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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            <s xml:space="preserve">Sit ſruſtum a e a pyramide, quæ triangularem baſim ha-
              <lb/>
            beat abſciſſum: </s>
            <s xml:space="preserve">cuius maior baſis triangulum a b c, minor
              <lb/>
            d e f; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">axis g h. </s>
            <s xml:space="preserve">ducto autem plano per axem & </s>
            <s xml:space="preserve">per lineã
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            d a, quod ſectionem faciat d a k l quadrilaterum; </s>
            <s xml:space="preserve">puncta
              <lb/>
            K l lineas b c, e f bifariam ſecabunt. </s>
            <s xml:space="preserve">nam cum g h ſit axis
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            ſruſti: </s>
            <s xml:space="preserve">erit h centrum grauitatis trianguli a b c: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">g
              <lb/>
            centrum trianguli d e f: </s>
            <s xml:space="preserve">cen-
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              <anchor type="figure" xlink:label="fig-0181-01a" xlink:href="fig-0181-01"/>
              <anchor type="note" xlink:label="note-0181-01a" xlink:href="note-0181-01"/>
            trum uero cuiuslibet triangu
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            li eſt in recta linea, quæ ab an-
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            gulo ipſius ad dimidiã baſim
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            ducitur ex decimatertia primi
              <lb/>
            libri Archimedis de cẽtro gra
              <lb/>
            uitatis planorum. </s>
            <s xml:space="preserve">quare cen-
              <lb/>
              <anchor type="note" xlink:label="note-0181-02a" xlink:href="note-0181-02"/>
            trũ grauitatis trapezii b c f e
              <lb/>
            eſt in linea _K_ l, quod ſit m: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">à
              <lb/>
            puncto m ad axem ducta m n
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            ipſi a k, uel d l æquidiſtante;
              <lb/>
            </s>
            <s xml:space="preserve">erit axis g h diuiſus in portio-
              <lb/>
            nes g n, n h, quas diximus: </s>
            <s xml:space="preserve">ean
              <lb/>
            dem enim proportionem ha-
              <lb/>
            bet g n ad n h, quã l m ad m _k_. </s>
            <s xml:space="preserve">
              <lb/>
            At l m ad m K habet eam, quã
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            duplum lateris maioris baſis
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            b c una cum latere minoris e f
              <lb/>
            ad duplum lateris e f unà cum
              <lb/>
            later b c, ex ultima eiuſdem
              <lb/>
            libri Archimedis. </s>
            <s xml:space="preserve">Itaque à li-
              <lb/>
            nea n g abſcindatur, quarta
              <lb/>
            pars, quæ ſit n p: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ab axe h g abſcindatur itidem
              <lb/>
            quarta pars h o: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">quam proportionem habet fruſtum ad
              <lb/>
            pyramidem, cuius maior baſis eſt triangulum a b c, & </s>
            <s xml:space="preserve">alti-
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            tudo ipſi æqualis; </s>
            <s xml:space="preserve">habeat o p ad p q. </s>
            <s xml:space="preserve">Dico centrum graui-
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            tatis fruſti eſſe in linea p o, & </s>
            <s xml:space="preserve">in puncto q. </s>
            <s xml:space="preserve">namque ipſum
              <lb/>
            eſſe in linea g h manifeſte conſtat. </s>
            <s xml:space="preserve">protractis enim fruſti pla</s>
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