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-div762" type="section" level="1" n="237">
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            <s xml:id="echoid-s8960" xml:space="preserve">
              <pb o="239" file="0277" n="277" rhead="Conicor. Lib. VI."/>
              <figure xlink:label="fig-0277-01" xlink:href="fig-0277-01a" number="322">
                <image file="0277-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0277-01"/>
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            ipſi K L, non eſſet eidem æqualis.) </s>
            <s xml:id="echoid-s8961" xml:space="preserve">His poſitis ſi educatur ex F linea ipſi
              <lb/>
            patallela cadet inter F G, F H, aut inter F I, F G; </s>
            <s xml:id="echoid-s8962" xml:space="preserve">ſitque F N; </s>
            <s xml:id="echoid-s8963" xml:space="preserve">igitur
              <lb/>
              <note position="right" xlink:label="note-0277-01" xlink:href="note-0277-01a" xml:space="preserve">12. lib. 1.</note>
            quadratum F N ad I N in N H eſt, vt D B ad B E: </s>
            <s xml:id="echoid-s8964" xml:space="preserve">quod eſt abſurdum;
              <lb/>
            </s>
            <s xml:id="echoid-s8965" xml:space="preserve">quia quadratum F N maius eſt, quàm quadratum F G, & </s>
            <s xml:id="echoid-s8966" xml:space="preserve">N H in N I
              <lb/>
            minus eſt, quàm quadratum G H.</s>
            <s xml:id="echoid-s8967" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8968" xml:space="preserve">Poſtea habeat quadratum F G ad quadratum G H minorem propor-
              <lb/>
            tionem quàm babet D B ad B E; </s>
            <s xml:id="echoid-s8969" xml:space="preserve">& </s>
            <s xml:id="echoid-s8970" xml:space="preserve">circumſcribamus circa triangulum.
              <lb/>
            </s>
            <s xml:id="echoid-s8971" xml:space="preserve">H F I circulum ; </s>
            <s xml:id="echoid-s8972" xml:space="preserve">& </s>
            <s xml:id="echoid-s8973" xml:space="preserve">producamus F G quouſque occurrat circuli circum-
              <lb/>
            ferentię in O; </s>
            <s xml:id="echoid-s8974" xml:space="preserve">ergo quadratum F G ad quadratum G H, nempe ad F G
              <lb/>
            in G O habet minorem proportionem, quàm D B ad B E: </s>
            <s xml:id="echoid-s8975" xml:space="preserve">& </s>
            <s xml:id="echoid-s8976" xml:space="preserve">ponamus
              <lb/>
            F G ad G P, vt D B ad B E ; </s>
            <s xml:id="echoid-s8977" xml:space="preserve">& </s>
            <s xml:id="echoid-s8978" xml:space="preserve">per P ducamus P Q parallellam H I ; </s>
            <s xml:id="echoid-s8979" xml:space="preserve">
              <lb/>
            & </s>
            <s xml:id="echoid-s8980" xml:space="preserve">coniungamus F R, F Q; </s>
            <s xml:id="echoid-s8981" xml:space="preserve">quæ occurrant H I in S, N: </s>
            <s xml:id="echoid-s8982" xml:space="preserve">quare D B ad
              <lb/>
            B E eſt, vt F G ad G P, quæ eſt, vt F N ad N Q; </s>
            <s xml:id="echoid-s8983" xml:space="preserve">nempe vt quadra-
              <lb/>
            tum F N ad F N in N Q æquale ipſi I N in N H, atque vt quadra-
              <lb/>
            tum F S ad F S in S R, nempe vt quadratum F S ad I S in S H; </s>
            <s xml:id="echoid-s8984" xml:space="preserve">& </s>
            <s xml:id="echoid-s8985" xml:space="preserve">edu-
              <lb/>
            camus T V, K L, quæ ſubtendant duos angulos H F K, I F T, & </s>
            <s xml:id="echoid-s8986" xml:space="preserve">ſint
              <lb/>
              <note position="left" xlink:label="note-0277-02" xlink:href="note-0277-02a" xml:space="preserve">c</note>
            parallelæ ipſis F N, & </s>
            <s xml:id="echoid-s8987" xml:space="preserve">F S, & </s>
            <s xml:id="echoid-s8988" xml:space="preserve">æquales ipſi D B; </s>
            <s xml:id="echoid-s8989" xml:space="preserve">igitur duo plana per K
              <lb/>
              <note position="left" xlink:label="note-0277-03" xlink:href="note-0277-03a" xml:space="preserve">d</note>
            L, T V extenſa ſuper triangulum H F I ad angulos rectos eleuata, pro-
              <lb/>
            ducunt in cono H F I ſectiones hyperbolicas, quarum axes L M, V X,
              <lb/>
            & </s>
            <s xml:id="echoid-s8990" xml:space="preserve">inclinati ipſarum L K, T V, & </s>
            <s xml:id="echoid-s8991" xml:space="preserve">ſinguli earum ad ſuos erectos eandem
              <lb/>
            proportionem habent, quàm D B ad B E, & </s>
            <s xml:id="echoid-s8992" xml:space="preserve">propterea figuræ ſectionum
              <lb/>
              <note position="right" xlink:label="note-0277-04" xlink:href="note-0277-04a" xml:space="preserve">2. huius.</note>
            ſimiles ſunt, & </s>
            <s xml:id="echoid-s8993" xml:space="preserve">æquales, ideoque ſectiones, quarum axes ſunt L M, V
              <lb/>
            X ſunt æquales ſectioni A B.</s>
            <s xml:id="echoid-s8994" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8995" xml:space="preserve">Nec reperitur ſectio præter iam dictas, cuius vertex ſit ſuper aliquam
              <lb/>
              <note position="left" xlink:label="note-0277-05" xlink:href="note-0277-05a" xml:space="preserve">e</note>
            duarum linearum H F, F I, & </s>
            <s xml:id="echoid-s8996" xml:space="preserve">ſit æqualis ſectioni A B. </s>
            <s xml:id="echoid-s8997" xml:space="preserve">Quia ſi reperiri
              <lb/>
            poſſet, caderet eius axis in planum trianguli H F I, illiuſque axi educa-
              <lb/>
            tur parallela F Z a, quæ non cadet ſuper F R, neque ſuper F Q, eritq;
              <lb/>
            </s>
            <s xml:id="echoid-s8998" xml:space="preserve">quadratum F Z ad I Z in Z H, quod eſt æquale ipſi F Z in Z a, nempe
              <lb/>
            F Z ad Z a eandem proportionem haberet, quàm D B ad B E; </s>
            <s xml:id="echoid-s8999" xml:space="preserve">ſed D
              <lb/>
            B ad B E eſt, vt F G ad G P, nempe F Z ad Z b; </s>
            <s xml:id="echoid-s9000" xml:space="preserve">ergo proportio F </s>
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