Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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DE CENTRO GRAVIT. SOLID.
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            <s xml:space="preserve">
              <pb o="13" file="0137" n="137" rhead="DE CENTRO GRAVIT. SOLID."/>
            trianguli g h K, & </s>
            <s xml:space="preserve">ipſius ρ τ axis medium.</s>
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            <note position="left" xlink:label="note-0132-02" xlink:href="note-0132-02a" xml:space="preserve">5. huius</note>
            <figure xlink:label="fig-0133-01" xlink:href="fig-0133-01a">
              <image file="0133-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0133-01"/>
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            <note position="right" xlink:label="note-0133-01" xlink:href="note-0133-01a" xml:space="preserve">2. ſexti.</note>
            <note position="right" xlink:label="note-0133-02" xlink:href="note-0133-02a" xml:space="preserve">I1. quinti</note>
            <note position="right" xlink:label="note-0133-03" xlink:href="note-0133-03a" xml:space="preserve">2. ſexti.</note>
            <note position="left" xlink:label="note-0134-01" xlink:href="note-0134-01a" xml:space="preserve">19. ſexti</note>
            <figure xlink:label="fig-0134-01" xlink:href="fig-0134-01a">
              <image file="0134-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0134-01"/>
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            <note position="left" xlink:label="note-0134-02" xlink:href="note-0134-02a" xml:space="preserve">2. uel 121
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            quinti.</note>
            <note position="right" xlink:label="note-0135-01" xlink:href="note-0135-01a" xml:space="preserve">8. quinti.</note>
            <note position="right" xlink:label="note-0135-02" xlink:href="note-0135-02a" xml:space="preserve">28. unde
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            cimi</note>
            <note position="right" xlink:label="note-0135-03" xlink:href="note-0135-03a" xml:space="preserve">15. quinti</note>
            <note position="right" xlink:label="note-0135-04" xlink:href="note-0135-04a" xml:space="preserve">19. quinti
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            apud Cã
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            panum.</note>
            <figure xlink:label="fig-0136-01" xlink:href="fig-0136-01a">
              <image file="0136-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0136-01"/>
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          <p>
            <s xml:space="preserve">Sit priſma a g, cuius oppoſita plana ſint quadrilatera
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            a b c d, e f g h: </s>
            <s xml:space="preserve">ſecenturq; </s>
            <s xml:space="preserve">a e, b f, c g, d h bifariam: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">per di-
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            uiſiones planum ducatur; </s>
            <s xml:space="preserve">quod ſectionem faciat quadrila-
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            terum _K_ l m n. </s>
            <s xml:space="preserve">Deinde iuncta a c per lineas a c, a e ducatur
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            planum ſecãs priſma, quod ipſum diuidet in duo priſmata
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            triangulares baſes habentia a b c e f g, a d c e h g. </s>
            <s xml:space="preserve">Sint autẽ
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            triangulorum a b c, e f g gra-
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              <anchor type="figure" xlink:label="fig-0137-01a" xlink:href="fig-0137-01"/>
            uitatis centra o p: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">triangu-
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            lorum a d c, e h g centra q r:
              <lb/>
            </s>
            <s xml:space="preserve">iunganturq; </s>
            <s xml:space="preserve">o p, q r; </s>
            <s xml:space="preserve">quæ pla-
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            no _k_ l m n occurrant in pun-
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            ctis s t. </s>
            <s xml:space="preserve">erit ex iis, quæ demon
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            ſtrauimus, punctum s grauita
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            tis centrum trianguli k l m; </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">
              <lb/>
            ipſius priſmatis a b c e f g: </s>
            <s xml:space="preserve">pun
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            ctum uero t centrum grauita
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            tis trianguli _K_ n m, & </s>
            <s xml:space="preserve">priſma-
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            tis a d c, e h g. </s>
            <s xml:space="preserve">iunctis igitur
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            o q, p r, s t, erit in linea o q cẽ
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            trum grauitatis quadrilateri
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            a b c d, quod ſit u: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">in linea
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            p r cẽtrum quadrilateri e f g h
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            ſit autem x. </s>
            <s xml:space="preserve">deniqueiungatur
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            u x, quæ ſecet lineam ſ t in y. </s>
            <s xml:space="preserve">ſe
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            cabit enim cum ſint in eodem
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              <anchor type="note" xlink:label="note-0137-01a" xlink:href="note-0137-01"/>
            plano: </s>
            <s xml:space="preserve">atq; </s>
            <s xml:space="preserve">erit y grauitatis centrum quadril ateri _K_ lm n.
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            </s>
            <s xml:space="preserve">Dico idem punctum y centrum quoque gra uitatis eſſe to-
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            tius priſmatis. </s>
            <s xml:space="preserve">Quoniam enim quadri lateri k lm n graui-
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            tatis centrum eſt y: </s>
            <s xml:space="preserve">linea s y ad y t eandem proportionem
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            habebit, quam triangulum k n m ad triangulum k lm, ex 8
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            Archimedis de centro grauitatis planorum. </s>
            <s xml:space="preserve">Vtautem triã
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            gulum k n m ad ipſum k l m, hoc eſt ut triangulum a d c ad
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            triangulum a b c, æqualia enim ſunt, ita priſina a d c e h g</s>
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