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="331" file="0369" n="370" rhead="Conicor. Lib. VII."/>
            rentiæ H G, & </s>
            <s xml:id="echoid-s11627" xml:space="preserve">ideo H A minor erit, quàm H D: </s>
            <s xml:id="echoid-s11628" xml:space="preserve">ſecari ergo poterit H M
              <lb/>
            æqualis D H, quæmaior erit, quàm A H, ducaturq; </s>
            <s xml:id="echoid-s11629" xml:space="preserve">per M ad axim ordinatim
              <lb/>
            applicata N M n occurrens ſectioni in punctis N n, à quibus iungãtur C N, & </s>
            <s xml:id="echoid-s11630" xml:space="preserve">C
              <lb/>
              <figure xlink:label="fig-0369-01" xlink:href="fig-0369-01a" number="438">
                <image file="0369-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0369-01"/>
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            n, ijſdemque æquidiſtantes ducantur duæ diametri P Q, & </s>
            <s xml:id="echoid-s11631" xml:space="preserve">p q, quarum la-
              <lb/>
            tera recta P R, & </s>
            <s xml:id="echoid-s11632" xml:space="preserve">p r. </s>
            <s xml:id="echoid-s11633" xml:space="preserve">Oſtenàendum eſt P Q ſut erecti P R, atque p q ſui
              <lb/>
            erecti p r ſubtriplam eße, ſed duo figuræ latera P Q, P R æqualia eſſe alterius
              <lb/>
            figuræ lateribus p q, p r, & </s>
            <s xml:id="echoid-s11634" xml:space="preserve">inſuper P Q, P R minima eſſe laterum figuræ
              <lb/>
            cuiuſlibet alterius diametri eiuſdem ſectionis, & </s>
            <s xml:id="echoid-s11635" xml:space="preserve">latera figurarum minimis pro-
              <lb/>
            ximiora, eſſe minora lateribus figurarum remotiorum.</s>
            <s xml:id="echoid-s11636" xml:space="preserve"/>
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          <p style="it">
            <s xml:id="echoid-s11637" xml:space="preserve">Quia H M ad M G eandem proportionem habet quàm P Q ad P R, vel p
              <lb/>
              <note position="right" xlink:label="note-0369-01" xlink:href="note-0369-01a" xml:space="preserve">Prop. 6.
                <lb/>
              huius.</note>
            q ad p r, eſtque H M ſubtripla ipſius M G (cum M H facta ſit æqualis H D)
              <lb/>
            ergo P Q ipſius P R, pariterque p q ipſius p r ſubtripla eſt: </s>
            <s xml:id="echoid-s11638" xml:space="preserve">& </s>
            <s xml:id="echoid-s11639" xml:space="preserve">ſunt latera
              <lb/>
            figuræ Q P R æqualia lateribus q p r alterius figuræ, cum diametri Q P, & </s>
            <s xml:id="echoid-s11640" xml:space="preserve">
              <lb/>
            q p æquè recedant ab axi, & </s>
            <s xml:id="echoid-s11641" xml:space="preserve">habeant latus commune C M.</s>
            <s xml:id="echoid-s11642" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s11643" xml:space="preserve">Quod verò ſumma laterum figuræ Q P R minima ſit reliquarum ſummarũ
              <lb/>
            laterum figuræ cuiuſlibet diametri ſic oſtendetur.</s>
            <s xml:id="echoid-s11644" xml:space="preserve"/>
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          <p style="it">
            <s xml:id="echoid-s11645" xml:space="preserve">Quia A H, & </s>
            <s xml:id="echoid-s11646" xml:space="preserve">E H minora ſunt, quàm H M, ſiue D H, ergo rectangulum
              <lb/>
              <note position="right" xlink:label="note-0369-02" xlink:href="note-0369-02a" xml:space="preserve">Lem. 7.</note>
            ſub E D A in A H minus eſt quadrato D A, & </s>
            <s xml:id="echoid-s11647" xml:space="preserve">ſumma L I K minor eſt ſum-
              <lb/>
              <note position="right" xlink:label="note-0369-03" xlink:href="note-0369-03a" xml:space="preserve">Lem. 9.</note>
            ma C A F.</s>
            <s xml:id="echoid-s11648" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s11649" xml:space="preserve">Pariter quia M H æqualia eſt H D, & </s>
            <s xml:id="echoid-s11650" xml:space="preserve">H E minor eadem, ergo ambo non
              <lb/>
              <note position="right" xlink:label="note-0369-04" xlink:href="note-0369-04a" xml:space="preserve">Lem. 7.</note>
              <note position="right" xlink:label="note-0369-05" xlink:href="note-0369-05a" xml:space="preserve">Lem. 9.</note>
            erunt maiores eadem D H, ergo rectangulum ſub M D E in E H minus erit
              <lb/>
            quadrato D E, atque ſumma Q P R minor erit, quàm L I K.</s>
            <s xml:id="echoid-s11651" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s11652" xml:space="preserve">Rurſus quia V H maior, eſt quàm M H, ſeu quàm D H, erunt illæ non,
              <lb/>
              <note position="right" xlink:label="note-0369-06" xlink:href="note-0369-06a" xml:space="preserve">Lem. 6.</note>
              <note position="right" xlink:label="note-0369-07" xlink:href="note-0369-07a" xml:space="preserve">Lem. 9.</note>
            minores eadem D H, ergo rectangulum ſub V D M in H M maius erit qua-
              <lb/>
            drato D M, atque ſumma T S Z maior erit, quàm ſumma Q P R.</s>
            <s xml:id="echoid-s11653" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s11654" xml:space="preserve">In hyperbola reperire diametrum, cuius figuræ latera æqualia ſint lateribus
              <lb/>
              <note position="right" xlink:label="note-0369-08" xlink:href="note-0369-08a" xml:space="preserve">PROP. 3.
                <lb/>
              Addit.
                <lb/>
              ex 40.
                <lb/>
              huius.</note>
            figuræ axis: </s>
            <s xml:id="echoid-s11655" xml:space="preserve">oportet autem vt axis A C minor ſit triente erecti eius. </s>
            <s xml:id="echoid-s11656" xml:space="preserve">Reperia-
              <lb/>
            tur diameter P Q ſubtripla erecti eius P R, eiuſque latus ſit C M, & </s>
            <s xml:id="echoid-s11657" xml:space="preserve">fiat e
              <lb/>
            A ad A D, vt M A ad A H, & </s>
            <s xml:id="echoid-s11658" xml:space="preserve">lateris C e ducatur diameter a b, cuius ere-
              <lb/>
            ctus a c. </s>
            <s xml:id="echoid-s11659" xml:space="preserve">Dico hanc eße diametrum quæſitam: </s>
            <s xml:id="echoid-s11660" xml:space="preserve">quia e A ad A D eandem pro-
              <lb/>
            portionem habet, quàm M A ad A H, erit rectangulum ſub e D A in A </s>
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