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="14" file="0052" n="52" rhead="Apollonij Pergæi"/>
          <p style="it">
            <s xml:id="echoid-s1121" xml:space="preserve">Tandem ex eadem hypotheſi ſequitur, quod C B ad C A ſit vt E H ad H D:
              <lb/>
            </s>
            <s xml:id="echoid-s1122" xml:space="preserve">nam diuidenda eſt vt A C ad C B, ita D H ad H E; </s>
            <s xml:id="echoid-s1123" xml:space="preserve">ergo inuertendo B C ad C A
              <lb/>
            erit vt E H ad H D: </s>
            <s xml:id="echoid-s1124" xml:space="preserve">& </s>
            <s xml:id="echoid-s1125" xml:space="preserve">hæc argumentatio innominata fieri dicetur comparan-
              <lb/>
            do conſequentes ad derenifftias terminorum.</s>
            <s xml:id="echoid-s1126" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div66" type="section" level="1" n="43">
          <head xml:id="echoid-head68" xml:space="preserve">LEMMA II.</head>
          <p style="it">
            <s xml:id="echoid-s1127" xml:space="preserve">Si prima A B ad ſecundam B C maiorem proportionem habuerit quàm
              <lb/>
            tertia D E ad quartam E H: </s>
            <s xml:id="echoid-s1128" xml:space="preserve">comparando antecedentes ad terminorum.
              <lb/>
            </s>
            <s xml:id="echoid-s1129" xml:space="preserve">ſummas habebit AB ad AC maiorem proportionem quàm D E ad D H.</s>
            <s xml:id="echoid-s1130" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1131" xml:space="preserve">FIat A B ad B F, vt D E ad E H; </s>
            <s xml:id="echoid-s1132" xml:space="preserve">erit B F maior quàm B C, atque A F ma-
              <lb/>
              <note position="left" xlink:label="note-0052-01" xlink:href="note-0052-01a" xml:space="preserve">Lem. I.</note>
            ior quàm A C; </s>
            <s xml:id="echoid-s1133" xml:space="preserve">ergo A B ad A F eandem proportionem habebit quàm D E
              <lb/>
            ad D H; </s>
            <s xml:id="echoid-s1134" xml:space="preserve">ſed eadem A B ad minorem A C maiorem proportionem habet quàm
              <lb/>
            ad A F maiorem, ergo A B ad A C maiorem proportionem habet quàm D E
              <lb/>
            ad D H.</s>
            <s xml:id="echoid-s1135" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1136" xml:space="preserve">Secundò ijſdem poſitis, dico com-
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              <figure xlink:label="fig-0052-01" xlink:href="fig-0052-01a" number="22">
                <image file="0052-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0052-01"/>
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            parando terminorum ſummas ad an-
              <lb/>
            tecedẽtes A C ad A B habere minorem
              <lb/>
            proportionem quàm D H ad D E.
              <lb/>
            </s>
            <s xml:id="echoid-s1137" xml:space="preserve">Quoniam ex præcedenti caſu A B ad
              <lb/>
            A C maiorem proportionem habebat
              <lb/>
            quàm D E ad D H; </s>
            <s xml:id="echoid-s1138" xml:space="preserve">igitur inuertendo
              <lb/>
            C A ad A B minorem proportionem
              <lb/>
            habebit quàm D H ad D E.</s>
            <s xml:id="echoid-s1139" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1140" xml:space="preserve">Tertiò, dico quod comparando con-
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            ſequentes adterminorum ſummas B C
              <lb/>
            ad C A minorem proportionem habe-
              <lb/>
            bit quàm E H ad H D; </s>
            <s xml:id="echoid-s1141" xml:space="preserve">quia (ex hy-
              <lb/>
            pothcſi) A B ad B C maiorem proportionem habet quàm D E ad E H componen-
              <lb/>
            do A C ad C B maiorem proportionem habebit quàm D H ad H E, & </s>
            <s xml:id="echoid-s1142" xml:space="preserve">inuerten-
              <lb/>
            do B C ad C A minorem proportionem habebit, quàm E H ad H D.</s>
            <s xml:id="echoid-s1143" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1144" xml:space="preserve">Quartò, ij ſdem poſitis in quarta figura, dico quod comparando differentias
              <lb/>
            terminorum ad conſequentes A C ad C B maiorem proportionem habebit quàm
              <lb/>
            D H ad H E: </s>
            <s xml:id="echoid-s1145" xml:space="preserve">quia ex conſtructione A B ad B F eſt, vt D E ad E H, diuiden-
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            do A F ad F B erit vt D H ad H E; </s>
            <s xml:id="echoid-s1146" xml:space="preserve">ſed A C maior eſt quàm A F, & </s>
            <s xml:id="echoid-s1147" xml:space="preserve">C B mi-
              <lb/>
            nor, quàm F B; </s>
            <s xml:id="echoid-s1148" xml:space="preserve">igitur A C ad C B maiorem proportionem habebit quàm A F ad
              <lb/>
            F B; </s>
            <s xml:id="echoid-s1149" xml:space="preserve">& </s>
            <s xml:id="echoid-s1150" xml:space="preserve">propterea A C ad C B maiorem proportionem habebit, quàm D H ad H E.</s>
            <s xml:id="echoid-s1151" xml:space="preserve"/>
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          <p style="it">
            <s xml:id="echoid-s1152" xml:space="preserve">Quintò, dico quod è contra, comparando conſequentes ad differentias termi-
              <lb/>
            norum C B ad C A minorem proportionem habebit quàm E H ad H D. </s>
            <s xml:id="echoid-s1153" xml:space="preserve">Quia
              <lb/>
            (ex præcedenti caſu) A C ad C B maiorem proportionem habebat quàm D H ad
              <lb/>
            H E; </s>
            <s xml:id="echoid-s1154" xml:space="preserve">ergo inuertendo C B ad C A minorem proportionem habebit quàm E H
              <lb/>
            ad H D.</s>
            <s xml:id="echoid-s1155" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s1156" xml:space="preserve">Sextò, dico quod comparando antecedentes ad differentias terminorum B A ad
              <lb/>
            A C minorem proportionem habebit quàm E D ad D H. </s>
            <s xml:id="echoid-s1157" xml:space="preserve">Quia ex conſtructione
              <lb/>
              <note position="left" xlink:label="note-0052-02" xlink:href="note-0052-02a" xml:space="preserve">Ibidem.</note>
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