Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

< >
[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.]
[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.]
< >
page |< < of 213 > >|
FED. COMMANDINI
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div type="section" level="1" n="90">
          <p>
            <s xml:space="preserve">
              <pb file="0176" n="176" rhead="FED. COMMANDINI"/>
            pyramidem, uel conum, uel coni portionem candem pro-
              <lb/>
            portionem habet, quam baſes ab, cd unà cum e ſ ad ba-
              <lb/>
            ſim a b. </s>
            <s xml:space="preserve">quod demonſtrare uolebamus.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="1">
            <figure xlink:label="fig-0175-01" xlink:href="fig-0175-01a">
              <image file="0175-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0175-01"/>
            </figure>
            <figure xlink:label="fig-0175-02" xlink:href="fig-0175-02a">
              <image file="0175-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0175-02"/>
            </figure>
            <note position="right" xlink:label="note-0175-01" xlink:href="note-0175-01a" xml:space="preserve">6. 11. duo
              <lb/>
            decimi</note>
          </div>
          <p>
            <s xml:space="preserve">Fruſtum uero a d æquale eſſe pyramidi, uel co
              <lb/>
            no, uel coni portioni, cuius baſis conſtat ex baſi-
              <lb/>
            bus a b, c d, e f, & </s>
            <s xml:space="preserve">altitudo fruſti altitudini eſt æ-
              <lb/>
            qualis, hoc modo oſten demus.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">Sit fruſtum pyramidis a b c d e f, cuius maior baſis trian-
              <lb/>
            gulum a b c; </s>
            <s xml:space="preserve">minor d e f: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſecetur plano baſibus æquidi-
              <lb/>
            ſtante, quod ſectionem faciat triangulum g h k inter trian-
              <lb/>
            gula a b c, d e f proportionale. </s>
            <s xml:space="preserve">Iam ex iis, quæ demonſtrata
              <lb/>
            ſuntin 23. </s>
            <s xml:space="preserve">huius, patet ſruſtum a b c d e f diuidi in tres pyra
              <lb/>
            mides proportionales; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">earum maiorem eſſe pyramidẽ
              <lb/>
            a b c d minorẽ uero d e f b. </s>
            <s xml:space="preserve">ergo pyramis à triangulo g h k
              <lb/>
            conſtituta, quæ altitudinem habeat ſruſti altitudini æqua-
              <lb/>
            lem, proportionalis eſtinter pyramides a b c d, d e f b: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">
              <lb/>
            idcirco fruſtum a b c d e f tribus dictis pyramidibus æqua
              <lb/>
            le erit. </s>
            <s xml:space="preserve">Itaque ſi intelligatur alia pyra-
              <lb/>
              <anchor type="figure" xlink:label="fig-0176-01a" xlink:href="fig-0176-01"/>
            mis æque alta, quæ baſim habeat ex tri
              <lb/>
            bus baſibus a b c, d e f, g h k conſtan-
              <lb/>
            tem; </s>
            <s xml:space="preserve">perſpicuum eſtipſam eiſdem py-
              <lb/>
            ramidibus, & </s>
            <s xml:space="preserve">propterea ipſi fruſto æ-
              <lb/>
            qualem eſſe.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="2">
            <figure xlink:label="fig-0176-01" xlink:href="fig-0176-01a">
              <image file="0176-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0176-01"/>
            </figure>
          </div>
          <p>
            <s xml:space="preserve">Rurſus ſit ſruſtum pyramidis a g, cu
              <lb/>
            ius maior baſis quadrilaterum a b c d,
              <lb/>
            minor e f g h: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſecetur plano baſi-
              <lb/>
            bus æquidiſtante, ita ut fiat ſectio qua-
              <lb/>
            drilaterum K lm n, quod ſit proportio
              <lb/>
            nale inter quadrilatera a b c d, e f g h. </s>
            <s xml:space="preserve">Dico pyramidem,
              <lb/>
            cuius baſis ſit æqualis tribus quadrilateris a b c d, _k_ l m n,
              <lb/>
            e f g h, & </s>
            <s xml:space="preserve">altitudo æqualis altitudini fruſti, ipſi fruſto a g
              <lb/>
            æqualem eſſe. </s>
            <s xml:space="preserve">Ducatur enim planum per lineas f b, h d,</s>
          </p>
        </div>
      </text>
    </echo>