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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ARCHIMEDIS
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            tur ex parte 1. </s>
            <s xml:space="preserve">Quod ſi n o non ſecuerit ipſam ω k,
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            eadem nihilominus demonſtrabuntur.</s>
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            <figure xlink:label="fig-0055-01" xlink:href="fig-0055-01a">
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            <note position="right" xlink:label="note-0055-01" xlink:href="note-0055-01a" xml:space="preserve">10. quinti</note>
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          <head xml:space="preserve">PROPOSITIO VIII.</head>
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              <emph style="sc">Recta</emph>
            portio conoidis rectanguli, quando
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            axem habuerit maiorem quidem, quàm ſeſqui-
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            alterum eius, quæ uſque ad axem; </s>
            <s xml:space="preserve">minorem ue-
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            ro, quàm ut ad eam, quæ uſque ad axem propor-
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            tionem habeat, quam quindecim ad quatuor: </s>
            <s xml:space="preserve">ſi
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            in grauitate ad humidum habeat proportionem
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            minorem ea, quam quadratum, quod fit ab exceſ
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            ſu, quo axis maior eſt, quàm ſeſquialter eius, quæ
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            uſque ad axem, habet ad quadratum, quod ab
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            axe: </s>
            <s xml:space="preserve">demiſſa in humidum, ita ut baſis ipſius humi
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            dum non contingat; </s>
            <s xml:space="preserve">neque in rectum reſtitue-
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            tur, neque manebit inclinata, niſi quando axis
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            cum ſuperficie humidi angulum fecerit æqualẽ
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            ei, de quo infra dicetur.</s>
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            <s xml:space="preserve">SIT portio qualis dicta eſt; </s>
            <s xml:space="preserve">ſitque b d æqualis axi: </s>
            <s xml:space="preserve">& </s>
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            b k quidem dupla ipſius _K_ d: </s>
            <s xml:space="preserve">r _K_ uero æqualis ei, quæ uſ-
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            que ad axem: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſit c b ſeſquialtera b r. </s>
            <s xml:space="preserve">erit & </s>
            <s xml:space="preserve">c d ipſius
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            _k_ r ſeſquialtera. </s>
            <s xml:space="preserve">Quam uero portionem habet portio ad
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            humidum in grauitate, habeat quadratum f q ad quadra-
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            tum d b: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſit f dupla ipſius q. </s>
            <s xml:space="preserve">perſpicuum igitur eſt f q
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            ad d b proportionem minorem habere ea, quam habet
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            c b ad b d. </s>
            <s xml:space="preserve">eſt enim c b exceſſus, quo axis maior eſt, quàm
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            ſeſquialter eins, quæ uſque ad axem: </s>
            <s xml:space="preserve">quare f q minor eſt
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              <anchor type="note" xlink:label="note-0056-02a" xlink:href="note-0056-02"/>
            </s>
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