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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            I C cum exemplari N T, & </s>
            <s xml:id="echoid-s1058" xml:space="preserve">quadratum I L æquale eſt quadrato eiuſdem I C cum
              <lb/>
            exemplari Q Z. </s>
            <s xml:id="echoid-s1059" xml:space="preserve">Ergò exceſſus quadrati I A ſupra quadratum I L æqualis eſt
              <lb/>
            differentiæ exemplarium N T, & </s>
            <s xml:id="echoid-s1060" xml:space="preserve">Q Z. </s>
            <s xml:id="echoid-s1061" xml:space="preserve">Poſteà ducatur recta Q N: </s>
            <s xml:id="echoid-s1062" xml:space="preserve">quia trian-
              <lb/>
            gula Q N S, O N Q. </s>
            <s xml:id="echoid-s1063" xml:space="preserve">æqualia ſunt triangulo, cuius baſis æqualis eſt ſummæ re-
              <lb/>
            ctarum N S, & </s>
            <s xml:id="echoid-s1064" xml:space="preserve">O Q.
              <lb/>
            </s>
            <s xml:id="echoid-s1065" xml:space="preserve">altitudo verò V R, vel
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              <figure xlink:label="fig-0050-01" xlink:href="fig-0050-01a" number="19">
                <image file="0050-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0050-01"/>
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            M E, ſuntque illa duo
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            triãgula æqualia tra-
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            pezio N O Q ſiue-
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            exceſſui trianguli N
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            H S, ſupra triangu-
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            lum H O Q: </s>
            <s xml:id="echoid-s1066" xml:space="preserve">ergo triã-
              <lb/>
            gulum cuius baſis æ-
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            quatur ſumme ipſa-
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            rum N S, O Q alti-
              <lb/>
            tudo verò E M, æqua-
              <lb/>
            le eſt differentiæ triã-
              <lb/>
            gulorum N H S, O H
              <lb/>
            Q. </s>
            <s xml:id="echoid-s1067" xml:space="preserve">Et ſimiliter eorum dupla, ſcilicet rectangulum, cuius baſis æqualis eſt ſum-
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            mæ N S, O Q altitudo verò æqualis M E, erit differentia exemplarium rectã-
              <lb/>
            gulorum N T, & </s>
            <s xml:id="echoid-s1068" xml:space="preserve">Q Z; </s>
            <s xml:id="echoid-s1069" xml:space="preserve">ſed ſumma altitudinum V H, H R, ſeu ſumma abſciſ-
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            ſarum C M, C E ad ſum mam baſium N S, O Q eandem proportionem habet,
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            quam vna H V ad vnam O Q, ſeu quam latus tranſuerſum D C ad ſummam-
              <lb/>
            in hyperbola, & </s>
            <s xml:id="echoid-s1070" xml:space="preserve">ad differentiam in ellipſi laterum tranſuerſi D C, & </s>
            <s xml:id="echoid-s1071" xml:space="preserve">recti C F:
              <lb/>
            </s>
            <s xml:id="echoid-s1072" xml:space="preserve">Igitur differentia exemplar ium N T, Q Z, ſeu exceſſus quadrati I A ſupra-
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            quadratum I L æqualis eſt rectangulo contento ſub E M differentia abſciſſarum,
              <lb/>
            & </s>
            <s xml:id="echoid-s1073" xml:space="preserve">ſub ſumma ipſarum N S, & </s>
            <s xml:id="echoid-s1074" xml:space="preserve">O Q, ad quam ſumma abſcißarum eandem pro-
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            portionem habet, quam latus tranſuerſum ad ſummam in hyperbola, & </s>
            <s xml:id="echoid-s1075" xml:space="preserve">ad dif-
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            ferentiam in ellipſi laterum tranſuerſi, & </s>
            <s xml:id="echoid-s1076" xml:space="preserve">recti, quod fuerat propoſitum.</s>
            <s xml:id="echoid-s1077" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div62" type="section" level="1" n="41">
          <head xml:id="echoid-head66" xml:space="preserve">MONITVM.</head>
          <p style="it">
            <s xml:id="echoid-s1078" xml:space="preserve">E X varia diſpoſitione terminorum proportionalitatis ſcilicet duo-
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            rum antecedentium, & </s>
            <s xml:id="echoid-s1079" xml:space="preserve">duorum conſequentium conſurgunt
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            plures modi argumentandi, quorum aliqui in elementis ex-
              <lb/>
            poſiti non ſunt, aliqui verò ſignificantiſsimis vocibus, & </s>
            <s xml:id="echoid-s1080" xml:space="preserve">
              <lb/>
            breuiùs indicantur in textu Arabico, igitur, ne ſepius repetatur prolixa-
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            expoſitio modorum argumentandi in proportionalibus, & </s>
            <s xml:id="echoid-s1081" xml:space="preserve">non proportiona-
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            libus, qui cumulatè inſeruntur in demonſirationibus Apollonij opere pre-
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            tium erit eos ſemel hìc exponere.</s>
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