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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              <pb o="234" file="0272" n="272" rhead="Apollonij Pergæi"/>
              <figure xlink:label="fig-0272-01" xlink:href="fig-0272-01a" number="319">
                <image file="0272-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0272-01"/>
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            cireuli G C O B, & </s>
            <s xml:id="echoid-s8749" xml:space="preserve">G Q P L ſe ſe contingentes in communi puncto G rectæ li-
              <lb/>
            neæ G O ducaturque diameter L b Q æquidiſtans ipſi B C: </s>
            <s xml:id="echoid-s8750" xml:space="preserve">& </s>
            <s xml:id="echoid-s8751" xml:space="preserve">vt latus rectum
              <lb/>
            ad tranſuer ſum ſectionis X, ita fiat quadratum G d ad quadratum d A; </s>
            <s xml:id="echoid-s8752" xml:space="preserve">& </s>
            <s xml:id="echoid-s8753" xml:space="preserve">
              <lb/>
            coniungantur rectæ lineæ A G, & </s>
            <s xml:id="echoid-s8754" xml:space="preserve">A O, ducaturque ex puncto P recta linea P
              <lb/>
            N parallela ipſi O A occurrens G A in N, atque A, & </s>
            <s xml:id="echoid-s8755" xml:space="preserve">N fiant vertices duorum
              <lb/>
            conorum A B C, & </s>
            <s xml:id="echoid-s8756" xml:space="preserve">N L Q, & </s>
            <s xml:id="echoid-s8757" xml:space="preserve">ſecetur D d æqualis ſemiſſi potentis figuram
              <lb/>
            ſectionis X; </s>
            <s xml:id="echoid-s8758" xml:space="preserve">ducaturque per punctum D planum E M F æquidiſtans plano com-
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            muni A G O per axes ducto, efficiens in conicis ſuperficiebus ſectiones H I K, & </s>
            <s xml:id="echoid-s8759" xml:space="preserve">
              <lb/>
            T V c; </s>
            <s xml:id="echoid-s8760" xml:space="preserve">Dico eas eſſe hyperbolas quæſitas. </s>
            <s xml:id="echoid-s8761" xml:space="preserve">Quoniam propter parallelas A O, N
              <lb/>
            P eſt A G ad G O, vt N G ad G P, & </s>
            <s xml:id="echoid-s8762" xml:space="preserve">ad ſemißes conſequentium, ſcilicet A G
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            ad G d, atque N G ad G b proportionales erunt, ideoque A d, N b erunt pa-
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            rallelæ, & </s>
            <s xml:id="echoid-s8763" xml:space="preserve">A d ad d G, ſeu ad d C eſt vt N b ad b G, ſeu ad b Q; </s>
            <s xml:id="echoid-s8764" xml:space="preserve">eſtque
              <lb/>
            d C etiam parallela b Q; </s>
            <s xml:id="echoid-s8765" xml:space="preserve">ergo plana A B C, & </s>
            <s xml:id="echoid-s8766" xml:space="preserve">N L Q parallela ſunt, & </s>
            <s xml:id="echoid-s8767" xml:space="preserve">
              <lb/>
            anguli A d C, & </s>
            <s xml:id="echoid-s8768" xml:space="preserve">N b Q æquales ſunt, atque triangula A d C, & </s>
            <s xml:id="echoid-s8769" xml:space="preserve">N b Q
              <lb/>
            ſimilia crunt inter ſe; </s>
            <s xml:id="echoid-s8770" xml:space="preserve">ideoque circa angulos æquales C, & </s>
            <s xml:id="echoid-s8771" xml:space="preserve">Q erit A C ad C d,
              <lb/>
            vt N Q ad Q b, & </s>
            <s xml:id="echoid-s8772" xml:space="preserve">ad conſequentium duplas, ſcilicet A C ad C B, atq; </s>
            <s xml:id="echoid-s8773" xml:space="preserve">N Q
              <lb/>
            ad Q L proportionales erunt; </s>
            <s xml:id="echoid-s8774" xml:space="preserve">& </s>
            <s xml:id="echoid-s8775" xml:space="preserve">propterea triangula A B C, & </s>
            <s xml:id="echoid-s8776" xml:space="preserve">N L Q ſimilia
              <lb/>
            exunt, & </s>
            <s xml:id="echoid-s8777" xml:space="preserve">ſimiliter poſita, & </s>
            <s xml:id="echoid-s8778" xml:space="preserve">inter ſe parallela; </s>
            <s xml:id="echoid-s8779" xml:space="preserve">ergo efficient in duobus planis A O
              <lb/>
            G, & </s>
            <s xml:id="echoid-s8780" xml:space="preserve">M E F inter ſe æquidiſtantibus ſectionũ diametros I D, & </s>
            <s xml:id="echoid-s8781" xml:space="preserve">V a parallelas
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            conorũ axibus A d, & </s>
            <s xml:id="echoid-s8782" xml:space="preserve">N b, & </s>
            <s xml:id="echoid-s8783" xml:space="preserve">inter ſe; </s>
            <s xml:id="echoid-s8784" xml:space="preserve">quare conſtituent cum ſectionũ </s>
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