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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            quædam recta linea g i, ſectionibus a g q l, a x d interiecta,
              <lb/>
            & </s>
            <s xml:space="preserve">ipſi b d æquidiſtans; </s>
            <s xml:space="preserve">quæ mediam coni ſectionem in pun
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            cto h, & </s>
            <s xml:space="preserve">rectam
              <lb/>
              <anchor type="figure" xlink:label="fig-0100-01a" xlink:href="fig-0100-01"/>
            lineam r y in y
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            ſecet. </s>
            <s xml:space="preserve">demonſtra
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            bitur g h dupla
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            h i, quemadmo-
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            dum demonſtra
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            ta eſt o g ipſius
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            g x dupla. </s>
            <s xml:space="preserve">duca-
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            tur poſtea g ω cõ
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            tingens a g q l ſe
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            ctioneming: </s>
            <s xml:space="preserve">& </s>
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              <lb/>
            g c ad b d perpé
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            dicularis: </s>
            <s xml:space="preserve">iun-
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            ctaq; </s>
            <s xml:space="preserve">ai produ-
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            catur ad q. </s>
            <s xml:space="preserve">erit
              <lb/>
            ergo a i æqualis
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            i q: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">a q ipſi g ω
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            æquidiſtans. </s>
            <s xml:space="preserve">Demonſtrandũ eſt portionẽ in humidũ demiſ
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            fam, inclinatamq; </s>
            <s xml:space="preserve">adeo, ut baſis ipſius non cõtingat humi-
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            dũ, conſiſtere inclinatã ita, ut axis cum ſuperficie humidi
              <lb/>
            angulum faciat minorem angulo φ: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">baſis humidi ſuper-
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            ficiem nullo modo contingat. </s>
            <s xml:space="preserve">Demittatur enim in humi-
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            dum; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">conſiſtat ita, ut baſis ipſius in uno puncto contin-
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            gat ſuperficiem humidi. </s>
            <s xml:space="preserve">ſecta autem portione per axem,
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            plano ad humidi ſuperficiem recto, ſit portionis ſectio a n
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            z l rectanguli coni ſectio: </s>
            <s xml:space="preserve">ſuperficiei humidi a z: </s>
            <s xml:space="preserve">axis autẽ
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            portionis, & </s>
            <s xml:space="preserve">ſectionis diameter b d: </s>
            <s xml:space="preserve">ſeceturq; </s>
            <s xml:space="preserve">b d in pun-
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            ctis _K_ r, ut ſuperius dictum eſt: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ducatur n f quidem ipſi
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            a z æquidiſtans, & </s>
            <s xml:space="preserve">contingens coni ſectionem in pũcto n;
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            </s>
            <s xml:space="preserve">n t uero æquidiſtans ipſi b d: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">n s ad eandem perpendi-
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            cularis. </s>
            <s xml:space="preserve">Quoniam igitur portio ad humidum in grauitate,
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            cam habet proportionem, quam quadratum, quod fit à χ</s>
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