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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FED. COMMANDINI
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            æqualibus baſibus, quorum axes cum baſibus æquales an
              <lb/>
            gulos faciant. </s>
            <s xml:space="preserve">Dico ſolidum a b adſolidũ c d ita eſſe, ut axis
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            e f ad axem g h: </s>
            <s xml:space="preserve">nam ſi axes ad planum baſis recti ſint, il-
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            lud perſpicue conſtat: </s>
            <s xml:space="preserve">quoniam eadem linea, & </s>
            <s xml:space="preserve">axem & </s>
            <s xml:space="preserve">ſoli
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            di altitudinem determinabit. </s>
            <s xml:space="preserve">Si uero ſintinclinati, à pun-
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            ctis e g ad ſubiectum planum perpendiculares ducantur
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            e k, g l: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">iungantur f_k_, h l. </s>
            <s xml:space="preserve">rurſus quoniam axes cum ba
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            ſibus æquales faciunt angulos, eodem modo demonſtrabi
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            tur, triangulum e f K triangulo g h l ſimile eſſe: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">e k ad g l,
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            ut e f ad g h. </s>
            <s xml:space="preserve">Solidum autem a b ad ſolidum c d eſt, ut
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            e K ad g l. </s>
            <s xml:space="preserve">ergo & </s>
            <s xml:space="preserve">ut axis e f ad axem g h. </s>
            <s xml:space="preserve">quæ omnia de
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            monſtrare oportebat.</s>
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          </p>
          <p>
            <s xml:space="preserve">Ex iis quæ demonſtrata ſunt, facile conſtare
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            poteſt, priſmata omnia & </s>
            <s xml:space="preserve">pyramides, quæ trian-
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            gulares baſes habent, ſiue in eiſdem, ſiue in æqua
              <lb/>
            libus baſibus conſtituantur, eandem proportio-
              <lb/>
              <anchor type="note" xlink:label="note-0160-01a" xlink:href="note-0160-01"/>
            nem habere, quam altitudines: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſi axes cum ba
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            ſibus æquales angulos contineant, ſimiliter ean-
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            dem, quam axes, habere proportionem: </s>
            <s xml:space="preserve">ſunt
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              <anchor type="note" xlink:label="note-0160-02a" xlink:href="note-0160-02"/>
            enim ſolida parallelepipeda priſmatum triangula
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            res baſes habentiũ dupla; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">pyramidum ſextupla.</s>
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            <note position="left" xlink:label="note-0160-01" xlink:href="note-0160-01a" xml:space="preserve">15. quinti</note>
            <note position="left" xlink:label="note-0160-02" xlink:href="note-0160-02a" xml:space="preserve">28. unde-
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            cimi.</note>
          </div>
          <note position="left" xml:space="preserve">7. duode-
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          cimi.</note>
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          <head xml:space="preserve">THE OREMA XVI. PROPOSITIO XX.</head>
          <p>
            <s xml:space="preserve">Priſmata omnia & </s>
            <s xml:space="preserve">pyramides, quæ in eiſdem,
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            uel æqualibus baſibus conſtituuntur, eam inter
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            ſe proportionem habent, quam altitudines: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſi
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            axes cum baſibus faciant angulos æquales, eam
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            etiam, quam axes habent proportionem.</s>
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          </p>
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