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="5" file="0021" n="21" rhead="DE IIS QVAE VEH. IN AQVA."/>
            midi ſuperficie extare. </s>
            <s xml:space="preserve">Quare conſtat magnitudinem a
              <lb/>
            tanta ui ſurſum ferri, quãta deorſum premitur ab eo, quod
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            eſt ſupra; </s>
            <s xml:space="preserve">uidelicet à d, cũ neutra ab altera expellatur, ſed
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            d fertur deorſum tanta grauitate, quanta eſt c: </s>
            <s xml:space="preserve">ponebatur
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            enim grauitas eius, in quo d ipſi c æqualis. </s>
            <s xml:space="preserve">patet igitur
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            illud quod demonſtrare oportebat.</s>
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          </p>
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            <figure xlink:label="fig-0020-01" xlink:href="fig-0020-01a">
              <image file="0020-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0020-01"/>
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          <head xml:space="preserve">PROPOSITIO VII.</head>
          <p>
            <s xml:space="preserve">
              <emph style="sc">Solidae</emph>
            magnitudines humido grauiores
              <lb/>
            demiſſæ in humidum ferentur deorſum, donec
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            deſcendant: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">erunt in humido tanto leuiores,
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            quanta eſt grauitas humidi molem habentis ſoli-
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            dæ magnitudini æqualem.</s>
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          </p>
          <p>
            <s xml:space="preserve">SOLIDAS magnitudines humido grauiores, in hu-
              <lb/>
            midum demiſſas deorſum quidam ferri, donec deſcẽdant,
              <lb/>
            manifeſtum eſt: </s>
            <s xml:space="preserve">partes enim humidi, quæ ſub eis ſunt, pre-
              <lb/>
            muntur magis, quàm partes æqualiter ipſis adiacentes;
              <lb/>
            </s>
            <s xml:space="preserve">quoniam magnitudo ſolida humido grauior ponitur: </s>
            <s xml:space="preserve">le-
              <lb/>
            uiores autem eſſe uti dictum eſt, demonſtrabitur hoc mo-
              <lb/>
            do. </s>
            <s xml:space="preserve">Sit enim aliqua ma-
              <lb/>
              <anchor type="figure" xlink:label="fig-0021-01a" xlink:href="fig-0021-01"/>
            gnitudo a grauior hu-
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            mido: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">fit magnitudi-
              <lb/>
            nis quidem a grauitas
              <lb/>
            b c: </s>
            <s xml:space="preserve">humidi uero molẽ
              <lb/>
            habentis æqualem ipſi a
              <lb/>
            grauitas ſit b. </s>
            <s xml:space="preserve">demon-
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            ſtrandum eſt magnitudi
              <lb/>
            nem a in humido exiſtē
              <lb/>
            tem habere grauitatem
              <lb/>
            æqualem ipſi c. </s>
            <s xml:space="preserve">Accipia
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            tur enim alia aliqua magnitudo, in qua d, leuior humido;</s>
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