Apollonius <Pergaeus>, Apollonii Pergaei Conicorvm Lib. V. VI. VII. paraphraste Abalphato Asphahanensi : nunc primum editi ; additvs in calce Archimedis assvmptorvm liber, ex codibvs arabicis mss Abrahamus Ecchellensis Maronita latinos reddidit, Jo. Alfonsvs Borellvs curam in geometricis versione contulit & [et] notas vberiores in vniuersum opus adiecit

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        <div xml:id="echoid-div1011" type="section" level="1" n="320">
          <pb o="336" file="0374" n="375" rhead="Apollonij Pergæi"/>
        </div>
        <div xml:id="echoid-div1013" type="section" level="1" n="321">
          <head xml:id="echoid-head397" xml:space="preserve">In Sectionem VIII. Propoſit. XXXXIIII.
            <lb/>
          XXXXV. & XXXXVI.</head>
          <head xml:id="echoid-head398" xml:space="preserve">LEMM A.X.</head>
          <p style="it">
            <s xml:id="echoid-s11762" xml:space="preserve">SI rectæ lineæ G H bifariam ſectæ in D addantur ſegmenta H A,
              <lb/>
            & </s>
            <s xml:id="echoid-s11763" xml:space="preserve">H E atque proportio dupli E H ad H G eadem fuerit propor-
              <lb/>
            tioni G H ad H A: </s>
            <s xml:id="echoid-s11764" xml:space="preserve">dico duplum rectanguli ex G A, & </s>
            <s xml:id="echoid-s11765" xml:space="preserve">H E in H
              <lb/>
            A æquale eſſe quadratis ex G A, & </s>
            <s xml:id="echoid-s11766" xml:space="preserve">ex A H: </s>
            <s xml:id="echoid-s11767" xml:space="preserve">ſi verò proportio illa
              <lb/>
            maior fuerit, erit quoque rectangulum maius quadratis: </s>
            <s xml:id="echoid-s11768" xml:space="preserve">ſi verò propor-
              <lb/>
            tio fuerit minor, rectangulum minus erit quadratis.</s>
            <s xml:id="echoid-s11769" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s11770" xml:space="preserve">Primo quia ſi duplum E H ad H G, eſt vt G H ad H A, ergo duplum re-
              <lb/>
            ctanguli E H A æquale erit quadrato G H, & </s>
            <s xml:id="echoid-s11771" xml:space="preserve">addatur communiter duplum
              <lb/>
              <figure xlink:label="fig-0374-01" xlink:href="fig-0374-01a" number="444">
                <image file="0374-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0374-01"/>
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            rectanguli G A H, erit duplum
              <lb/>
            rectanguli ex ſumma G A, & </s>
            <s xml:id="echoid-s11772" xml:space="preserve">E H
              <lb/>
            in A H æquale duplo rectanguli G
              <lb/>
            A H cum quadrato G H; </s>
            <s xml:id="echoid-s11773" xml:space="preserve">his verò
              <lb/>
            ſpatijs æquantur quadrata ex G A,
              <lb/>
            & </s>
            <s xml:id="echoid-s11774" xml:space="preserve">ex A H, ergo duplum rectan-
              <lb/>
            guli ex ſumma G A, E H in A H æquale erit duobus quadratis ex G A, & </s>
            <s xml:id="echoid-s11775" xml:space="preserve">
              <lb/>
            ex A H.</s>
            <s xml:id="echoid-s11776" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s11777" xml:space="preserve">Secundo, quia duplum E H ad H G, maiorem proportionem habet, quàm
              <lb/>
            G H ad A H, ergo duplum rectanguli E H A maius eſt quadrato G H, & </s>
            <s xml:id="echoid-s11778" xml:space="preserve">ad-
              <lb/>
            dito communiter duplo rectanguli G A H, erit duplum rectanguli ex G A, E
              <lb/>
            H in A H maius duobus quadratis ex G A, & </s>
            <s xml:id="echoid-s11779" xml:space="preserve">ex A H.</s>
            <s xml:id="echoid-s11780" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s11781" xml:space="preserve">Tertio, quia duplum E H ad H G minorem proportionem habet, quàm G H
              <lb/>
            ad A H, ergo duplum rectanguli E H A minus eſt quadrato G H, & </s>
            <s xml:id="echoid-s11782" xml:space="preserve">addito
              <lb/>
            duplo rectanguli G A H, erit duplum rectanguli ex G A, E H in A H minus
              <lb/>
            quadratis ex G A, & </s>
            <s xml:id="echoid-s11783" xml:space="preserve">ex A H.</s>
            <s xml:id="echoid-s11784" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div1015" type="section" level="1" n="322">
          <head xml:id="echoid-head399" xml:space="preserve">LEMM A XI.</head>
          <p style="it">
            <s xml:id="echoid-s11785" xml:space="preserve">SI recta linea G H ſecetur exterius in A, E, & </s>
            <s xml:id="echoid-s11786" xml:space="preserve">ſit eadem G H
              <lb/>
            differentia nedum ſegmentorum G E, & </s>
            <s xml:id="echoid-s11787" xml:space="preserve">E H, ſed etiam duo-
              <lb/>
            rum ſegmentorum G A, & </s>
            <s xml:id="echoid-s11788" xml:space="preserve">A H: </s>
            <s xml:id="echoid-s11789" xml:space="preserve">dico quod quadrata ex maximo,
              <lb/>
            & </s>
            <s xml:id="echoid-s11790" xml:space="preserve">ex vno intermediorum ſegmentorum, ſcilicet ex G E, & </s>
            <s xml:id="echoid-s11791" xml:space="preserve">ex E H
              <lb/>
              <figure xlink:label="fig-0374-02" xlink:href="fig-0374-02a" number="445">
                <image file="0374-02" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0374-02"/>
              </figure>
            æqualia ſunt quadratis ex
              <lb/>
            reliquo intermediorum, & </s>
            <s xml:id="echoid-s11792" xml:space="preserve">
              <lb/>
            ex minimo ſegmento, ſci-
              <lb/>
            licet ex G A, & </s>
            <s xml:id="echoid-s11793" xml:space="preserve">ex A
              <lb/>
            H vna cum duplo </s>
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