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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FED. COMMANDINI
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          <p>
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            da figura, & </s>
            <s xml:space="preserve">altera circumſcribatur ex cylindris, uel cylin-
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            dri portionibus, ſicuti dictum eſt, ita ut exceſſus, quo figu-
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            ra circumſcripta inſcriptam ſuperat, ſit ſolido g minor.
              <lb/>
            </s>
            <s xml:space="preserve">Itaque centrum grauitatis cylindri, uel cylindri portionis
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            q r eſt in linea p o; </s>
            <s xml:space="preserve">cylindri, uel cylindri portionis st cen-
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            trum in linea on; </s>
            <s xml:space="preserve">centrum u x in linea n m; </s>
            <s xml:space="preserve">y z in m b; </s>
            <s xml:space="preserve">η @
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            in 1k; </s>
            <s xml:space="preserve">λ μ in K h; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">denique ν π centrum in h d. </s>
            <s xml:space="preserve">ergo figu-
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              <anchor type="figure" xlink:label="fig-0152-01a" xlink:href="fig-0152-01"/>
            ræ inſcriptæ centrum eſt in linea p d. </s>
            <s xml:space="preserve">Sitautem ρ: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">iun-
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            cta ρ e protendatur, ut cum linea, quæ à pũctoc ducta fue-
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            rit axi æquidiſtans, conueniat in σ. </s>
            <s xml:space="preserve">erit σ ζ ad ρ e, ut c d
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            ad d f: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">conus, ſeu coni portio ad exceſſum, quo circum-
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            ſcripta figura inſcriptam ſuperat, habebit maiorem pro-
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            portionem, quàm σ ζ ad ρ e. </s>
            <s xml:space="preserve">ergo ad partem exceſſus, quæ
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            intra ipſius ſuperficiem comprehenditur, multo maiorem
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            proportionem habebit. </s>
            <s xml:space="preserve">habeat eam, quam τ ρ ad ρ e. </s>
            <s xml:space="preserve">erit</s>
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