Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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page |< < (47) of 213 > >|
DE CENTRO GRAVIT. SOLID.
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              <pb o="47" file="0205" n="205" rhead="DE CENTRO GRAVIT. SOLID."/>
            eani proportionem habeat, quam a b c d fruſtum ad por-
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            tionem a g d; </s>
            <s xml:space="preserve">erit punctum l eius fruſti grauitatis cẽtrum:
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            </s>
            <s xml:space="preserve">habebitq; </s>
            <s xml:space="preserve">componendo K l ad 1 h proportionem eandem,
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            quam portio conoidis b gc ad a g d portionem. </s>
            <s xml:space="preserve">Itaq; </s>
            <s xml:space="preserve">quo
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              <anchor type="note" xlink:label="note-0205-01a" xlink:href="note-0205-01"/>
            niam quadratum b f ad quadratum a e, hoc eſt quadratum
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            b c ad quadratum a d eſt, ut linea f g ad g e: </s>
            <s xml:space="preserve">erunt duæ ter-
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            tiæ quadrati b c ad duas tertias quadrati a d, ut h g ad g _k_:
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            </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ſi à duabus tertiis quadrati b c demptæ fuerint duæ ter-
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            tiæ quadrati a d: </s>
            <s xml:space="preserve">erit diuidẽdo id, quod relinquitur ad duas
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            tertias quadrati a d, ut h k ad k g. </s>
            <s xml:space="preserve">Rurſus duæ tertiæ quadra
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            ti a d ad duas tertias quadrati b c ſunt, ut _k_ g ad g h: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">duæ
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            tertiæ quadrati b c ad tertiã partẽ ipſius, ut g h ad h f. </s>
            <s xml:space="preserve">ergo
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            ex æ quali id, quod relinquitur ex duabus tertiis quadrati
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            b c, demptis ab ipſis quadrati a d duabus tertiis, ad tertiã
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            partem quadrati b c, ut _k_ h ad h f: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">ad portionem eiuſdẽ
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            tertiæ partis, ad quam unà cum ipſa portione, duplam pro
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            portionem habeat eius, quæ eſt quadrati b c ad quadratũ
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            a d, ut K 1 ad 1 h. </s>
            <s xml:space="preserve">habet enim _K_l ad 1 h ean dem proportio-
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            nem, quam conoidis portio b g c ad portionem a g d: </s>
            <s xml:space="preserve">por-
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            tio autem b g c ad portionem a g d duplam proportionem
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            habet eius, quæ eſt baſis b c ad baſim a d: </s>
            <s xml:space="preserve">hoc eſt quadrati
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            b c ad quadratum a d; </s>
            <s xml:space="preserve">ut proxime demonſtratum eſt. </s>
            <s xml:space="preserve">quare
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              <anchor type="note" xlink:label="note-0205-02a" xlink:href="note-0205-02"/>
            dempto a d quadrato à duabus tertiis quadrati b c, erit id,
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            quod relin quitur unà cum dicta portione tertiæ partis ad
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            reliquam eiuſdem portionem, ut el ad 1 f. </s>
            <s xml:space="preserve">Cum igitur cen-
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            trum grauitatis fruſti a b c d ſit l, à quo axis e f in eam, quã
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            diximus, proportionem diuidatur; </s>
            <s xml:space="preserve">conſtat uerũ eſſe illud,
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            quod demonſtrandum propoſuimus.</s>
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            <figure xlink:label="fig-0204-01" xlink:href="fig-0204-01a">
              <image file="0204-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/4E7V2WGH/figures/0204-01"/>
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            <note position="right" xlink:label="note-0205-01" xlink:href="note-0205-01a" xml:space="preserve">20. I. coni
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            corum.</note>
            <note position="right" xlink:label="note-0205-02" xlink:href="note-0205-02a" xml:space="preserve">30. huius</note>
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        </div>
        <div type="section" level="1" n="97">
          <head xml:space="preserve">FINIS LIBRI DE CENTRO
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          GRAVITATIS SOLIDORVM.</head>
          <p>
            <s xml:space="preserve">Impreſſ. </s>
            <s xml:space="preserve">Bononiæ cum licentia Superiorum.</s>
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