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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DE CENTRO GRAVIT. SOLID.
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              <pb o="28" file="0167" n="167" rhead="DE CENTRO GRAVIT. SOLID."/>
            uel coni portionis axis à centro grauitatis ita diui
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            ditur, ut pars, quæ terminatur ad uerticem reli-
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            quæ partis, quæ ad baſim, ſit tripla.</s>
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          </p>
          <p>
            <s xml:space="preserve">Sit pyramis, cuius baſis triangulum a b c; </s>
            <s xml:space="preserve">axis d e; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">gra
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            uitatis centrum _K_. </s>
            <s xml:space="preserve">Dico lineam d k ipſius _K_ e triplam eſſe.
              <lb/>
            </s>
            <s xml:space="preserve">trianguli enim b d c centrum grauitatis ſit punctum f; </s>
            <s xml:space="preserve">triã
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            guli a d c centrũ g; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">trianguli a d b ſit h: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">iungantur a f,
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            b g, c h. </s>
            <s xml:space="preserve">Quoniam igitur centrũ grauitatis pyramidis in axe
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            cõſiſtit: </s>
            <s xml:space="preserve">ſuntq; </s>
            <s xml:space="preserve">d e, a f, b g, c h eiuſdẽ pyramidis axes: </s>
            <s xml:space="preserve">conue
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              <anchor type="note" xlink:label="note-0167-01a" xlink:href="note-0167-01"/>
            nient omnes in idẽ punctũ _k_, quod eſt grauitatis centrum.
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            </s>
            <s xml:space="preserve">Itaque animo concipiamus hanc pyramidem diuiſam in
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            quatuor pyramides, quarum baſes ſint ipſa pyramidis
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            triangula; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">axis pun-
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              <anchor type="handwritten" xlink:label="hd-0167-01a" xlink:href="hd-0167-01"/>
              <anchor type="figure" xlink:label="fig-0167-01a" xlink:href="fig-0167-01"/>
            ctum k quæ quidem py-
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            ramides inter ſe æquales
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            ſunt, ut demõſtrabitur.
              <lb/>
            </s>
            <s xml:space="preserve">Ducatur enĩ per lineas
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            d c, d e planum ſecãs, ut
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            ſit ipſius, & </s>
            <s xml:space="preserve">baſis a b c cõ
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            munis ſectio recta linea
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            c e l: </s>
            <s xml:space="preserve">eiuſdẽ uero & </s>
            <s xml:space="preserve">triã-
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            guli a d b ſitlinea d h l. </s>
            <s xml:space="preserve">
              <lb/>
            erit linea a l æqualis ipſi
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            l b: </s>
            <s xml:space="preserve">nam centrum graui-
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            tatis trianguli conſiſtit
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            in linea, quæ ab angulo
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            ad dimidiam baſim per-
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            ducitur, ex tertia deci-
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            ma Archimedis. </s>
            <s xml:space="preserve">quare
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              <anchor type="note" xlink:label="note-0167-02a" xlink:href="note-0167-02"/>
            triangulum a c l æquale
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            eſt triangulo b c l: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">propterea pyramis, cuius baſis trian-
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            gulum a c l, uertex d, eſt æqualis pyramidi, cuius baſis b c l
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            triangulum, & </s>
            <s xml:space="preserve">idem uertex. </s>
            <s xml:space="preserve">pyramides enim, quæ ab eodẽ
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              <anchor type="note" xlink:label="note-0167-03a" xlink:href="note-0167-03"/>
            </s>
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