              <lb/>
            matum altitudini æqualis, eam inter ſe proportionem ha-
              <lb/>
            bebunt, quam altitudines.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="1">
            <figure xlink:label="fig-0161-01" xlink:href="fig-0161-01a">
              <image file="0161-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0161-01"/>
            </figure>
            <note position="right" xlink:label="note-0161-01" xlink:href="note-0161-01a" xml:space="preserve">12. quinti</note>
          </div>
          <p>
            <s xml:space="preserve">Si uero priſmata baſes æquales habeant, nõ eaſdem, ſint
              <lb/>
            duo eiuſmodi priſmata a e, f l: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſit baſis priſmatis a e qua
              <lb/>
            drilaterum a b c d; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">priſmatis f l quadrilaterum f g h k.
              <lb/>
            </s>
            <s xml:space="preserve">Dico priſma a e ad priſma f l ita eſſe, ut altitudo illius ad
              <lb/>
            huius altitudinem. </s>
            <s xml:space="preserve">nam ſi altitudo ſit eadem, intelligãtur
              <lb/>
            duæ pyramides a b c d e, f g h k l. </s>
            <s xml:space="preserve">quæ ĩter ſe æquales erũt,
              <lb/>
              <anchor type="note" xlink:label="note-0161-02a" xlink:href="note-0161-02"/>
            cum æ quales baſes, & </s>
            <s xml:space="preserve">altitudinem eandem habeant. </s>
            <s xml:space="preserve">quare
              <lb/>
            & </s>
            <s xml:space="preserve">priſmata a e, f l, quæ ſunt harù pyramidum tripla, æqua-
              <lb/>
              <anchor type="note" xlink:label="note-0161-03a" xlink:href="note-0161-03"/>
            lia ſint neceſſe eſt. </s>
            <s xml:space="preserve">ex quibus perſpicue conſtat propoſitũ.
              <lb/>
            </s>
            <s xml:space="preserve">Si uero altitudo priſmatis f l ſit maior, à priſmate f l ab-
              <lb/>
            ſcindatur priſma fm, quod æque altum ſit, atq; </s>
            <s xml:space="preserve">ipſum a e.</s>
            <s xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>