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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DE CENTRO GRAVIT. SOLID.
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          <head xml:space="preserve">THEOREMA X. PROPOSITIO XIIII.</head>
          <p>
            <s xml:space="preserve">Cuiuslibet pyramidis, & </s>
            <s xml:space="preserve">cuiuslibet coni, uel
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            coni portionis, centrum grauitatis in axe cõſiſtit.</s>
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          <p>
            <s xml:space="preserve">SIT pyramis, cuius baſis triangulum a b c: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">axis d e.
              <lb/>
            </s>
            <s xml:space="preserve">Dico in linea d e ipſius grauitatis centrum ineſſe. </s>
            <s xml:space="preserve">Si enim
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            fieri poteſt, ſit centrum f: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ab f ducatur ad baſim pyrami
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            dis linea f g, axi æquidiſtans: </s>
            <s xml:space="preserve">iunctaq; </s>
            <s xml:space="preserve">e g ad latera trian-
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            guli a b c producatur in h. </s>
            <s xml:space="preserve">quam uero proportionem ha-
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            bet linea h e ad e g, habeat pyramis ad aliud ſolidum, in
              <lb/>
            quo K: </s>
            <s xml:space="preserve">inſcribaturq; </s>
            <s xml:space="preserve">in pyramide ſolida figura, & </s>
            <s xml:space="preserve">altera cir
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            cumſcribatur ex priſmatibus æqualem habentibus altitu-
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            dinem, ita ut circumſcripta inſcriptam exuperet magnitu-
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            dine, quæ ſolido _k_ ſit minor. </s>
            <s xml:space="preserve">Et quoniam in pyramide pla
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            num baſi æquidiſtans ductum ſectionem facit figuram ſi-
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            milem ei, quæ eſt baſis; </s>
            <s xml:space="preserve">centrumq; </s>
            <s xml:space="preserve">grauitatis in axe haben
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            tem: </s>
            <s xml:space="preserve">erit priſmatis s t grauitatis centrũ in linear q; </s>
            <s xml:space="preserve">priſ-
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            matis u x centrum in linea q p; </s>
            <s xml:space="preserve">priſmatis y z in linea p o; </s>
            <s xml:space="preserve">
              <lb/>
            priſmatis η θ in l_i_nea o n; </s>
            <s xml:space="preserve">priſmatis λ μ in linea n m; </s>
            <s xml:space="preserve">priſ-
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            matis ν π in m l; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">denique priſmatis ρ σ in l e. </s>
            <s xml:space="preserve">quare to-</s>
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