Archimedes, Archimedis De iis qvae vehvntvr in aqva libri dvo

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ARCHIMEDIS
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          <pb file="0074" n="74" rhead="ARCHIMEDIS"/>
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        <div type="section" level="1" n="43">
          <head xml:space="preserve">LEMMA II.</head>
          <p style="it">
            <s xml:space="preserve">Sint duæ portionis ſimiles, contentæ rectis lineis, & </s>
            <s xml:space="preserve">
              <lb/>
            rectangulorum conorum ſectionibus; </s>
            <s xml:space="preserve">a b c quidem ma-
              <lb/>
            ior, cuius diameter b d; </s>
            <s xml:space="preserve">e f c uero minor, cuius diameter
              <lb/>
            fg: </s>
            <s xml:space="preserve">aptenturq; </s>
            <s xml:space="preserve">inter ſeſe, ita ut maior minorem includat
              <lb/>
            & </s>
            <s xml:space="preserve">ſint earum baſes a c, e c in eadem recta linea, ut idẽ
              <lb/>
            punctum c ſit utriuſque terminus: </s>
            <s xml:space="preserve">ſumatur deinde in ſe
              <lb/>
            ctione a b c quodlibet punctum b: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">iungatur h c. </s>
            <s xml:space="preserve">Di
              <lb/>
            co lineam h c ad partem ſui ipſius, quæ inter c, & </s>
            <s xml:space="preserve">ſe-
              <lb/>
            ctionem e f c interiicitur, eam proportionẽ habere, quam
              <lb/>
            habet a c ad c e.</s>
            <s xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:space="preserve">_
              <emph style="sc">Dvcatvr</emph>
            _ b c, quæ tranſibit per f. </s>
            <s xml:space="preserve">quoniam enim portiones
              <lb/>
            ſimiles ſunt, diametri cú baſibus æquales continent angulos. </s>
            <s xml:space="preserve">quare
              <lb/>
            æquidiſtant inter ſe ſe b d, f g: </s>
            <s xml:space="preserve">éſtq; </s>
            <s xml:space="preserve">b d ad a c, ut f g ad e c:
              <lb/>
            </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">permu-
              <lb/>
              <anchor type="figure" xlink:label="fig-0074-01a" xlink:href="fig-0074-01"/>
            tando b d ad
              <lb/>
            f g, ut a c ad
              <lb/>
            c e: </s>
            <s xml:space="preserve">hoc eſt
              <lb/>
              <anchor type="note" xlink:label="note-0074-01a" xlink:href="note-0074-01"/>
            ut earum di-
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            midiæ d c ad
              <lb/>
            c g. </s>
            <s xml:space="preserve">ergo ex
              <lb/>
            antecedēti lé
              <lb/>
            mate ſequi-
              <lb/>
            tur lineá b c
              <lb/>
            per punctum
              <lb/>
            f tranſire.
              <lb/>
            </s>
            <s xml:space="preserve">Ducatur præ
              <lb/>
            terea à puncto h ad diametrum b d linea h K, æquidiſtans baſi
              <lb/>
            a c: </s>
            <s xml:space="preserve">& </s>
            <s xml:space="preserve">iuncta k c, quæ diametrum f g ſecet in l; </s>
            <s xml:space="preserve">per l ducatur</s>
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