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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DE IIS QVAE VEH. IN AQVA.
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              <pb o="24" file="0059" n="59" rhead="DE IIS QVAE VEH. IN AQVA."/>
            humidum ſecundum perpendicularem, quæ per z ad hu-
              <lb/>
            midi ſuperficiem ducta fuerit: </s>
            <s xml:space="preserve">quæ autem eſt extra humi-
              <lb/>
            dum ſecundum eam, quæ per gintra humidum feretur. </s>
            <s xml:space="preserve">nõ
              <lb/>
            ergo manebit portio ſic inclinata, ut ponitur: </s>
            <s xml:space="preserve">ſed neque re
              <lb/>
            ſtituecur recta: </s>
            <s xml:space="preserve">quoniam perpendicularium per z g ducta
              <lb/>
            rum, quæ quidem per z ducitur ad eas partes cadit, in qui
              <lb/>
            bus eſt l; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">quæ per g ad eas, in quibus eſt a. </s>
            <s xml:space="preserve">quare ſequi-
              <lb/>
            tur centrum z ſurſum ferri: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">g deorſum. </s>
            <s xml:space="preserve">ergo partes to
              <lb/>
            tius ſolidi, quæ ſunt ad a deorſum, quæ uero ad l ſurſum
              <lb/>
            ferentur. </s>
            <s xml:space="preserve">Rurſus alia eadem ponantur: </s>
            <s xml:space="preserve">axis autem
              <lb/>
            portionis cum ſuperficie humidi angulum faciat minorẽ
              <lb/>
            eo, qui eſt ad b. </s>
            <s xml:space="preserve">minorem igitur proportionem habet qua
              <lb/>
              <anchor type="note" xlink:label="note-0059-01a" xlink:href="note-0059-01"/>
            dratum p i ad quadratum i y, quàm quadratum e ψ ad
              <lb/>
            ψ b quadratum: </s>
            <s xml:space="preserve">quare k r ad i y minorem proportionẽ
              <lb/>
            habet, quàm dimidium k r ad ψ b: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">propterea i y maior
              <lb/>
            eſt, quam dupla ψ b. </s>
            <s xml:space="preserve">eſt autem ipſius o i dupla. </s>
            <s xml:space="preserve">ergo o i
              <lb/>
            ipſa ψ b maior e-
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              <anchor type="figure" xlink:label="fig-0059-01a" xlink:href="fig-0059-01"/>
            rit. </s>
            <s xml:space="preserve">ſed tota o ω eſt
              <lb/>
            æqualis ipſi r b:
              <lb/>
            </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">reliqua ω i mi-
              <lb/>
            nor quàm ψ r. </s>
            <s xml:space="preserve">qua
              <lb/>
            re & </s>
            <s xml:space="preserve">p h minor e-
              <lb/>
            rit, quàm f. </s>
            <s xml:space="preserve">Quòd
              <lb/>
            cum m p ipſi f q
              <lb/>
            ſit æqualis, cõſtat
              <lb/>
            p m maiorẽ eſſe,
              <lb/>
            quàm ſeſquialterã
              <lb/>
            ipſius p h: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">p h
              <lb/>
            minorem, quam
              <lb/>
            duplam h m. </s>
            <s xml:space="preserve">Sit
              <lb/>
            p z ipſius z m du
              <lb/>
            pla. </s>
            <s xml:space="preserve">Rurſus to-
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            tius quidem ſolidi centrum grauitatis erit pũctum t; </s>
            <s xml:space="preserve">eius
              <lb/>
            uero partis, quæ intra humidum z: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">iuncta z t inuenia-</s>
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