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-div66" type="section" level="1" n="43">
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              <pb o="15" file="0053" n="53" rhead="Conicor. Lib. V."/>
            A B ad B F eſt, vt D E ad E H; </s>
            <s xml:id="echoid-s1158" xml:space="preserve">ergo A B ad A F eſt, vt E D ad D H; </s>
            <s xml:id="echoid-s1159" xml:space="preserve">ſed B A
              <lb/>
            ad maiorem C A habet minorem proportionem quàm ad F A; </s>
            <s xml:id="echoid-s1160" xml:space="preserve">igitur B A ad A C
              <lb/>
            minorem proportionem habet quàm E D ad D H.</s>
            <s xml:id="echoid-s1161" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1162" xml:space="preserve">Septimò, dico è contra, quod comparando differentias terminorum ad ante-
              <lb/>
            cedentes C A ad A B maiorem proportionem habebit quàm H D ad D E. </s>
            <s xml:id="echoid-s1163" xml:space="preserve">Quo-
              <lb/>
            niam, ex præcedenti caſu, B A ad A C minorem proportionem habebat quàm E
              <lb/>
            D ad D H; </s>
            <s xml:id="echoid-s1164" xml:space="preserve">igitur inuertendo C A ad A B maiorem proportionem habebit quàm
              <lb/>
            H D ad D E.</s>
            <s xml:id="echoid-s1165" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div70" type="section" level="1" n="44">
          <head xml:id="echoid-head69" xml:space="preserve">LEMMA III.</head>
          <p style="it">
            <s xml:id="echoid-s1166" xml:space="preserve">Si quatuor quantitates eandem rationem habuerint homologorum ſum-
              <lb/>
            mæ, vel differentiæ in eadem ratione erunt.</s>
            <s xml:id="echoid-s1167" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1168" xml:space="preserve">OStenſum enim fuit in elemen-
              <lb/>
              <figure xlink:label="fig-0053-01" xlink:href="fig-0053-01a" number="23">
                <image file="0053-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0053-01"/>
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            tis, quod proportionalium om-
              <lb/>
            nes antecedentes ad omnes conſequen-
              <lb/>
            tes eandem proportionem habent,
              <lb/>
            quàm vna antecedentium ad vnam
              <lb/>
            conſequentium. </s>
            <s xml:id="echoid-s1169" xml:space="preserve">Similiter oſtenſum
              <lb/>
            fuit, quod ſi totum ad totum eandem
              <lb/>
            rationem habuerit, quàm ablatum
              <lb/>
            ad ablatum, & </s>
            <s xml:id="echoid-s1170" xml:space="preserve">reliquum ad reliquũ,
              <lb/>
            vt totum ad totum ſe habebit; </s>
            <s xml:id="echoid-s1171" xml:space="preserve">ſed
              <lb/>
            vno verbo homologorum ſummæ, vel
              <lb/>
            differentiæ in eadem ratione erunt
              <lb/>
            iuxtà Arabici expoſitoris compendium.</s>
            <s xml:id="echoid-s1172" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div72" type="section" level="1" n="45">
          <head xml:id="echoid-head70" xml:space="preserve">LEMMA IV.</head>
          <p style="it">
            <s xml:id="echoid-s1173" xml:space="preserve">Si prima A B ad ſecundam D E maiorem proportionem habuerit,
              <lb/>
            quàm tertia B C ad qnartam E H: </s>
            <s xml:id="echoid-s1174" xml:space="preserve">dico, quod comparando homologorum
              <lb/>
            ſummas A B ad D E maiorem proportionem habebit, quàm prima cum
              <lb/>
            tertia, ideſt A C ad ſecundam cum quarta, ideſt D H.</s>
            <s xml:id="echoid-s1175" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1176" xml:space="preserve">FIat B F ad E H, vt A B ad D E: </s>
            <s xml:id="echoid-s1177" xml:space="preserve">ergo A B ad D E eſt, vt A F ad D H; </s>
            <s xml:id="echoid-s1178" xml:space="preserve">ſed
              <lb/>
              <note position="right" xlink:label="note-0053-01" xlink:href="note-0053-01a" xml:space="preserve">Lem. 3.</note>
            A F maior eſt quàm A C, igitur A F ad eandem D H maiorem proportio-
              <lb/>
            nem habet, quàm A C: </s>
            <s xml:id="echoid-s1179" xml:space="preserve">& </s>
            <s xml:id="echoid-s1180" xml:space="preserve">ideo A B ad D E maiorem proportionem habet, quàm
              <lb/>
            A C ad D H.</s>
            <s xml:id="echoid-s1181" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1182" xml:space="preserve">Secundò ijſdem poſitis, dico, quod tertia B C ad quartam E H minorem pro-
              <lb/>
            portionem habet quàm A C ad D H.</s>
            <s xml:id="echoid-s1183" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1184" xml:space="preserve">Fiat vt B C ad E H, ita I B ad D E, ergo C B ad E H eſt, vt C I ad H D;
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            </s>
            <s xml:id="echoid-s1185" xml:space="preserve">
              <note position="right" xlink:label="note-0053-02" xlink:href="note-0053-02a" xml:space="preserve">Ibidem.</note>
            ſed A B maior eſt quàm I B, & </s>
            <s xml:id="echoid-s1186" xml:space="preserve">ideo C A maior quàm C I; </s>
            <s xml:id="echoid-s1187" xml:space="preserve">igitur I C ad </s>
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