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="16" file="0043" n="43" rhead="DE IIS QVAE VEH. IN AQVA."/>
            dratum n o ad quadratum p f. </s>
            <s xml:space="preserve">quadratum igitur n o ad
              <lb/>
            quadratum p f non maiorem proportionem habet, quàm
              <lb/>
            ad quadratum m o. </s>
            <s xml:space="preserve">ex quo eſſicitur, ut p f non ſit minor
              <lb/>
              <anchor type="note" xlink:label="note-0043-01a" xlink:href="note-0043-01"/>
            ipſa o m; </s>
            <s xml:space="preserve">neque p b ipſa o h. </s>
            <s xml:space="preserve">quæ ergo ab h ducitur ad
              <lb/>
              <anchor type="note" xlink:label="note-0043-02a" xlink:href="note-0043-02"/>
            rectos angulos ipſi n o, coibit cum b p inter p & </s>
            <s xml:space="preserve">b. </s>
            <s xml:space="preserve">co-
              <lb/>
            eatin t. </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">quoniam in rectanguli coniſectione p f eſt æqui
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            diſtans diametro n o; </s>
            <s xml:space="preserve">h t autem ad diametrum perpẽ-
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            dicularis: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">r h æqualis ei, quæ uſque ad axem: </s>
            <s xml:space="preserve">conſtat r t
              <lb/>
            productam ſacere angulos rectos cum ipſa k p ω. </s>
            <s xml:space="preserve">quare
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            & </s>
            <s xml:space="preserve">cum is. </s>
            <s xml:space="preserve">ergo rt perpendicularis eſt ad ſuperſiciem hu
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            midi. </s>
            <s xml:space="preserve">et ſi per b g puncta ducantur æquidiſtantes ipſirt,
              <lb/>
            ad ſuperſiciem humidi perpendicular es erunt. </s>
            <s xml:space="preserve">portio igi
              <lb/>
            tur, qnæ eſt extra humidum, deorſum in humidum feretur
              <lb/>
            ſecundum perpendicularem per b ductam; </s>
            <s xml:space="preserve">quæ uero in-
              <lb/>
            tra humidum ſecundum perpendicularem per g ſurſum
              <lb/>
            feretur: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">non manebit ſolida portio a p o l, ſedintra hu
              <lb/>
            midum mouebitur, donecutique ipſa n o ſecundum per-
              <lb/>
            pendicularem ſiat.</s>
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            <figure xlink:label="fig-0042-01" xlink:href="fig-0042-01a">
              <image file="0042-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0042-01"/>
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            <note position="left" xlink:label="note-0042-01" xlink:href="note-0042-01a" xml:space="preserve">11. quin-
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            ti.</note>
            <note position="left" xlink:label="note-0042-02" xlink:href="note-0042-02a" xml:space="preserve">A</note>
            <note position="left" xlink:label="note-0042-03" xlink:href="note-0042-03a" xml:space="preserve">B</note>
            <note position="right" xlink:label="note-0043-01" xlink:href="note-0043-01a" xml:space="preserve">C</note>
            <note position="right" xlink:label="note-0043-02" xlink:href="note-0043-02a" xml:space="preserve">D</note>
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        <div type="section" level="1" n="28">
          <head xml:space="preserve">COMMENTARIVS.</head>
          <p style="it">
            <s xml:space="preserve">_Quare non maiorem proportionem habet tota portio_
              <lb/>
              <anchor type="note" xlink:label="note-0043-03a" xlink:href="note-0043-03"/>
            _ad eam, quæ eſt extra humidum, quam quadratum n o ad_
              <lb/>
            _quadratum m o]_ cum enim magnitudo portionis in bumidum
              <lb/>
            demerſa ad totam portionem non maiorem proportionem babeat,
              <lb/>
            quàm exceſſus, quo quadratum n o excedit quadratum m o, ad ip-
              <lb/>
            ſum no quadratum: </s>
            <s xml:space="preserve">conuertendo per uigeſimáſextam quinti ele-
              <lb/>
            mentorum ex traditione Campani, tota portio ad magnitudinem de
              <lb/>
            merſam non minorem proportionem babebit, quàm quadratum n o
              <lb/>
            ad exceſſum, quo ipſum quadratum no excedit quadratum m o. </s>
            <s xml:space="preserve">In
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            telligatur portio, quæ extra bumidum, magnitudo prima: </s>
            <s xml:space="preserve">quæ in bu
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            mido demerſa est, ſecunda: </s>
            <s xml:space="preserve">tertia autem magnitudo ſit quadratum
              <lb/>
            mo: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">exceſſus, quo quadratum n o excedit quadratum m o ſit
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            quarta. </s>
            <s xml:space="preserve">ex his igitur magnitudinibus, primæ & </s>
            <s xml:space="preserve">ſecundæ ad ſecun-</s>
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