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="48" file="0086" n="86" rhead="Apollonij Pergæi"/>
          <p>
            <s xml:id="echoid-s2276" xml:space="preserve">Igitur C a eſt li-
              <lb/>
              <note position="right" xlink:label="note-0086-01" xlink:href="note-0086-01a" xml:space="preserve">o</note>
              <figure xlink:label="fig-0086-01" xlink:href="fig-0086-01a" number="63">
                <image file="0086-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0086-01"/>
              </figure>
            nea quinta propor-
              <lb/>
            tionalis aliarum.
              <lb/>
            </s>
            <s xml:id="echoid-s2277" xml:space="preserve">quatuor, &</s>
            <s xml:id="echoid-s2278" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2279" xml:space="preserve">Quia
              <lb/>
            poſitæ fuerunt qua-
              <lb/>
            tuor rectæ lineæ F C,
              <lb/>
            N C, O C, C A con-
              <lb/>
            tinuè proportionales,
              <lb/>
            eſt que C A ad C a, vt
              <lb/>
            O C ad C A; </s>
            <s xml:id="echoid-s2280" xml:space="preserve">ergò pri-
              <lb/>
              <note position="left" xlink:label="note-0086-02" xlink:href="note-0086-02a" xml:space="preserve">37. lib. 1.</note>
            ma F C ad tertiam,
              <lb/>
            O C eamdem propor-
              <lb/>
            tionem habet, quàm
              <lb/>
            O C ad quintam C a
              <lb/>
            continuè proportio-
              <lb/>
            nalium, quare com-
              <lb/>
            parando homologorũ
              <lb/>
              <note position="left" xlink:label="note-0086-03" xlink:href="note-0086-03a" xml:space="preserve">Lem. 4.
                <lb/>
              præmiff.</note>
            differentias F O ad
              <lb/>
            O a eſt, vt F C ad C
              <lb/>
            O; </s>
            <s xml:id="echoid-s2281" xml:space="preserve">ſedfacta fuit vt
              <lb/>
            F O, ad O C, ita f O
              <lb/>
            ad O B; </s>
            <s xml:id="echoid-s2282" xml:space="preserve">ergo compo-
              <lb/>
            nendo in hyperbola,
              <lb/>
            & </s>
            <s xml:id="echoid-s2283" xml:space="preserve">comparando dif-
              <lb/>
            ferentias terminorũ
              <lb/>
              <note position="left" xlink:label="note-0086-04" xlink:href="note-0086-04a" xml:space="preserve">Lem. 2.
                <lb/>
              præm.</note>
            ad conſequentes in,
              <lb/>
            ellipſi, eſt F C ad C O, ſeu F O ad O a, vt f B ad B O; </s>
            <s xml:id="echoid-s2284" xml:space="preserve">nempe vt f h ad eandem O a,
              <lb/>
            propter ſimilitudinẽ triangulorum B fh, & </s>
            <s xml:id="echoid-s2285" xml:space="preserve">B O a; </s>
            <s xml:id="echoid-s2286" xml:space="preserve">& </s>
            <s xml:id="echoid-s2287" xml:space="preserve">ideo F O, & </s>
            <s xml:id="echoid-s2288" xml:space="preserve">fh æquales ſunt.</s>
            <s xml:id="echoid-s2289" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">p</note>
          <p>
            <s xml:id="echoid-s2290" xml:space="preserve">Et propterea fi ad i h maiorem proportionem habet, quàm ad f g, &</s>
            <s xml:id="echoid-s2291" xml:space="preserve">c.
              <lb/>
            </s>
            <s xml:id="echoid-s2292" xml:space="preserve">Quia F O, ſeu g f oſtenſa fuit æqualis fh erit g h ſecta bifariam in f, & </s>
            <s xml:id="echoid-s2293" xml:space="preserve">non bifa-
              <lb/>
            riam in i propterea (ex lemmate ſexto huius lib.) </s>
            <s xml:id="echoid-s2294" xml:space="preserve">habebit fh ad ih, ſcilicet B f ad
              <lb/>
            di (propter ſimilitudinem triangulorum B fh, dih) maiorem proportionem, quàm
              <lb/>
            ig ad gf, ſed B f ad V i portionem ipſius d i habet maiorem proportionem, quàm ad
              <lb/>
              <note position="left" xlink:label="note-0086-06" xlink:href="note-0086-06a" xml:space="preserve">Lem. 5.
                <lb/>
              In nota
                <lb/>
              litere n
                <lb/>
              præm.</note>
            di; </s>
            <s xml:id="echoid-s2295" xml:space="preserve">ergo B f ad V i habet maiorem proportionem, quàm i g ad g f, ergo rectangulum
              <lb/>
            B f g, nempe rectangulum g C (quod eſt oſtenſum ei æquale) maius eſt rectangulo
              <lb/>
            V i g.</s>
            <s xml:id="echoid-s2296" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2297" xml:space="preserve">Et ponamus rectangulum g e commune, &</s>
            <s xml:id="echoid-s2298" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2299" xml:space="preserve">Et addamus in hyperbola, & </s>
            <s xml:id="echoid-s2300" xml:space="preserve">
              <lb/>
              <note position="right" xlink:label="note-0086-07" xlink:href="note-0086-07a" xml:space="preserve">q</note>
            auferamus in ellipſi rectangulum g e communiter.</s>
            <s xml:id="echoid-s2301" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2302" xml:space="preserve">Et propterea E K ad e V, nempe K ad Y e, &</s>
            <s xml:id="echoid-s2303" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2304" xml:space="preserve">Sunt enim triangula E K Y,
              <lb/>
              <note position="right" xlink:label="note-0086-08" xlink:href="note-0086-08a" xml:space="preserve">r</note>
            & </s>
            <s xml:id="echoid-s2305" xml:space="preserve">V e Y ſimilia, ergo E K ad e V eſt, vt K Y ad Y e, quarè K Y ad Y e maiorem pro-
              <lb/>
            portionem habet, quàm e M ad M K, & </s>
            <s xml:id="echoid-s2306" xml:space="preserve">componendo, eadem K e maiorem propor-
              <lb/>
            tionem habet ad e Y, quàm ad M K, ſeu ad F D; </s>
            <s xml:id="echoid-s2307" xml:space="preserve">vnde patet, quod e Y minor ſit,
              <lb/>
            quam F D.</s>
            <s xml:id="echoid-s2308" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2309" xml:space="preserve">Et conſtat quemadmodum antea demonſtrauimus, &</s>
            <s xml:id="echoid-s2310" xml:space="preserve">c. </s>
            <s xml:id="echoid-s2311" xml:space="preserve">Quoniam e Y mi-
              <lb/>
              <note position="right" xlink:label="note-0086-09" xlink:href="note-0086-09a" xml:space="preserve">ſ</note>
            nor oſtenſa eſt, quam K M ergo eadem E I ad r e, ſeu I X ad V e (propter ſimilitu-
              <lb/>
            dinem triangulorum E I X, r e V) maiorem proportionem habebit, quàm E I ad
              <lb/>
            M K, ſeu I C ad C S, veladei æqualem c e; </s>
            <s xml:id="echoid-s2312" xml:space="preserve">igitur comparando homologorum </s>
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