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="201" file="0239" n="239" rhead="Conicor. Lib. VI."/>
          <p style="it">
            <s xml:id="echoid-s7539" xml:space="preserve">Et quia N O ad O A eſt vt P Q ad Q D inuertamus proportionem,
              <lb/>
              <note position="left" xlink:label="note-0239-01" xlink:href="note-0239-01a" xml:space="preserve">d</note>
            deinde bifariam ſecemus duas tertias partes, & </s>
            <s xml:id="echoid-s7540" xml:space="preserve">inuertamus eas quoque
              <lb/>
            fiet N O ad O R, nempe N L ad L T in eadem ratione ipſi V Z, nempe
              <lb/>
            L B ad B Z, vt D Q ad Q T, nempe P M ad P X æqualem ipſi Y a,
              <lb/>
            nempe M E ad E a, &</s>
            <s xml:id="echoid-s7541" xml:space="preserve">c. </s>
            <s xml:id="echoid-s7542" xml:space="preserve">Quoniam L O ad O I oſtenſa fuit vt M Q ad Q
              <lb/>
            K, & </s>
            <s xml:id="echoid-s7543" xml:space="preserve">propter parallelas I A, L N, nec non D K, M P eſt N O ad O A, vt L O
              <lb/>
            ad O I; </s>
            <s xml:id="echoid-s7544" xml:space="preserve">pariterq; </s>
            <s xml:id="echoid-s7545" xml:space="preserve">P Q ad Q D eſt vt M Q ad Q K; </s>
            <s xml:id="echoid-s7546" xml:space="preserve">igitur N O ad O A eandẽ
              <lb/>
            proportionẽ habet, quàm P Q ad Q D, & </s>
            <s xml:id="echoid-s7547" xml:space="preserve">comparando antecedentes ad ſemidif-
              <lb/>
            ferentias, vel ſemisũmas terminorũ erit N O ad R A, vt P Q ad S D: </s>
            <s xml:id="echoid-s7548" xml:space="preserve">& </s>
            <s xml:id="echoid-s7549" xml:space="preserve">pro-
              <lb/>
              <figure xlink:label="fig-0239-01" xlink:href="fig-0239-01a" number="272">
                <image file="0239-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0239-01"/>
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            pterea N O ad O R ſummã, vel differentiã conſequentium eandem proportionem
              <lb/>
            habebit, quàm P Q ad Q S; </s>
            <s xml:id="echoid-s7550" xml:space="preserve">ſed propter parallelas R T, & </s>
            <s xml:id="echoid-s7551" xml:space="preserve">O L eſt L N ad T L,
              <lb/>
            vt N O ad O R: </s>
            <s xml:id="echoid-s7552" xml:space="preserve">pariterque (propter parallelas S X, & </s>
            <s xml:id="echoid-s7553" xml:space="preserve">Q M) eſt P M ad X
              <lb/>
            M, vt P Q ad Q S; </s>
            <s xml:id="echoid-s7554" xml:space="preserve">igitur N L ad L T eandem proportionem habet, quàm
              <lb/>
            P M ad M X: </s>
            <s xml:id="echoid-s7555" xml:space="preserve">ſuntque in parallelogrammis V L, & </s>
            <s xml:id="echoid-s7556" xml:space="preserve">γ M latera oppoſita æqua-
              <lb/>
            lia V Z ipſi T L, atque a γ ipſi X M; </s>
            <s xml:id="echoid-s7557" xml:space="preserve">igitur N L ad V Z eandem proportio-
              <lb/>
            nem habet, quàm P M ad γ a, & </s>
            <s xml:id="echoid-s7558" xml:space="preserve">ita erunt earum quadrata; </s>
            <s xml:id="echoid-s7559" xml:space="preserve">ſed vt quadratũ
              <lb/>
              <note position="right" xlink:label="note-0239-02" xlink:href="note-0239-02a" xml:space="preserve">20 lib. 1.</note>
            N L ad quadratum V Z ita eſt abſciſſa L B ad abſcißam B Z, pariterque vt
              <lb/>
            quadratum P M ad quadratum γ a, ita eſt abſciſſa M E ad abſcißam E a; </s>
            <s xml:id="echoid-s7560" xml:space="preserve">er-
              <lb/>
            go L B ad B Z eandem proportiònem habet, quàm M E ad E a.</s>
            <s xml:id="echoid-s7561" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s7562" xml:space="preserve">Et occurrere faciamus par pari remanet O R ad R b, vt Q S ad S c, &</s>
            <s xml:id="echoid-s7563" xml:space="preserve">c.
              <lb/>
            </s>
            <s xml:id="echoid-s7564" xml:space="preserve">
              <note position="left" xlink:label="note-0239-03" xlink:href="note-0239-03a" xml:space="preserve">e</note>
            Quoniam oſtenſa fuit O N ad O R, vt Q P ad Q S, per conuerſionem rationis
              <lb/>
            O N ad N R erit vt Q P ad P S, pariterque oſtenſa fuit b N ad N O, vt
              <lb/>
            c P ad P Q; </s>
            <s xml:id="echoid-s7565" xml:space="preserve">ergo ex æquali b N ad N R eſt vt c P ad S P, & </s>
            <s xml:id="echoid-s7566" xml:space="preserve">diuidendo b R
              <lb/>
            ad R N erit vt c S ad S P; </s>
            <s xml:id="echoid-s7567" xml:space="preserve">ſed erat inuertendo R N ad N O, vt S P ad P Q;
              <lb/>
            </s>
            <s xml:id="echoid-s7568" xml:space="preserve">quare comparando antecedentes ad differentias terminorum erit N R ad R O vt
              <lb/>
            P S ad S Q; </s>
            <s xml:id="echoid-s7569" xml:space="preserve">ideoq; </s>
            <s xml:id="echoid-s7570" xml:space="preserve">rurſus ex æqualitate b R ad R O erit vt c S ad S Q; </s>
            <s xml:id="echoid-s7571" xml:space="preserve">eſtq; </s>
            <s xml:id="echoid-s7572" xml:space="preserve">
              <lb/>
            V R ad R b vt γ S ad S c (eo quod triangula V R b, & </s>
            <s xml:id="echoid-s7573" xml:space="preserve">γ S c ſunt ſimilia
              <lb/>
            triangulis ſimilibus O N L, & </s>
            <s xml:id="echoid-s7574" xml:space="preserve">Q M P propter æquidiſtantes) ergo ex æquali
              <lb/>
            ordinata V R ad R O eandem proportionem habet, quàm γ S ad S Q.</s>
            <s xml:id="echoid-s7575" xml:space="preserve"/>
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