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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ARCHIMEDIS
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            q o; </s>
            <s xml:space="preserve">uidelicet ut h g ad f p: </s>
            <s xml:space="preserve">quod proxime demonſtr atum eſt. </s>
            <s xml:space="preserve">At
              <lb/>
              <anchor type="note" xlink:label="note-0052-01a" xlink:href="note-0052-01"/>
            ueroipſi g q æquales ſunt duæ lineæ ſimul ſumptæ qb, hoc eſt h b,
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              <anchor type="note" xlink:label="note-0052-02a" xlink:href="note-0052-02"/>
            & </s>
            <s xml:space="preserve">b g: </s>
            <s xml:space="preserve">atque ipſi q a æqualis eſt h f. </s>
            <s xml:space="preserve">Sienim ab æqualibus h b,
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            bq, æqualia fb,
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              <anchor type="figure" xlink:label="fig-0052-01a" xlink:href="fig-0052-01"/>
            ba demantur, re
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            manentia æqua-
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            lia erunt. </s>
            <s xml:space="preserve">ergo
              <lb/>
            dempta h g ex
              <lb/>
            duabus lineis h
              <lb/>
            b, h g, relinqui-
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            tur dupla ipſius
              <lb/>
            b g; </s>
            <s xml:space="preserve">hoc eſt o h:
              <lb/>
            </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">dempta p f ex
              <lb/>
            f h, reliqua est
              <lb/>
            b p. </s>
            <s xml:space="preserve">quare o h
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              <anchor type="note" xlink:label="note-0052-03a" xlink:href="note-0052-03"/>
            ad h p, eſt ut g q
              <lb/>
            ad q a. </s>
            <s xml:space="preserve">Sed ut
              <lb/>
            g q ad q a, ita
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            h q ad q o; </s>
            <s xml:space="preserve">hoc
              <lb/>
            eſt h g ad n c:
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            </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ut o h ad h p,
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              <anchor type="note" xlink:label="note-0052-04a" xlink:href="note-0052-04"/>
            ita g b ad c k. </s>
            <s xml:space="preserve">eſt
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            cnim o h dupla
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            g b, & </s>
            <s xml:space="preserve">h p item
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            dupla gf; </s>
            <s xml:space="preserve">hoc eſt
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            c k. </s>
            <s xml:space="preserve">eandem igitur proportionem habet h g ad n c, qnam g b ad
              <lb/>
            c k: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">permutando n c ad c k eandem habet, quam b g ad g b.</s>
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          <div type="float" level="2" n="2">
            <note position="left" xlink:label="note-0052-01" xlink:href="note-0052-01a" xml:space="preserve">2. lem:</note>
            <note position="left" xlink:label="note-0052-02" xlink:href="note-0052-02a" xml:space="preserve">4. lem.</note>
            <figure xlink:label="fig-0052-01" xlink:href="fig-0052-01a">
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            <note position="left" xlink:label="note-0052-03" xlink:href="note-0052-03a" xml:space="preserve">19. quinti</note>
            <note position="left" xlink:label="note-0052-04" xlink:href="note-0052-04a" xml:space="preserve">15. quin-
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            ti.</note>
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          <p style="it">
            <s xml:space="preserve">Sumatur deinde aliud quod uis punctum in ſectum in ſectione,
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            quod ſit s: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">per s duæ lineæ ducantur: </s>
            <s xml:space="preserve">st quidem
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            æquidistans ipſi db, diametrumque in puncto t ſecans;
              <lb/>
            </s>
            <s xml:space="preserve">s u uero æquidistans ac, & </s>
            <s xml:space="preserve">ſecans c e in u. </s>
            <s xml:space="preserve">Dico u c
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            ad ck maiorem proportionem habere, quamtg ad gb.</s>
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