Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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        <div xml:id="echoid-div281" type="section" level="1" n="94">
          <p>
            <s xml:id="echoid-s5041" xml:space="preserve">
              <pb o="45" file="0201" n="201" rhead="DE CENTRO GRAVIT. SOLID."/>
            ad punctum ω. </s>
            <s xml:id="echoid-s5042" xml:space="preserve">Sed quoniam π circum ſcripta itidem alia
              <lb/>
            figura æquali interuallo ad portionis centrum accedit, ubi
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            primum φ applieuerit ſe ad ω, & </s>
            <s xml:id="echoid-s5043" xml:space="preserve">π ad punctũ ψ, hoc eſt ad
              <lb/>
            portionis centrum ſe applicabit. </s>
            <s xml:id="echoid-s5044" xml:space="preserve">quod fieri nullo modo
              <lb/>
            poſſe perſpicuum eſt. </s>
            <s xml:id="echoid-s5045" xml:space="preserve">non aliter idem abſurdum ſequetur,
              <lb/>
            ſi ponamus centrum portionis recedere à medio ad par-
              <lb/>
            tes ω; </s>
            <s xml:id="echoid-s5046" xml:space="preserve">eſſet enim aliquando centrum figuræ inſcriptæ idem
              <lb/>
            quod portionis centrũ. </s>
            <s xml:id="echoid-s5047" xml:space="preserve">ergo punctum e centrum erit gra
              <lb/>
            uitatis portionis a b c. </s>
            <s xml:id="echoid-s5048" xml:space="preserve">quod demonſtrare oportebat.</s>
            <s xml:id="echoid-s5049" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5050" xml:space="preserve">Quod autem ſupra demõſtratum eſt in portione conoi-
              <lb/>
            dis recta per figuras, quæ ex cylindris æqualem altitudi-
              <lb/>
            dinem habentibus conſtant, idem ſimiliter demonſtrabi-
              <lb/>
            mus per figuras ex cylindri portionibus conſtantes in ea
              <lb/>
            portione, quæ plano non ad axem recto abſcinditur. </s>
            <s xml:id="echoid-s5051" xml:space="preserve">ut
              <lb/>
            enim tradidimus in commentariis in undecimam propoſi
              <lb/>
            tionem libri Archimedis de conoidibus & </s>
            <s xml:id="echoid-s5052" xml:space="preserve">ſphæroidibus.
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            </s>
            <s xml:id="echoid-s5053" xml:space="preserve">portiones cylindri, quæ æquali ſunt altitudine eam inter ſe
              <lb/>
            ſe proportionem habent, quam ipſarum baſes; </s>
            <s xml:id="echoid-s5054" xml:space="preserve">baſes autẽ
              <lb/>
            quæ ſunt ellipſes ſimiles eandem proportionem habere,
              <lb/>
              <note position="right" xlink:label="note-0201-01" xlink:href="note-0201-01a" xml:space="preserve">corol. 15
                <lb/>
              deconoi-
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              dibus &
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              ſphæroi-
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              dibus.</note>
            quam quadrata diametrorum eiuſdem rationis, ex corol-
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            lario ſeptimæ propoſitionis libri de conoidibus, & </s>
            <s xml:id="echoid-s5055" xml:space="preserve">ſphæ-
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            roidibus, manifeſte apparet.</s>
            <s xml:id="echoid-s5056" xml:space="preserve"/>
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        <div xml:id="echoid-div284" type="section" level="1" n="95">
          <head xml:id="echoid-head102" xml:space="preserve">THEOREMA XXIIII. PROPOSITIO XXX.</head>
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            <s xml:id="echoid-s5057" xml:space="preserve">SI à portione conoidis rectanguli alia portio
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            abſcindatur, plano baſi æquidiſtante; </s>
            <s xml:id="echoid-s5058" xml:space="preserve">habebit
              <lb/>
            portio tota ad eam, quæ abſciſſa eſt, duplam pro
              <lb/>
            portio nem eius, quæ eſt baſis maioris portionis
              <lb/>
            ad baſi m minoris, uel quæ axis maioris ad axem
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            minoris.</s>
            <s xml:id="echoid-s5059" xml:space="preserve"/>
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