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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            ſuperficiem recto, ſit portionis ſectio anzg; </s>
            <s xml:space="preserve">ſuperficiei
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            humidi ez: </s>
            <s xml:space="preserve">a-
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              <anchor type="figure" xlink:label="fig-0098-01a" xlink:href="fig-0098-01"/>
            xis portionis,
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            & </s>
            <s xml:space="preserve">ſectionis dia-
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            meter b d: </s>
            <s xml:space="preserve">ſece-
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            turq, b d in pũ-
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            ctis _K_r, ſicuti
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            prius; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">duca-
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            tur n l quidem
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            ipſi e z æquidi-
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            ſtans, quæ con-
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            tingat ſectionẽ
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            a n z g in n; </s>
            <s xml:space="preserve">& </s>
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              <lb/>
            n t æquidiſtans
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            ipſi b d; </s>
            <s xml:space="preserve">n s ue-
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            ro ad b d perpẽ
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            dicularis. </s>
            <s xml:space="preserve">Itaq;
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            </s>
            <s xml:space="preserve">quoniam portio ad humidum in grauitate eam proportio
              <lb/>
            nem habet, quam quadratum, quod fit à linea ψ ad quadra
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            tum b d: </s>
            <s xml:space="preserve">erit ψ ipſi n t æqualis: </s>
            <s xml:space="preserve">quod ſimiliter demonſtrabi
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            tur, ut ſuperius. </s>
            <s xml:space="preserve">quare & </s>
            <s xml:space="preserve">n t eſt æqualis ipſi u i. </s>
            <s xml:space="preserve">portiones
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            igitur a u q, e n z inter ſe ſunt æquales. </s>
            <s xml:space="preserve">Et cum in æquali-
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            bus, & </s>
            <s xml:space="preserve">ſimilibus portionibus a u q l, a n z g ductæ ſint a q
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            e z, quæ æquales portiones auferunt; </s>
            <s xml:space="preserve">illa quidem ab extre
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            mitate baſis; </s>
            <s xml:space="preserve">hæc autem non ab extremitate: </s>
            <s xml:space="preserve">minorem fa-
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            ciet acutum angulum cum portionis diametro, quæ ab ex-
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            tremitate baſis ducitur. </s>
            <s xml:space="preserve">At triangulorum n l s, u ω c angu
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            lus ad l angulo ad ω maior eſt. </s>
            <s xml:space="preserve">ergo b s minor erit, quam
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            b c: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſ r maior, quàm c r: </s>
            <s xml:space="preserve">ideoq; </s>
            <s xml:space="preserve">n χ maior, quam u h; </s>
            <s xml:space="preserve">& </s>
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              <lb/>
            χ t minor, quàm h i. </s>
            <s xml:space="preserve">Quoniam igitur u y dupla eſt ipſius
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            y i; </s>
            <s xml:space="preserve">conſtat n χ maiorem eſſe, quàm duplã χ t. </s>
            <s xml:space="preserve">Sit n m dupla
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            ipſius m t. </s>
            <s xml:space="preserve">perſpicuũ eſt ex iis, quæ dicta ſunt, non manere
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            portionẽ; </s>
            <s xml:space="preserve">ſed in clinari, donec eius baſis contingat ſuperfi-
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            ciem humidi: </s>
            <s xml:space="preserve">contingat autem in puncto uno, ut patet in fi</s>
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