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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            ioris baſis ad quadratum minoris: </s>
            <s xml:space="preserve">centrum ſit in
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            eo axis puncto, quo ita diuiditur ut pars, quæ mi
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            norem baſim attingit ad alteram partem eandem
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            proportionem habeat, quam dempto quadrato
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            minoris baſis à duabus tertiis quadrati maioris,
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            habet id, quod reliquum eſt unà cum portione à
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            tertia quadrati maioris parte dempta, ad reliquà
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            eiuſdem tertiæ portionem.</s>
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            <s xml:space="preserve">SIT fruſtum à portione rectanguli conoidis abſciſſum
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            a b c d, cuius maior baſis circulus, uel ellipſis circa diame-
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            trum b c, minor circa diametrum a d; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">axis e f. </s>
            <s xml:space="preserve">deſcriba-
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            tur autem portio conoidis, à quo illud abſciſſum eſt, & </s>
            <s xml:space="preserve">pla-
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              <anchor type="figure" xlink:label="fig-0204-01a" xlink:href="fig-0204-01"/>
            no per axem ducto ſecetur; </s>
            <s xml:space="preserve">ut ſuperficiei ſectio ſit parabo-
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            le b g c, cuius diameter, & </s>
            <s xml:space="preserve">axis portionis g f: </s>
            <s xml:space="preserve">deinde g f diui
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            datur in puncto h, ita ut g h ſit dupla h f: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">rurſus g e in ean
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            dem proportionem diuidatur: </s>
            <s xml:space="preserve">ſitq; </s>
            <s xml:space="preserve">g _k_ ipſius k e dupla. </s>
            <s xml:space="preserve">Iã
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            ex iis, quæ proxime demonſtrauimus, conſtat centrum gra
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            uitatis portionis b g c eſſe h punctum: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">portionis a g c
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            punctum k. </s>
            <s xml:space="preserve">ſumpto igitur infra h punctol, ita ut k h ad h l</s>
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