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="5" file="0121" n="121" rhead="DE CENTRO GRAVIT. SOLID."/>
            quo ſcilicet ln, om conueniunt. </s>
            <s xml:space="preserve">Poſtremo in figura
              <lb/>
            a p l q b r m s c t n u d x o y centrum grauitatis trian
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            guli pay, & </s>
            <s xml:space="preserve">trapezii ploy eſtin linea a z: </s>
            <s xml:space="preserve">trapeziorum
              <lb/>
            uero lqxo, q b d x centrum eſtin linea z k: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">trapeziorũ
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            b r u d, r m n u in k φ: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">denique trapezii m s t n; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">triangu
              <lb/>
            li s c t in φ c. </s>
            <s xml:space="preserve">quare magnitudinis ex his compoſitæ centrū
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            in linea a c conſiſtit. </s>
            <s xml:space="preserve">Rurſus trianguli q b r, & </s>
            <s xml:space="preserve">trapezii q l
              <lb/>
            m r centrum eſt in linea b χ: </s>
            <s xml:space="preserve">trapeziorum l p s m, p a c s,
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            a y t c, y o n t in linea χ φ: </s>
            <s xml:space="preserve">trapeziiq; </s>
            <s xml:space="preserve">o x u n, & </s>
            <s xml:space="preserve">trianguli
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            x d u centrum in ψ d. </s>
            <s xml:space="preserve">totius ergo magnitudinis centrum
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            eſtin linea b d. </s>
            <s xml:space="preserve">ex quo ſequitur, centrum grauitatis figuræ
              <lb/>
            a p l q b r m s c t n u d x o y eſſe punctū _K_, lineis ſcilicet a c,
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            b d commune, quæ omnia demonſtrare oportebat.</s>
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            <note position="right" xlink:label="note-0119-01" xlink:href="note-0119-01a" xml:space="preserve">8. primi</note>
            <figure xlink:label="fig-0119-01" xlink:href="fig-0119-01a">
              <image file="0119-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0119-01"/>
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            <note position="right" xlink:label="note-0119-02" xlink:href="note-0119-02a" xml:space="preserve">33. primit</note>
            <note position="left" xlink:label="note-0120-01" xlink:href="note-0120-01a" xml:space="preserve">28. primi.</note>
            <figure xlink:label="fig-0120-01" xlink:href="fig-0120-01a">
              <image file="0120-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0120-01"/>
            </figure>
            <note position="left" xlink:label="note-0120-02" xlink:href="note-0120-02a" xml:space="preserve">13. Archi
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            medis.</note>
            <note position="left" xlink:label="note-0120-03" xlink:href="note-0120-03a" xml:space="preserve">Vltima.</note>
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          <head xml:space="preserve">THE OREMA III. PROPOSITIO III.</head>
          <p>
            <s xml:space="preserve">Cuiuslibet portio-
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              <anchor type="figure" xlink:label="fig-0121-01a" xlink:href="fig-0121-01"/>
            nis circuli, & </s>
            <s xml:space="preserve">ellipſis,
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            quæ dimidia non ſit
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            maior, centrum graui
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            tatis in portionis dia-
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            metro conſiſtit.</s>
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          </p>
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            <figure xlink:label="fig-0121-01" xlink:href="fig-0121-01a">
              <image file="0121-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0121-01"/>
            </figure>
          </div>
          <p>
            <s xml:space="preserve">HOC eodem prorſus
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            modo demonſtrabitur,
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            quo in libro de centro gra
              <lb/>
            uitatis planorum ab Ar-
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            chimede demonſtratũ eſt,
              <lb/>
            in portione cõtenta recta
              <lb/>
            linea, & </s>
            <s xml:space="preserve">rectanguli coni ſe
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            ctione grauitatis cẽtrum
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            eſſe in diametro portio-
              <lb/>
            nis. </s>
            <s xml:space="preserve">Etita demonſtrari po
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            </s>
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