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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ARCHIMEDIS
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          <head xml:space="preserve">PROPOSITIO III.</head>
          <p>
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              <emph style="sc">Solidarvm</emph>
            magnitudinum, quæ æqualẽ
              <lb/>
            molem habentes æque graues ſunt, atque humi-
              <lb/>
            dum; </s>
            <s xml:space="preserve">in humidum demiſſæ demergentur ita, vt
              <lb/>
            ex humidi ſuperficie nihil extet: </s>
            <s xml:space="preserve">non tamen ad
              <lb/>
            huc deorſum ferentur.</s>
            <s xml:space="preserve"/>
          </p>
          <p>
            <s xml:space="preserve">SIT magnitudo aliqua æque grauis, atque humidum:
              <lb/>
            </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſi fieri poteſt, in humidum demiſſa extet ex ſuperficie ip
              <lb/>
            ſius: </s>
            <s xml:space="preserve">conſiſtat autem humidum, maneatq;</s>
            <s xml:space="preserve">: & </s>
            <s xml:space="preserve">intelligatur
              <lb/>
            aliquod planum ductũ
              <lb/>
              <anchor type="figure" xlink:label="fig-0016-01a" xlink:href="fig-0016-01"/>
            per cẽtrum terræ, & </s>
            <s xml:space="preserve">hu
              <lb/>
            midi, ac per ſolidam ma
              <lb/>
            gnitudinem, ut ſit ſuper
              <lb/>
            ficiei quidem humidi ſe
              <lb/>
            ctio a b c d; </s>
            <s xml:space="preserve">ſolidæ uero
              <lb/>
            magnitudinis inſiden-
              <lb/>
            tis e h t f; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">terræ cen-
              <lb/>
            trum k: </s>
            <s xml:space="preserve">ſitq; </s>
            <s xml:space="preserve">ſolidæ ma-
              <lb/>
            gnitudinis pars, quæ in
              <lb/>
            humido eſt, b h t c; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">
              <lb/>
            quæ extra humidum b e f c. </s>
            <s xml:space="preserve">intelligatur etiam ſolida figu-
              <lb/>
            ra comprehenſa pyramide, baſim quidem habente paralle
              <lb/>
            logrammum, quod eſt in ſuperficie humidi; </s>
            <s xml:space="preserve">uerticem au-
              <lb/>
            tem centrum terræ: </s>
            <s xml:space="preserve">ſitq; </s>
            <s xml:space="preserve">ſectio plani, in quo eſt a b c d cir-
              <lb/>
            cunferentia, & </s>
            <s xml:space="preserve">planorum pyramidis k l, k m: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">deſcriba-
              <lb/>
            tur quædam alterius ſphæræ ſuperficies x o p circa centrũ
              <lb/>
            k, in humido ſub e f h t, ut ſit ipſa x o p ſectio facta à ſuper fi
              <lb/>
            cie plani. </s>
            <s xml:space="preserve">Sumatur præterea alia quædam pyramis æqua-
              <lb/>
            lis, & </s>
            <s xml:space="preserve">ſimilis comprehendenti ſolidam figuram, ipſi con-</s>
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