Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

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[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.]
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DE CENTRO GRAVIT. SOLID.
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            <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>
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            <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"/>
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            <note position="right" xlink:label="note-0161-01" xlink:href="note-0161-01a" xml:space="preserve">12. quinti</note>
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          <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"/>
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