Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of handwritten notes

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[Handwritten note 1]
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[Handwritten note 2]
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[Handwritten note 3]
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[Handwritten note 4]
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[Handwritten note 5]
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[Handwritten note 8]
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            <s xml:id="echoid-s3469" xml:space="preserve">
              <pb o="13" file="0137" n="137" rhead="DE CENTRO GRAVIT. SOLID."/>
            trianguli g h K, & </s>
            <s xml:id="echoid-s3470" xml:space="preserve">ipſius ρ τ axis medium.</s>
            <s xml:id="echoid-s3471" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3472" xml:space="preserve">Sit priſma a g, cuius oppoſita plana ſint quadrilatera
              <lb/>
            a b c d, e f g h: </s>
            <s xml:id="echoid-s3473" xml:space="preserve">ſecenturq; </s>
            <s xml:id="echoid-s3474" xml:space="preserve">a e, b f, c g, d h bifariam: </s>
            <s xml:id="echoid-s3475" xml:space="preserve">& </s>
            <s xml:id="echoid-s3476" xml:space="preserve">per di-
              <lb/>
            uiſiones planum ducatur; </s>
            <s xml:id="echoid-s3477" xml:space="preserve">quod ſectionem faciat quadrila-
              <lb/>
            terum _K_ l m n. </s>
            <s xml:id="echoid-s3478" 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:id="echoid-s3479" xml:space="preserve">Sint autẽ
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            triangulorum a b c, e f g gra-
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              <figure xlink:label="fig-0137-01" xlink:href="fig-0137-01a" number="92">
                <image file="0137-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0137-01"/>
              </figure>
            uitatis centra o p: </s>
            <s xml:id="echoid-s3480" xml:space="preserve">& </s>
            <s xml:id="echoid-s3481" xml:space="preserve">triangu-
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            lorum a d c, e h g centra q r:
              <lb/>
            </s>
            <s xml:id="echoid-s3482" xml:space="preserve">iunganturq; </s>
            <s xml:id="echoid-s3483" xml:space="preserve">o p, q r; </s>
            <s xml:id="echoid-s3484" 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:id="echoid-s3485" xml:space="preserve">erit ex iis, quæ demon
              <lb/>
            ſtrauimus, punctum s grauita
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            tis centrum trianguli k l m; </s>
            <s xml:id="echoid-s3486" xml:space="preserve">& </s>
            <s xml:id="echoid-s3487" xml:space="preserve">
              <lb/>
            ipſius priſmatis a b c e f g: </s>
            <s xml:id="echoid-s3488" 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:id="echoid-s3489" xml:space="preserve">priſma-
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            tis a d c, e h g. </s>
            <s xml:id="echoid-s3490" 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:id="echoid-s3491" xml:space="preserve">& </s>
            <s xml:id="echoid-s3492" 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:id="echoid-s3493" xml:space="preserve">deniqueiungatur
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            u x, quæ ſecet lineam ſ t in y. </s>
            <s xml:id="echoid-s3494" xml:space="preserve">ſe
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            cabit enim cum ſint in eodem
              <lb/>
              <note position="right" xlink:label="note-0137-01" xlink:href="note-0137-01a" xml:space="preserve">5. huius.</note>
            plano: </s>
            <s xml:id="echoid-s3495" xml:space="preserve">atq; </s>
            <s xml:id="echoid-s3496" xml:space="preserve">erit y grauitatis centrum quadril ateri _K_ lm n.
              <lb/>
            </s>
            <s xml:id="echoid-s3497" xml:space="preserve">Dico idem punctum y centrum quoque gra uitatis eſſe to-
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            tius priſmatis. </s>
            <s xml:id="echoid-s3498" xml:space="preserve">Quoniam enim quadri lateri k lm n graui-
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            tatis centrum eſt y: </s>
            <s xml:id="echoid-s3499" 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:id="echoid-s3500" 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 </s>
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