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 IIS QVAE VEH. IN AQVA.
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              <pb o="15" file="0041" n="41" rhead="DE IIS QVAE VEH. IN AQVA."/>
            _quare per o ductaipſi al æquidiſtans cadet extra ſectionem ex 17._
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            </s>
            <s xml:space="preserve">_primi conicorum: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">cum b p producta coibit inſra p. </s>
            <s xml:space="preserve">ergò & </s>
            <s xml:space="preserve">per-_
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            _pendicularis ducta per b cum eadem infra b coibit, at que inter b &_</s>
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              <lb/>
            _p neceſſario cadet. </s>
            <s xml:space="preserve">multo autem magis illud idem ſequetur, ſi pona-_
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            _mus pf ipſa om maiorem eſſe._</s>
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          </p>
          <div type="float" level="2" n="6">
            <note position="left" xlink:label="note-0040-08" xlink:href="note-0040-08a" xml:space="preserve">G</note>
            <figure xlink:label="fig-0040-01" xlink:href="fig-0040-01a">
              <image file="0040-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0040-01"/>
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          <p>
            <s xml:space="preserve">Et quoniam p f quidem æquidiſtans eſt diametro, htau
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              <anchor type="note" xlink:label="note-0041-01a" xlink:href="note-0041-01"/>
            tem ad diametrum perpendicularis; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">rh æqualis ei, quæ
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            uſque ad axem, ducta linea ab r ad e, & </s>
            <s xml:space="preserve">producta angulos
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            rectos facere cum linea ſectionem in p contingente.</s>
            <s xml:space="preserve">]
              <lb/>
            _Hoc ſuperius à nobis demonſtratum eſt in ſecundam buin
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            s._</s>
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            <note position="right" xlink:label="note-0041-01" xlink:href="note-0041-01a" xml:space="preserve">H</note>
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          <head xml:space="preserve">PROPOSITIO V.</head>
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              <emph style="sc">Recta</emph>
            portio conoidis rectanguli, quando
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            leuior humido axem habuerit maiorem, quàm
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            ſeſquialterum eius, quæ uſque ad axem; </s>
            <s xml:space="preserve">ſi ad hu-
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            midum in grauitate non maiorem proportionẽ
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            habeat, quàm exceſſus, quo quadratum quod ſit
              <lb/>
            ab axe maius eſt quadrato, quod ab exceſſu, quo
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            axis maior eſt, quàm ſeſquialter eius, quæ uſque
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            ad axem, ad quadratum, quod ab axe: </s>
            <s xml:space="preserve">demiſſa in
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            humidum, ita ut baſis ipſius tota ſit in humido;
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            </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">poſita inclinata non manebit inclinata, ſed re-
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            ſtituetur ita, ut axis ipſius ſecundum perpendi-
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            cularem fiat.</s>
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          </p>
          <p>
            <s xml:space="preserve">DEMITTATVR enim in humidum portio aliqna,
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            qualis dicta eſt: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſit baſis ipſius tota in humido. </s>
            <s xml:space="preserve">Secta au-
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            tem ipſa plano per axem, recto ad ſuperſiciem humidi, erit
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            ſectio rectanguli coniſectio, quæ ſit apol: </s>
            <s xml:space="preserve">axis portionis,</s>
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