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-div447" type="section" level="1" n="137">
          <pb o="123" file="0161" n="161" rhead="Conicor. Lib. V."/>
        </div>
        <div xml:id="echoid-div450" type="section" level="1" n="138">
          <head xml:id="echoid-head184" xml:space="preserve">Notæ in Propoſ. XXIII. XXIV.</head>
          <p>
            <s xml:id="echoid-s4862" xml:space="preserve">EContra linea maxima, ſi non egredia-
              <lb/>
              <note position="left" xlink:label="note-0161-01" xlink:href="note-0161-01a" xml:space="preserve">a</note>
              <figure xlink:label="fig-0161-01" xlink:href="fig-0161-01a" number="154">
                <image file="0161-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0161-01"/>
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            tur ex centro, continet cum mẽſura
              <lb/>
            angulum acutum, & </s>
            <s xml:id="echoid-s4863" xml:space="preserve">proportio illius in-
              <lb/>
            uerſæ ad abſciſſam eius potentialis ex mẽ-
              <lb/>
            ſura cum origine, eſt vt proportio figuræ
              <lb/>
            recti. </s>
            <s xml:id="echoid-s4864" xml:space="preserve">Si verò fuerit extra centrum, erit
              <lb/>
            perpendicularis ſuper rectum, &</s>
            <s xml:id="echoid-s4865" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4866" xml:space="preserve">Mani-
              <lb/>
            feſtè nõ nulla in textu Arabicc
              <unsure/>
            deficiunt; </s>
            <s xml:id="echoid-s4867" xml:space="preserve">ali-
              <lb/>
            qua verò immutari debent; </s>
            <s xml:id="echoid-s4868" xml:space="preserve">alioquin propo-
              <lb/>
            ſitio vera non eſſet, itaque legendum puto: </s>
            <s xml:id="echoid-s4869" xml:space="preserve">E
              <lb/>
            contra ſi maximi rami origo ponatur in axi
              <lb/>
            minore, &</s>
            <s xml:id="echoid-s4870" xml:space="preserve">c: </s>
            <s xml:id="echoid-s4871" xml:space="preserve">Vt in textu babetur.</s>
            <s xml:id="echoid-s4872" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s4873" xml:space="preserve">Sit ſectio A B C elliptica, & </s>
            <s xml:id="echoid-s4874" xml:space="preserve">E origo, & </s>
            <s xml:id="echoid-s4875" xml:space="preserve">E F linea maxima, &</s>
            <s xml:id="echoid-s4876" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4877" xml:space="preserve">Ad-
              <lb/>
              <note position="left" xlink:label="note-0161-02" xlink:href="note-0161-02a" xml:space="preserve">b</note>
            didi pariter in bac expoſitione verba, quæ deſiciunt; </s>
            <s xml:id="echoid-s4878" xml:space="preserve">nimirum: </s>
            <s xml:id="echoid-s4879" xml:space="preserve">Sit centrum
              <lb/>
            D, & </s>
            <s xml:id="echoid-s4880" xml:space="preserve">origo E, quæ ſit in axi minori A C.</s>
            <s xml:id="echoid-s4881" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s4882" xml:space="preserve">Et ideo D C ad dimidium erecti eſt linea minor, quàm D C, & </s>
            <s xml:id="echoid-s4883" xml:space="preserve">ſit D
              <lb/>
              <note position="left" xlink:label="note-0161-03" xlink:href="note-0161-03a" xml:space="preserve">c</note>
            G ad G E, &</s>
            <s xml:id="echoid-s4884" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4885" xml:space="preserve">Nonnulla adiungi debent buic textui corruptiſsimo, ne ſint
              <lb/>
            verba nil prorſus ſignificantia, itaque ſic legendum puto. </s>
            <s xml:id="echoid-s4886" xml:space="preserve">Et ideo aliqua minor,
              <lb/>
            quàm D C ad reſiduam vſque ad E eandem proportionem babebit, quàm D C ad
