Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

Table of handwritten notes

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            <s xml:id="echoid-s5082" xml:space="preserve">
              <pb o="46" file="0203" n="203" rhead="DE CENTRO GRAVIT. SOLID."/>
            ro ita demonſtrabitur. </s>
            <s xml:id="echoid-s5083" xml:space="preserve">Ducatur à puncto b ad planum ba-
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            ſis a c perpendicularis linea b h, quæ ipſam e fin K ſecet.
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            </s>
            <s xml:id="echoid-s5084" xml:space="preserve">erit b h altitudo coni, uel coni portionis a b c: </s>
            <s xml:id="echoid-s5085" xml:space="preserve">& </s>
            <s xml:id="echoid-s5086" xml:space="preserve">b K altitu
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              <note position="right" xlink:label="note-0203-01" xlink:href="note-0203-01a" xml:space="preserve">16. unde-
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              cimi.</note>
            do e f g. </s>
            <s xml:id="echoid-s5087" xml:space="preserve">Quod cum lineæ a c, e f inter ſe æ quidiſtent, ſunt
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            enim planorum æ quidiſtantium ſectiones: </s>
            <s xml:id="echoid-s5088" xml:space="preserve">habebit d b ad
              <lb/>
              <note position="right" xlink:label="note-0203-02" xlink:href="note-0203-02a" xml:space="preserve">4 ſexti.</note>
            b g proportionem ean dem, quam h b ad b k. </s>
            <s xml:id="echoid-s5089" xml:space="preserve">quare por-
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            tio conoidis a b c ad portionem e f g proportionem habet
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            compoſitam ex proportione baſis a c ad baſim e f; </s>
            <s xml:id="echoid-s5090" xml:space="preserve">& </s>
            <s xml:id="echoid-s5091" xml:space="preserve">ex
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            proportione d b axis ad axem b g. </s>
            <s xml:id="echoid-s5092" xml:space="preserve">Sed circulus, uel
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              <note position="right" xlink:label="note-0203-03" xlink:href="note-0203-03a" xml:space="preserve">2. duode
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              cimi</note>
            ellipſis circa diametrum a c ad circulum, uel ellipſim
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              <note position="right" xlink:label="note-0203-04" xlink:href="note-0203-04a" xml:space="preserve">7. de co-
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              noidibus
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              & ſphæ-
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              roidibus</note>
            circa e f, eſt ut quadratum a c ad quadratum e f; </s>
            <s xml:id="echoid-s5093" xml:space="preserve">hoc eſt ut
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            quadratũ a d ad quadratũ e g. </s>
            <s xml:id="echoid-s5094" xml:space="preserve">& </s>
            <s xml:id="echoid-s5095" xml:space="preserve">quadratum a d ad quadra
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            tum e g eſt, ut linea d b ad lineam b g. </s>
            <s xml:id="echoid-s5096" xml:space="preserve">circulus igitur, uel el
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            lipſis circa diametrum a c ad circulũ, uel ellipſim circa e f,
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              <note position="right" xlink:label="note-0203-05" xlink:href="note-0203-05a" xml:space="preserve">15. quinti</note>
            hoc eſt baſis ad baſim eandem proportionem habet, quã
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              <note position="right" xlink:label="note-0203-06" xlink:href="note-0203-06a" xml:space="preserve">20. primi
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              conicorũ</note>
            d b axis ad axem b g. </s>
            <s xml:id="echoid-s5097" xml:space="preserve">ex quibus ſequitur portionem a b c
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            ad portionem e b f habere proportionem duplam eius,
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            quæ eſt baſis a c ad bafim e f: </s>
            <s xml:id="echoid-s5098" xml:space="preserve">uel axis d b ad b g axem. </s>
            <s xml:id="echoid-s5099" xml:space="preserve">quod
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            demonſtrandum proponebatur.</s>
            <s xml:id="echoid-s5100" xml:space="preserve"/>
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        <div xml:id="echoid-div286" type="section" level="1" n="96">
          <head xml:id="echoid-head103" xml:space="preserve">THEOREMA XXV. PROPOSITIO XXXI.</head>
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            <s xml:id="echoid-s5101" xml:space="preserve">Cuiuslibet fruſti à portione rectanguli conoi
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            dis abſcisſi, centrum grauitatis eſt in axe, ita ut
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            demptis primum à quadrato, quod fit ex diame-
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            tro maioris baſis, tertia ipſius parte, & </s>
            <s xml:id="echoid-s5102" xml:space="preserve">duabus
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            tertiis quadrati, quod fit ex diametro baſis mino-
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            ris: </s>
            <s xml:id="echoid-s5103" xml:space="preserve">deinde à tertia parte quadrati maioris baſis
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            rurſus dempta portione, ad quam reliquum qua
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            drati baſis maioris unà cum dicta portione duplã
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            proportionem habeat eius, quæ eſt quadrati </s>
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