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 |< < (46) of 213 > >|
DE CENTRO GRAVIT. SOLID.
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div type="section" level="1" n="95">
          <p>
            <s xml:space="preserve">
              <pb o="46" file="0203" n="203" rhead="DE CENTRO GRAVIT. SOLID."/>
            ro ita demonſtrabitur. </s>
            <s xml:space="preserve">Ducatur à puncto b ad planum ba-
              <lb/>
            ſis a c perpendicularis linea b h, quæ ipſam e fin K ſecet.
              <lb/>
            </s>
            <s xml:space="preserve">erit b h altitudo coni, uel coni portionis a b c: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">b K altitu
              <lb/>
              <anchor type="note" xlink:label="note-0203-01a" xlink:href="note-0203-01"/>
            do e f g. </s>
            <s xml:space="preserve">Quod cum lineæ a c, e f inter ſe æ quidiſtent, ſunt
              <lb/>
            enim planorum æ quidiſtantium ſectiones: </s>
            <s xml:space="preserve">habebit d b ad
              <lb/>
              <anchor type="note" xlink:label="note-0203-02a" xlink:href="note-0203-02"/>
            b g proportionem ean dem, quam h b ad b k. </s>
            <s xml:space="preserve">quare por-
              <lb/>
            tio conoidis a b c ad portionem e f g proportionem habet
              <lb/>
            compoſitam ex proportione baſis a c ad baſim e f; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ex
              <lb/>
            proportione d b axis ad axem b g. </s>
            <s xml:space="preserve">Sed circulus, uel
              <lb/>
              <anchor type="note" xlink:label="note-0203-03a" xlink:href="note-0203-03"/>
            ellipſis circa diametrum a c ad circulum, uel ellipſim
              <lb/>
              <anchor type="note" xlink:label="note-0203-04a" xlink:href="note-0203-04"/>
            circa e f, eſt ut quadratum a c ad quadratum e f; </s>
            <s xml:space="preserve">hoc eſt ut
              <lb/>
            quadratũ a d ad quadratũ e g. </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">quadratum a d ad quadra
              <lb/>
            tum e g eſt, ut linea d b ad lineam b g. </s>
            <s xml:space="preserve">circulus igitur, uel el
              <lb/>
            lipſis circa diametrum a c ad circulũ, uel ellipſim circa e f,
              <lb/>
              <anchor type="note" xlink:label="note-0203-05a" xlink:href="note-0203-05"/>
            hoc eſt baſis ad baſim eandem proportionem habet, quã
              <lb/>
              <anchor type="note" xlink:label="note-0203-06a" xlink:href="note-0203-06"/>
            d b axis ad axem b g. </s>
            <s xml:space="preserve">ex quibus ſequitur portionem a b c
              <lb/>
            ad portionem e b f habere proportionem duplam eius,
              <lb/>
            quæ eſt baſis a c ad bafim e f: </s>
            <s xml:space="preserve">uel axis d b ad b g axem. </s>
            <s xml:space="preserve">quod
              <lb/>
            demonſtrandum proponebatur.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="1">
            <figure xlink:label="fig-0202-01" xlink:href="fig-0202-01a">
              <image file="0202-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0202-01"/>
            </figure>
            <note position="right" xlink:label="note-0203-01" xlink:href="note-0203-01a" xml:space="preserve">16. unde-
              <lb/>
            cimi.</note>
            <note position="right" xlink:label="note-0203-02" xlink:href="note-0203-02a" xml:space="preserve">4 ſexti.</note>
            <note position="right" xlink:label="note-0203-03" xlink:href="note-0203-03a" xml:space="preserve">2. duode
              <lb/>
            cimi</note>
            <note position="right" xlink:label="note-0203-04" xlink:href="note-0203-04a" xml:space="preserve">7. de co-
              <lb/>
            noidibus
              <lb/>
            & ſphæ-
              <lb/>
            roidibus</note>
            <note position="right" xlink:label="note-0203-05" xlink:href="note-0203-05a" xml:space="preserve">15. quinti</note>
            <note position="right" xlink:label="note-0203-06" xlink:href="note-0203-06a" xml:space="preserve">20. primi
              <lb/>
            conicorũ</note>
          </div>
        </div>
        <div type="section" level="1" n="96">
          <head xml:space="preserve">THEOREMA XXV. PROPOSITIO XXXI.</head>
          <p>
            <s xml:space="preserve">Cuiuslibet fruſti à portione rectanguli conoi
              <lb/>
            dis abſcisſi, centrum grauitatis eſt in axe, ita ut
              <lb/>
            demptis primum à quadrato, quod fit ex diame-
              <lb/>
            tro maioris baſis, tertia ipſius parte, & </s>
            <s xml:space="preserve">duabus
              <lb/>
            tertiis quadrati, quod fit ex diametro baſis mino-
              <lb/>
            ris: </s>
            <s xml:space="preserve">deinde à tertia parte quadrati maioris baſis
              <lb/>
            rurſus dempta portione, ad quam reliquum qua
              <lb/>
            drati baſis maioris unà cum dicta portione duplã
              <lb/>
            proportionem habeat eius, quæ eſt quadrati ma-</s>
          </p>
        </div>
      </text>
    </echo>