              <lb/>
            ſemiſſem erecti; </s>
            <s xml:id="echoid-s4887" xml:space="preserve">& </s>
            <s xml:id="echoid-s4888" xml:space="preserve">ſit D G ad G E, &</s>
            <s xml:id="echoid-s4889" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4890" xml:space="preserve">Quæ verba breuiſsimè more Apollonij
              <lb/>
            expoſita ſic confirmantur. </s>
            <s xml:id="echoid-s4891" xml:space="preserve">Quia E C oſtenſa eſt minor dimidio erecti axis mi-
              <lb/>
            noris C A, fiat C K æqualis dimidio erecti; </s>
            <s xml:id="echoid-s4892" xml:space="preserve">erit E C minor quàm C K,
              <lb/>
            & </s>
            <s xml:id="echoid-s4893" xml:space="preserve">ablata communi D C erit D E minor, quàm K D; </s>
            <s xml:id="echoid-s4894" xml:space="preserve">& </s>
            <s xml:id="echoid-s4895" xml:space="preserve">propterea D E ad ean-
              <lb/>
            dem D C minorem proportionem babebit, quàm K D: </s>
            <s xml:id="echoid-s4896" xml:space="preserve">fiat E D a d D G, vt K
              <lb/>
            D ad D C, erit D G minor, quàm D C: </s>
            <s xml:id="echoid-s4897" xml:space="preserve">& </s>
            <s xml:id="echoid-s4898" xml:space="preserve">componendo, E G ad G D eandem
              <lb/>
            proportionem babebit, quàm K C ad C D, & </s>
            <s xml:id="echoid-s4899" xml:space="preserve">inuertendo, D G ad G E eandem
              <lb/>
            proportionem babebit, quàm D C ſemiſsis axis recti ad C K ſemiſsim erecti
              <lb/>
            eiuſdem axis; </s>
            <s xml:id="echoid-s4900" xml:space="preserve">& </s>
            <s xml:id="echoid-s4901" xml:space="preserve">ex G ducatur G F perpendicularis ad axim, quàm, dico, oc-
              <lb/>
            currere ſectioni in F termino maximi rami E F.</s>
            <s xml:id="echoid-s4902" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s4903" xml:space="preserve">Et ſi maxima fuerit extra centrum, vt D B erit perpendicularis, &</s>
            <s xml:id="echoid-s4904" xml:space="preserve">c.
              <lb/>
            </s>
            <s xml:id="echoid-s4905" xml:space="preserve">
              <note position="left" xlink:label="note-0161-04" xlink:href="note-0161-04a" xml:space="preserve">d</note>
            Textus euidenter corruptus ſic corrigi debet. </s>
            <s xml:id="echoid-s4906" xml:space="preserve">Si verò ramus maximus educatur
              <lb/>
            ex centro, vt D B, &</s>
            <s xml:id="echoid-s4907" xml:space="preserve">c.</s>
            <s xml:id="echoid-s4908" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div455" type="section" level="1" n="139">
          <head xml:id="echoid-head185" xml:space="preserve">Notæ in Propoſ. XXXV.</head>
          <p>
            <s xml:id="echoid-s4909" xml:space="preserve">SI producatur vna linearum maximarum, vt E B ad latus illius originis
              <lb/>
              <note position="left" xlink:label="note-0161-05" xlink:href="note-0161-05a" xml:space="preserve">a</note>
            E ad punctum F, fiet maxima linearum egredientium ab illo puncto
              <lb/>
            F G, F H, F I, F A ad ſectionem B I A in directum, & </s>
            <s xml:id="echoid-s4910" xml:space="preserve">propinquior illi
              <lb/>
            maior eſt remotiore, &</s>
            <s xml:id="echoid-s4911" xml:space="preserve">c. </s>
            <s xml:id="echoid-s4912" xml:space="preserve">Immutaui nonnulla, quæ ad propoſitionis integrita-
              <lb/>
            tem facerc videbantur: </s>
            <s xml:id="echoid-s4913" xml:space="preserve">vt in textu babetur.</s>
            <s xml:id="echoid-s4914" xml:space="preserve"/>
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