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="3" file="0017" n="17" rhead="DE IIS QVAE VEH. IN AQVA."/>
            iuncta, & </s>
            <s xml:space="preserve">continuata: </s>
            <s xml:space="preserve">ſitq; </s>
            <s xml:space="preserve">ſectio planorũ ipſius K m K n:
              <lb/>
            </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">in humido intelligatur quædam magnitudo r s q y ex ip
              <lb/>
            ſo humido conſtans, æqualis, & </s>
            <s xml:space="preserve">ſimilis ſolidæ b h t c, quæ
              <lb/>
            quidem pars eſt ſolidæ magnitudinis in humido demerſa. </s>
            <s xml:space="preserve">
              <lb/>
            partes igitur humidi, quæ ſcilicet in prima pyramide ſuper
              <lb/>
            ficie x o continetur, & </s>
            <s xml:space="preserve">quæ in altera continetur p o, æquali
              <lb/>
            ter ſunt poſitæ, & </s>
            <s xml:space="preserve">continuatæ ſed non ſimiliter premun-
              <lb/>
            tur. </s>
            <s xml:space="preserve">nam contenta quidem x o, premitur ſolido e h t f, & </s>
            <s xml:space="preserve">
              <lb/>
            humido interiecto inter ſuperficies x o, l m, & </s>
            <s xml:space="preserve">plana pyra-
              <lb/>
            midis; </s>
            <s xml:space="preserve">contenta uero p o premitur ſolido r s q y, & </s>
            <s xml:space="preserve">humi-
              <lb/>
            do inter ſuperficies o p, m n, & </s>
            <s xml:space="preserve">pyramidis plana interiecto. </s>
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              <lb/>
            minor autem eſt grauitas humidi, quod eſt inter m n, o p,
              <lb/>
            quàm eius, quod inter l m, x o. </s>
            <s xml:space="preserve">ſolidum enim r s q y eſt mi
              <lb/>
            nus ſolido e h t f: </s>
            <s xml:space="preserve">cum ſit æquale ipſi b h t c; </s>
            <s xml:space="preserve">quia magnitu
              <lb/>
            dine æquale, & </s>
            <s xml:space="preserve">æque graue ponitur ſolidum, atque humi-
              <lb/>
            dum: </s>
            <s xml:space="preserve">reliquum autem reliquo inæquale eſt. </s>
            <s xml:space="preserve">conſtatigitur
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            partem contentã ſuperficie o p, expelli ab ea, quæ ipſa x o
              <lb/>
            continetur: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">non conſiſtere humidum. </s>
            <s xml:space="preserve">ponebatur au-
              <lb/>
            tem conſiſtens, & </s>
            <s xml:space="preserve">manens: </s>
            <s xml:space="preserve">non ergo ex ſuperficie humidi
              <lb/>
            extat aliquid ſolidæ magnitudinis. </s>
            <s xml:space="preserve">ſed neque demerſum
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            ſolidum ad inferiora feretur. </s>
            <s xml:space="preserve">Similiter enim prementur
              <lb/>
            omnes partes humidi æqualiter poſitæ, cum ſolidum ſit æ-
              <lb/>
            que graue, atque humidum.</s>
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            <figure xlink:label="fig-0016-01" xlink:href="fig-0016-01a">
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          <head xml:space="preserve">PROPOSITIO IIII.</head>
          <p>
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              <emph style="sc">Solidarvm</emph>
            magnitudinum, quæcunque
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            leuior humido fuerit, demiſſa in humidum non
              <lb/>
            demergetur tota, ſed aliqua pars ipſius ex humi-
              <lb/>
            di ſuperficie extabit.</s>
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          </p>
          <p>
            <s xml:space="preserve">SIT magnitudo ſolida humido leuior; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">demiſſa in hu
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            midum demergatur tota, ſi fieri poteſt, ut nulla pars ipſius</s>
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