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-s1187" xml:space="preserve">
              <pb o="16" file="0054" n="54" rhead="Apollonij Pergæi"/>
            D H minorem proportionem habet quàm A C, & </s>
            <s xml:id="echoid-s1188" xml:space="preserve">propterea B C ad E H minorem
              <lb/>
            proportionem habebit quàm A C ad D H.</s>
            <s xml:id="echoid-s1189" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1190" xml:space="preserve">Tertiò ijſdem poſitis in ſexta fi-
              <lb/>
            gura, dico quod comparando homolo-
              <lb/>
              <figure xlink:label="fig-0054-01" xlink:href="fig-0054-01a" number="24">
                <image file="0054-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0054-01"/>
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            gorum differentias prima A B ad ſe-
              <lb/>
            cundam D E minorem proportionem
              <lb/>
            habet quàm differentia A C ad diffe-
              <lb/>
            rentiam D H.</s>
            <s xml:id="echoid-s1191" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1192" xml:space="preserve">Fiat B F ad E H, vt A B ad D
              <lb/>
            E, ergo A F ad D H eſt vt A B ad
              <lb/>
              <note position="left" xlink:label="note-0054-01" xlink:href="note-0054-01a" xml:space="preserve">Lem.3.</note>
            D E, ſed A F minor eſt quam A C,
              <lb/>
            ergo A F ad eandem D H minorem
              <lb/>
            proportionem habet quàm A C: </s>
            <s xml:id="echoid-s1193" xml:space="preserve">& </s>
            <s xml:id="echoid-s1194" xml:space="preserve">
              <lb/>
            propterea A B ad D E minorem pro-
              <lb/>
            portionem habet quàm A C ad D H.</s>
            <s xml:id="echoid-s1195" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1196" xml:space="preserve">Quartò, dico, quod tertia C B ad quartam H E minorem proportionem habet
              <lb/>
              <note position="left" xlink:label="note-0054-02" xlink:href="note-0054-02a" xml:space="preserve">Ibidem.</note>
            quàm differentia A C ad differentiam D H. </s>
            <s xml:id="echoid-s1197" xml:space="preserve">Quoniam ex conſtructione A B ad
              <lb/>
            D E eſt vt F B ad H E, erit F B ad H E, vt A F ad D H; </s>
            <s xml:id="echoid-s1198" xml:space="preserve">ſed C B minor
              <lb/>
            eſt quàm F B, atque A C maior quàm A F, & </s>
            <s xml:id="echoid-s1199" xml:space="preserve">A F ad eandem D H minorem
              <lb/>
            proportionem habet quàm A C; </s>
            <s xml:id="echoid-s1200" xml:space="preserve">igitur C B ad H E eo magis habebit minorem
              <lb/>
            proportionem quàm A C ad D H quæ erant oſtendenda.</s>
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        <div xml:id="echoid-div78" type="section" level="1" n="46">
          <head xml:id="echoid-head71" xml:space="preserve">SECTIO TERTIA</head>
          <head xml:id="echoid-head72" xml:space="preserve">Continens VIII. IX. X. Propoſ. Apollonij.</head>
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            <s xml:id="echoid-s1202" xml:space="preserve">SI menſura fuerit maior comparata, dummodo in ellipſi minor
              <lb/>
            ſit medietate axis tranſuerſi, tunc minimus ramorum in ſe-
              <lb/>
            ctionibus eſt, cuius potentialis abſcindit à menſura verſus origi-
              <lb/>
            nem in parabola (8) lineam æqualem comparatæ, in hyperbo-
              <lb/>
            la verò (9) & </s>
            <s xml:id="echoid-s1203" xml:space="preserve">in ellipſi (10.) </s>
            <s xml:id="echoid-s1204" xml:space="preserve">lineam, cuius inuerſæ proportio
              <lb/>
            ad illam eſt, vt proportio figuræ & </s>
            <s xml:id="echoid-s1205" xml:space="preserve">reliqui rami, quo accedunt
              <lb/>
            ad minimum ſunt minores remotioribus; </s>
            <s xml:id="echoid-s1206" xml:space="preserve">& </s>
            <s xml:id="echoid-s1207" xml:space="preserve">quadratum minimæ
              <lb/>
            minus eſt quadrato cuiuslibet rami aſſignati in parabola quidem
              <lb/>
            (8) quadrato exceſſus ſuarum abſciſſarum, & </s>
            <s xml:id="echoid-s1208" xml:space="preserve">in hyperbola (9)
              <lb/>
            & </s>
            <s xml:id="echoid-s1209" xml:space="preserve">ellipſi (10.) </s>
            <s xml:id="echoid-s1210" xml:space="preserve">exemplari applicato ad exceſſum ſuarum inuer-
              <lb/>
            ſarum.</s>
            <s xml:id="echoid-s1211" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s1212" xml:space="preserve">SIt itaque ſectio A B C, & </s>
            <s xml:id="echoid-s1213" xml:space="preserve">menſura I C, inclinatus, ſiue tranſuerſa E C,
              <lb/>
              <note position="right" xlink:label="note-0054-03" xlink:href="note-0054-03a" xml:space="preserve">b</note>
            dimidium erecti C G, centrum F, origo I, & </s>
            <s xml:id="echoid-s1214" xml:space="preserve">I H in parabola ſit equa-
              <lb/>
            lis C G, & </s>
            <s xml:id="echoid-s1215" xml:space="preserve">in hyperbola, & </s>
            <s xml:id="echoid-s1216" xml:space="preserve">ellipſi F H ad H I ſit, vt F C dimidium incli-
              <lb/>
            nati, ſeu tranſuerſæ ad C G, dimidium erecti, & </s>
            <s xml:id="echoid-s1217" xml:space="preserve">educta ex H perpendi-
              <lb/>
            culari H N, & </s>
            <s xml:id="echoid-s1218" xml:space="preserve">coniuncta recta N I; </s>
            <s xml:id="echoid-s1219" xml:space="preserve">Dico N I minimum eſſe </s>
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