Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

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[31. LEMMAI.]
[32. LEMMA II.]
[33. LEMMA III.]
[34. LEMMA IIII.]
[35. PROPOSITIO VII.]
[36. PROPOSITIO VIII.]
[37. COMMENTARIVS.]
[38. PROPOSITIO IX.]
[39. COMMENTARIVS.]
[40. PROPOSITIO X.]
[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.]
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DE IIS QVAE VEH. IN AQVA.
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          <head xml:space="preserve">DEMONSTRATIO SECVNDAE PARTIS.</head>
          <p>
            <s xml:space="preserve">ITAQVE primum habeat portio ad humidum in
              <lb/>
            grauitate proportionem quidem maiorem, quàm qua dra
              <lb/>
            tum x o ad quadratum b d; </s>
            <s xml:space="preserve">minorem uero, quàm quadra
              <lb/>
            tum, quod fit ab exceſſu, quo axis eſt maior, quàm ſeſquial-
              <lb/>
            ter eius, quæ uſque ad axem, ad quadratum b d: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">quam
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            proportionem habet portio ad humidum in grauitate, eã
              <lb/>
            habeat quadratum, quod fit à linea ψ ad quadratum b d:
              <lb/>
            </s>
            <s xml:space="preserve">erit ψ maior quidem, quàm x o, minor uero, quàm exceſ-
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            ſus, quo axis eſt maior, quàm ſeſquialter eius, quæ uſque ad
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            axem. </s>
            <s xml:space="preserve">aptetur quædam recta linea m n conicis ſectioni-
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            bus a m q l,
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              <anchor type="figure" xlink:label="fig-0085-01a" xlink:href="fig-0085-01"/>
            a x d interiecta,
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            ac media, quæ li
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            neæ ψ ſit æqua-
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            lis; </s>
            <s xml:space="preserve">ſecetq; </s>
            <s xml:space="preserve">reli-
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            quã coni ſectio
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            nem in pun cto
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            h; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">rectam li-
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            neam r g in u.
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            </s>
            <s xml:space="preserve">demõſtrabitur
              <lb/>
              <anchor type="note" xlink:label="note-0085-02a" xlink:href="note-0085-02"/>
            m h dupla ip-
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            ſius h n, ſicuti
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            demonſtratum
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            eſt o g ipſius g x
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            duplam eſſe. </s>
            <s xml:space="preserve">à
              <lb/>
            puncto autẽ m
              <lb/>
            ducatur m y contingens ſectionem a m q l in m: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">m c a d
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            b d perpendicularis. </s>
            <s xml:space="preserve">poſtea ducta a n, & </s>
            <s xml:space="preserve">producta ad q li
              <lb/>
            neæ a n, n q inter ſe æquales erunt. </s>
            <s xml:space="preserve">quoniã enim in ſimi-
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              <anchor type="note" xlink:label="note-0085-03a" xlink:href="note-0085-03"/>
            libus portionibus a m q l, a x d ductæ ſunt à baſibus ad
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            portiones lineæ a q, a n, quæ æquales angulos continent
              <lb/>
            cum ipſis baſibus, eandem proportionem habebit q a ad
              <lb/>
            an, quam la ad a d. </s>
            <s xml:space="preserve">æqualis eſt ergo a n ipſi n q; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">a q
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            </s>
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