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="84">
          <p>
            <s xml:space="preserve">
              <pb file="0160" n="160" rhead="FED. COMMANDINI"/>
            æqualibus baſibus, quorum axes cum baſibus æquales an
              <lb/>
            gulos faciant. </s>
            <s xml:space="preserve">Dico ſolidum a b adſolidũ c d ita eſſe, ut axis
              <lb/>
            e f ad axem g h: </s>
            <s xml:space="preserve">nam ſi axes ad planum baſis recti ſint, il-
              <lb/>
            lud perſpicue conſtat: </s>
            <s xml:space="preserve">quoniam eadem linea, & </s>
            <s xml:space="preserve">axem & </s>
            <s xml:space="preserve">ſoli
              <lb/>
            di altitudinem determinabit. </s>
            <s xml:space="preserve">Si uero ſintinclinati, à pun-
              <lb/>
            ctis e g ad ſubiectum planum perpendiculares ducantur
              <lb/>
            e k, g l: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">iungantur f_k_, h l. </s>
            <s xml:space="preserve">rurſus quoniam axes cum ba
              <lb/>
            ſibus æquales faciunt angulos, eodem modo demonſtrabi
              <lb/>
            tur, triangulum e f K triangulo g h l ſimile eſſe: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">e k ad g l,
              <lb/>
            ut e f ad g h. </s>
            <s xml:space="preserve">Solidum autem a b ad ſolidum c d eſt, ut
              <lb/>
            e K ad g l. </s>
            <s xml:space="preserve">ergo & </s>
            <s xml:space="preserve">ut axis e f ad axem g h. </s>
            <s xml:space="preserve">quæ omnia de
              <lb/>
            monſtrare oportebat.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">Ex iis quæ demonſtrata ſunt, facile conſtare
              <lb/>
            poteſt, priſmata omnia & </s>
            <s xml:space="preserve">pyramides, quæ trian-
              <lb/>
            gulares baſes habent, ſiue in eiſdem, ſiue in æqua
              <lb/>
            libus baſibus conſtituantur, eandem proportio-
              <lb/>
              <anchor type="note" xlink:label="note-0160-01a" xlink:href="note-0160-01"/>
            nem habere, quam altitudines: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſi axes cum ba
              <lb/>
            ſibus æquales angulos contineant, ſimiliter ean-
              <lb/>
            dem, quam axes, habere proportionem: </s>
            <s xml:space="preserve">ſunt
              <lb/>
              <anchor type="note" xlink:label="note-0160-02a" xlink:href="note-0160-02"/>
            enim ſolida parallelepipeda priſmatum triangula
              <lb/>
            res baſes habentiũ dupla; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">pyramidum ſextupla.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="4">
            <note position="left" xlink:label="note-0160-01" xlink:href="note-0160-01a" xml:space="preserve">15. quinti</note>
            <note position="left" xlink:label="note-0160-02" xlink:href="note-0160-02a" xml:space="preserve">28. unde-
              <lb/>
            cimi.</note>
          </div>
          <note position="left" xml:space="preserve">7. duode-
            <lb/>
          cimi.</note>
        </div>
        <div type="section" level="1" n="85">
          <head xml:space="preserve">THE OREMA XVI. PROPOSITIO XX.</head>
          <p>
            <s xml:space="preserve">Priſmata omnia & </s>
            <s xml:space="preserve">pyramides, quæ in eiſdem,
              <lb/>
            uel æqualibus baſibus conſtituuntur, eam inter
              <lb/>
            ſe proportionem habent, quam altitudines: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſi
              <lb/>
            axes cum baſibus faciant angulos æquales, eam
              <lb/>
            etiam, quam axes habent proportionem.</s>
            <s xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>