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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              <pb o="20" file="0151" n="151" rhead="DE CENTRO GRAVIT. SOLID."/>
            beat eam, quam χ τ ad τ f. </s>
            <s xml:space="preserve">erit diuidendo ut χ f ad f τ, ita fi
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            gura ſolida inſcripta ad partem exceſſus, quæ eſtintra pyra
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            midem. </s>
            <s xml:space="preserve">Cum ergo à pyramide, cuius grauitatis cẽtrum eſt
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            punctum f, ſolida figura inſcripta auferatur, cuius centrũ
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            τ: </s>
            <s xml:space="preserve">reliquæ magnitudinis conſtantis ex parte exceſſus, quæ
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            eſtintra pyramidem, centrum grauitatis erit in linea τ f
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            producta, & </s>
            <s xml:space="preserve">in puncto χ. </s>
            <s xml:space="preserve">quod fieri non poteſt. </s>
            <s xml:space="preserve">Sequitur
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            igitur, ut centrum grauitatis pyramidis in linea d e; </s>
            <s xml:space="preserve">hoc
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            eſt in eius axe conſiſtat.</s>
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            <figure xlink:label="fig-0150-01" xlink:href="fig-0150-01a">
              <image file="0150-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0150-01"/>
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            <s xml:space="preserve">Sit conus, uel coni portio, cuius axis b d: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſecetur plano
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            per axem, ut ſectio ſit triangulum a b c. </s>
            <s xml:space="preserve">Dico centrum gra
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            uitatis ipſius eſſe in linea b d. </s>
            <s xml:space="preserve">Sit enim, ſi fieri poteſt, centrũ
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              <anchor type="figure" xlink:label="fig-0151-01a" xlink:href="fig-0151-01"/>
            e: </s>
            <s xml:space="preserve">perq; </s>
            <s xml:space="preserve">e ducatur e f axi æquidiſtans: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">quam propor-
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            tionem habet c d ad d f, habeat conus, uel coni portio ad
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            ſolidum g. </s>
            <s xml:space="preserve">inſcribatur ergo in cono, uel coni portione ſoli</s>
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