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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            <s xml:id="echoid-s7336" xml:space="preserve">
              <pb o="194" file="0232" n="232" rhead="Apollonij Pergæi"/>
              <figure xlink:label="fig-0232-01" xlink:href="fig-0232-01a" number="262">
                <image file="0232-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0232-01"/>
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            ad E K, nempe P M ad D K potentia, nempe M Q ad Q K, & </s>
            <s xml:id="echoid-s7337" xml:space="preserve">per con-
              <lb/>
            uerſionem rationis O L ad L I erit, vt Q M ad M K: </s>
            <s xml:id="echoid-s7338" xml:space="preserve">eſtque I L ad L B,
              <lb/>
            vt K M ad M E; </s>
            <s xml:id="echoid-s7339" xml:space="preserve">ergo O L ad L B eſt, vt Q M ad M E, & </s>
            <s xml:id="echoid-s7340" xml:space="preserve">L B ad L N
              <lb/>
            eſt, vt E M ad M P (propter ſimilitudinem duarum ſectionum) ergo ex
              <lb/>
              <note position="right" xlink:label="note-0232-01" xlink:href="note-0232-01a" xml:space="preserve">c</note>
              <note position="left" xlink:label="note-0232-02" xlink:href="note-0232-02a" xml:space="preserve">Defin. 2.</note>
            æqualitate O L ad L N erit, vt Q M ad M P; </s>
            <s xml:id="echoid-s7341" xml:space="preserve">ſuntque M, & </s>
            <s xml:id="echoid-s7342" xml:space="preserve">L duo an-
              <lb/>
            guli recti; </s>
            <s xml:id="echoid-s7343" xml:space="preserve">ergo N L O ſimile eſt P M Q; </s>
            <s xml:id="echoid-s7344" xml:space="preserve">& </s>
            <s xml:id="echoid-s7345" xml:space="preserve">per R, S ſemipartitiones ip-
              <lb/>
            ſarum N A, D P ducamus ipſas T V, X Y parallelas duobus axibus, & </s>
            <s xml:id="echoid-s7346" xml:space="preserve">
              <lb/>
            ex duobus punctis V, Y, educamus perpendiculares V Z, Y a ſuper duos
              <lb/>
            axes. </s>
            <s xml:id="echoid-s7347" xml:space="preserve">Et quia N O ad O A eſt, vt P Q ad Q D comparando antecedẽ-
              <lb/>
            tes ad ſemiſſes differentiarum terminorum vel ad ſemiſummas eorũ fiet N
              <lb/>
              <note position="right" xlink:label="note-0232-03" xlink:href="note-0232-03a" xml:space="preserve">d</note>
            O ad R O, nempe N L ad L T, quæ eſt æqualis ipſi V Z, nempe L B
              <lb/>
            ad B Z longitudine (19. </s>
            <s xml:id="echoid-s7348" xml:space="preserve">ex 1.) </s>
            <s xml:id="echoid-s7349" xml:space="preserve">vt P Q ad Q S, nempe P M ad X M æ-
              <lb/>
            qualem ipſi Y a, nempe longitudine, vt M E ad E a (19. </s>
            <s xml:id="echoid-s7350" xml:space="preserve">ex 1) igitur
              <lb/>
              <note position="left" xlink:label="note-0232-04" xlink:href="note-0232-04a" xml:space="preserve">20. lib. 1.</note>
            comparando differentias terminorum ad antecedentes, erit Z L ad L B,
              <lb/>
            vt a M ad M E, & </s>
            <s xml:id="echoid-s7351" xml:space="preserve">L B ad L O eſt, vt M E ad M Q; </s>
            <s xml:id="echoid-s7352" xml:space="preserve">ergo ex æqualitate
              <lb/>
            L Z ad L O, nempe N b ad N O eſt, vt M a ad M Q, nempe P c ad P Q
              <lb/>
              <note position="left" xlink:label="note-0232-05" xlink:href="note-0232-05a" xml:space="preserve">Ibidem.</note>
            crat autem prius N R ad N O, vt S P ad P Q, & </s>
            <s xml:id="echoid-s7353" xml:space="preserve">comparando ſemisũ-
              <lb/>
              <note position="right" xlink:label="note-0232-06" xlink:href="note-0232-06a" xml:space="preserve">e</note>
            mas, vel ſemidifferentias terminorum ad eorundem differentias O R ad
              <lb/>
            R b erit, vt Q S ad S c, & </s>
            <s xml:id="echoid-s7354" xml:space="preserve">R b ad R V eſt, vt S c ad S Y; </s>
            <s xml:id="echoid-s7355" xml:space="preserve">quia
              <lb/>
            duo triangula V R b, Y S c ſunt ſimilia; </s>
            <s xml:id="echoid-s7356" xml:space="preserve">ergo R O ad R V eandem pro-
              <lb/>
            portionem habet, quàm Q S ad S Y; </s>
            <s xml:id="echoid-s7357" xml:space="preserve">ſed tangens in V perueniens ad L O
              <lb/>
              <note position="right" xlink:label="note-0232-07" xlink:href="note-0232-07a" xml:space="preserve">f</note>
            æqualis eſt O R, cui parallela eſt; </s>
            <s xml:id="echoid-s7358" xml:space="preserve">quia cadit inter duas lineas parallelas;
              <lb/>
            </s>
            <s xml:id="echoid-s7359" xml:space="preserve">& </s>
            <s xml:id="echoid-s7360" xml:space="preserve">ſimiliter tangens in Y parallela eſt S Q, & </s>
            <s xml:id="echoid-s7361" xml:space="preserve">ei æqualis; </s>
            <s xml:id="echoid-s7362" xml:space="preserve">ergo V R ab-
              <lb/>
            ſciſſa ad tangentem eſt, vt abſciſſa S Y ad eius tangentem, & </s>
            <s xml:id="echoid-s7363" xml:space="preserve">angulus Q
              <lb/>
            æqualis eſt angulo O; </s>
            <s xml:id="echoid-s7364" xml:space="preserve">igitur duo ſegmenta N V A, P Y D ſunt ſimilia
              <lb/>
            (16. </s>
            <s xml:id="echoid-s7365" xml:space="preserve">ex 6.) </s>
            <s xml:id="echoid-s7366" xml:space="preserve">& </s>
            <s xml:id="echoid-s7367" xml:space="preserve">pariter duo ſegmenta A B C, D E F, atque duo ſegmen-
              <lb/>
              <note position="right" xlink:label="note-0232-08" xlink:href="note-0232-08a" xml:space="preserve">g</note>
            ta N B, P E ſunt ſimilia inter ſe, & </s>
            <s xml:id="echoid-s7368" xml:space="preserve">ſimiliter poſita.</s>
            <s xml:id="echoid-s7369" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7370" xml:space="preserve">Deinde ponamus aliud ſegmentum P d. </s>
            <s xml:id="echoid-s7371" xml:space="preserve">Dico non eſſe ſimile alicui
              <lb/>
              <note position="right" xlink:label="note-0232-09" xlink:href="note-0232-09a" xml:space="preserve">h</note>
            prædictorum ſegmentorum, quia non abſcinduntur à duabus ordinationi-
              <lb/>
            bus vnius axis (18. </s>
            <s xml:id="echoid-s7372" xml:space="preserve">ex 6.)</s>
            <s xml:id="echoid-s7373" xml:space="preserve">. </s>
            <s xml:id="echoid-s7374" xml:space="preserve">Et hoc erat oſtendendum.</s>
            <s xml:id="echoid-s7375" xml:space="preserve"/>
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