Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

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[41. COMMENTARIVS.]
[42. LEMMA I.]
[43. LEMMA II.]
[44. LEMMA III.]
[45. LEMMA IIII.]
[46. LEMMA V.]
[47. LEMMA VI.]
[48. II.]
[49. III.]
[50. IIII.]
[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.]
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DE CENTRO GRAVIT. SOLID.
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              <pb o="33" file="0177" n="177" rhead="DE CENTRO GRAVIT. SOLID."/>
            quod diuidat fruſtum in duo fruſta triangulares baſes ha-
              <lb/>
            bentia, uidelicet in fruſtum a b d e f h, & </s>
            <s xml:space="preserve">in fruſtũ b c d f g h.
              <lb/>
            </s>
            <s xml:space="preserve">erit triangulum k l n proportionale inter triangula a b d,
              <lb/>
            e f h: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">triangulum l m n proportionale inter b c d, f g h. </s>
            <s xml:space="preserve">
              <lb/>
            ſed pyramis æque alta, cuius baſis conſtat ex tribus trian-
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            gulis a b d, k l n, e f h, demonſtrata
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              <anchor type="figure" xlink:label="fig-0177-01a" xlink:href="fig-0177-01"/>
            eſt ſruſto a b d e f h æqualis. </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſi-
              <lb/>
            militer pyramis, cuius baſis con-
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            ſtat ex triangulis b c d, l m n, f g h
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            æqualis fruſto b c d f g h: </s>
            <s xml:space="preserve">compo-
              <lb/>
            nuntur autem tria quadrilatera a
              <lb/>
            b c d, _k_ l m n, e f g h è ſex triangu-
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            lis iam dictis. </s>
            <s xml:space="preserve">pyramis igitur ba-
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            ſim habens æqualem tribus qua-
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            drilateris, & </s>
            <s xml:space="preserve">altitudinem eandem
              <lb/>
            ipſi fruſto a g eſt æqualis. </s>
            <s xml:space="preserve">Eodem
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            modo illud demõſtrabitur in aliis
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            eiuſmodi fruſtis.</s>
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              <image file="0177-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0177-01"/>
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            <s xml:space="preserve">Sit fruſtum coni, uel coni, uel coni portionis a d; </s>
            <s xml:space="preserve">cuius maior ba-
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            ſis circulus, uel ellipſis circa diametrum a b; </s>
            <s xml:space="preserve">minor circa
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            c d: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſecetur plano, quod baſibus æquidiſtet, faciatq; </s>
            <s xml:space="preserve">ſe-
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            ctionem circulum, uel ellipſim circa diametrum e f, ita ut
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            inter circulos, uel ellipſes a b, c d ſit proportionalis. </s>
            <s xml:space="preserve">Dico
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            conum, uel coni portionem, cuius baſis eſt æqualis tribus
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            circulis, uel tribus ellipſibus a b, e f, c d; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">altitudo eadem,
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            quæ fruſti a d, ipſi fruſto æqualem eſſe. </s>
            <s xml:space="preserve">producatur enim
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            fruſti ſuperficies quouſque coeat in unum punctum, quod
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            ſit g: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">coni, uel coni portionis a g b axis ſit g h, occurrens
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            planis a b, e f, c d in punctis h _k_ l: </s>
            <s xml:space="preserve">circa circulum uero de-
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            ſcribatur quadratum m n o p, & </s>
            <s xml:space="preserve">circa ellipſim rectangulũ
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            m n o p, quod ex ipſius diametris conſtat: </s>
            <s xml:space="preserve">iunctisq; </s>
            <s xml:space="preserve">g m,
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            g n, g o, g p, ex eodem uertice intelligatur pyramis baſim
              <lb/>
            habens dictum quadratum, uel rectangulum: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">plana in
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            quibus ſunt circuli, uel ellipſes e f, c d uſque ad eius latera</s>
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