Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

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[21. ARCHIMEDIS DE IIS QVAE VEHVNTVR IN AQVA LIBER SECVNDVS. CVM COMMENTARIIS FEDERICI COMMANDINI VRBINATIS. PROPOSITIO I.]
[22. PROPOSITIO II.]
[23. COMMENTARIVS.]
[24. PROPOSITIO III.]
[25. PROPOSITIO IIII.]
[26. COMMENTARIVS.]
[27. PROPOSITIO V.]
[28. COMMENTARIVS.]
[29. PROPOSITIO VI.]
[30. COMMENTARIVS.]
[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.]
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DE CENTRO GRAVIT. SOLID.
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              <pb o="15" file="0141" n="141" rhead="DE CENTRO GRAVIT. SOLID."/>
            bere proportionem, quam ſpacium g h ad dictã
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            figuram, hoc modo demonſtrabimus.</s>
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          <p>
            <s xml:space="preserve">Intelligatur circulus, uel ellipſis x æqualis figuræ rectili-
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            neæ in g h ſpacio deſcriptæ: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ab x conſtituatur conus, uel
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              <anchor type="figure" xlink:label="fig-0141-01a" xlink:href="fig-0141-01"/>
            coni portio, altitudinẽ habens eandẽ, quã cylindrus uel cy
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            lindri portio c e. </s>
            <s xml:space="preserve">Sit deinde rectilinea figura, in quay eade,
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            quæ in ſpacio g h deſcripta eſt: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ab hac pyramis æquealta
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            conſtituatur. </s>
            <s xml:space="preserve">Dico conũ uel coni portionẽ x pyramidiy æ-
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            qualẽ eſſe. </s>
            <s xml:space="preserve">niſi enim ſit æqualis, uel maior, uel minor erit.</s>
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          </p>
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            <figure xlink:label="fig-0141-01" xlink:href="fig-0141-01a">
              <image file="0141-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0141-01"/>
            </figure>
          </div>
          <p>
            <s xml:space="preserve">Sit primum maior, et exuperet ſolido z. </s>
            <s xml:space="preserve">Itaque in circu
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            lo, uel ellipſi x deſcribatur figura rectilinea; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">in ea pyra-
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            mis eandem, quam conus, uel coni portio altitudinem ha-
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            bens, ita ut portiones relictæ minores ſint ſolido z, quem-
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            admodum docetur in duodecimo libro elementorum pro
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            poſitione undecima. </s>
            <s xml:space="preserve">erit pyramis x adhuc pyramide y ma
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            ior. </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">quoniam piramides æque altæ inter ſe ſunt, ſicuti ba
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            ſes; </s>
            <s xml:space="preserve">pyramis x ad piramidem y eandem proportionem ha-
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            bet, quàm figura rectilinea x ad figuram y. </s>
            <s xml:space="preserve">Sed ſigura recti</s>
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