Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of contents

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[11. PROPOSITIO IIII.]
[12. PROPOSITIO V.]
[13. PROPOSITIO VI.]
[14. PROPOSITIO VII.]
[15. POSITIO II.]
[16. COMMENTARIVS.]
[17. PROPOSITIO VIII.]
[18. COMMENTARIVS.]
[19. PROPOSITIO IX.]
[20. COMMENTARIVS.]
[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.]
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FED. COMMANDINI
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              <pb file="0138" n="138" rhead="FED. COMMANDINI"/>
            ad priſma a b c e f g. </s>
            <s xml:space="preserve">quare linea s y ad y t eandem propor-
              <lb/>
            tionem habet, quam priſma a d c e h g ad priſma a b c e f g.
              <lb/>
            </s>
            <s xml:space="preserve">Sed priſmatis a b c e f g centrum grauitatis eſts: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">priſma-
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            tis a d c e h g centrum t. </s>
            <s xml:space="preserve">magnitudinis igitur ex his compo
              <lb/>
            ſitæ, hoc eſt totius priſmatis a g centrum grauitatis eſt pun
              <lb/>
            ctum y; </s>
            <s xml:space="preserve">medium ſcilicet axis u x, qui oppoſitorum plano-
              <lb/>
            rum centra coniungit.</s>
            <s xml:space="preserve"/>
          </p>
          <div type="float" level="2" n="3">
            <figure xlink:label="fig-0137-01" xlink:href="fig-0137-01a">
              <image file="0137-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0137-01"/>
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            <note position="right" xlink:label="note-0137-01" xlink:href="note-0137-01a" xml:space="preserve">5. huius.</note>
          </div>
          <p>
            <s xml:space="preserve">Rurſus ſit priſma baſim habens pentagonum a b c d e:
              <lb/>
            </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">quod ei opponitur ſit f g h _K_ l: </s>
            <s xml:space="preserve">ſec enturq; </s>
            <s xml:space="preserve">a f, b g, c h,
              <lb/>
            d _k_, el bifariam: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">per diuiſiones ducto plano, ſectio ſit pẽ
              <lb/>
            tagonũ m n o p q. </s>
            <s xml:space="preserve">deinde iuncta e b per lineas le, e b aliud
              <lb/>
            planum ducatur, diuidẽs priſ
              <lb/>
              <anchor type="figure" xlink:label="fig-0138-01a" xlink:href="fig-0138-01"/>
            ma a k in duo priſmata, in priſ
              <lb/>
            ma ſcilicet al, cuius plana op-
              <lb/>
            poſita ſint triangula a b e f g l:
              <lb/>
            </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">in prima b _k_ cuius plana op
              <lb/>
            poſita ſint quadrilatera b c d e
              <lb/>
            g h _k_ l. </s>
            <s xml:space="preserve">Sint autem triangulo-
              <lb/>
            rum a b e, f g l centra grauita
              <lb/>
            tis puncta r ſ: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">b c d e, g h _k_ l
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            quadrilaterorum centra tu: </s>
            <s xml:space="preserve">
              <lb/>
            iunganturq; </s>
            <s xml:space="preserve">r s, t u o ccurren-
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            tes plano m n o p q in punctis
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            x y. </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">itidem iungãtur r t, ſu,
              <lb/>
            x y. </s>
            <s xml:space="preserve">erit in linea r t cẽtrum gra
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            uitatis pentagoni a b c d e; </s>
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              <lb/>
            quod ſit z: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">in linea ſu cen-
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            trum pentagoni f g h k l: </s>
            <s xml:space="preserve">ſit au
              <lb/>
            tem χ: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ducatur z χ, quæ di-
              <lb/>
            cto plano in χ occurrat. </s>
            <s xml:space="preserve">Itaq; </s>
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              <lb/>
            punctum x eſt centrum graui
              <lb/>
            tatis trianguli m n q, ac priſ-
              <lb/>
            matis al: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">y grauitatis centrum quadrilateri n o p q, ac
              <lb/>
            priſmatis b k. </s>
            <s xml:space="preserve">quare y centrum erit pentagoni m n o p q. </s>
            <s xml:space="preserve">&</s>
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