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-div317" type="section" level="1" n="106">
          <p style="it">
            <s xml:id="echoid-s3335" xml:space="preserve">
              <pb o="80" file="0118" n="118" rhead="Apollonij Pergæi"/>
              <figure xlink:label="fig-0118-01" xlink:href="fig-0118-01a" number="99">
                <image file="0118-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0118-01"/>
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            & </s>
            <s xml:id="echoid-s3336" xml:space="preserve">quia A H cadit infra A G ad partes axis cum D A, ad quam illa perpen-
              <lb/>
            dicularis eſt, extendatur vltra axim A E, nec poſsit inter tangentem A G, & </s>
            <s xml:id="echoid-s3337" xml:space="preserve">
              <lb/>
            ſectionem conicam A B, aliqua recta linea intercipi; </s>
            <s xml:id="echoid-s3338" xml:space="preserve">igitur A H cadit intra
              <lb/>
            coniſectionem, & </s>
            <s xml:id="echoid-s3339" xml:space="preserve">angulus E A H eſt acutus.</s>
            <s xml:id="echoid-s3340" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s3341" xml:space="preserve">Quoniam ex D non educitur ad ſectionem A C vllus breuiſecans, & </s>
            <s xml:id="echoid-s3342" xml:space="preserve">c.
              <lb/>
            </s>
            <s xml:id="echoid-s3343" xml:space="preserve">
              <note position="right" xlink:label="note-0118-01" xlink:href="note-0118-01a" xml:space="preserve">b</note>
            Sequitur quidem ex hac hypotheſi, quod menſura E A non ſit maior ſemierecto
              <lb/>
              <note position="left" xlink:label="note-0118-02" xlink:href="note-0118-02a" xml:space="preserve">Ex 49. 50.
                <lb/>
              huius.</note>
            aut ſi maior eſt, ſit quoque perpendicularis D E maior Trutina F, ex conuerſa
              <lb/>
            propoſitione 51. </s>
            <s xml:id="echoid-s3344" xml:space="preserve">52. </s>
            <s xml:id="echoid-s3345" xml:space="preserve">huius per deductionem ad inconueniens.</s>
            <s xml:id="echoid-s3346" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s3347" xml:space="preserve">Quare ſi centro D interuallo D B, &</s>
            <s xml:id="echoid-s3348" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3349" xml:space="preserve">Circulus enim B I L H A ra-
              <lb/>
              <note position="right" xlink:label="note-0118-03" xlink:href="note-0118-03a" xml:space="preserve">c</note>
            dio D B deſcriptus tranſibit per verticem A cum radius D B poſitus ſit æqualis
              <lb/>
            D A, cumque angulus D B I ſit acutus, ex Lemmate nono, cadet neceſſario B
              <lb/>
            I intra circulum B I L.</s>
            <s xml:id="echoid-s3350" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s3351" xml:space="preserve">Ig tur circulus ſecat coniſectionem, &</s>
            <s xml:id="echoid-s3352" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3353" xml:space="preserve">Quia B I cadit extra coniſe-
              <lb/>
              <note position="right" xlink:label="note-0118-04" xlink:href="note-0118-04a" xml:space="preserve">d</note>
            ctionem, quàm tangit, & </s>
            <s xml:id="echoid-s3354" xml:space="preserve">intra circulum B L A, vt dictum eſt, è contra re-
              <lb/>
            cta A H cadit intra eandem coniſectionem, & </s>
            <s xml:id="echoid-s3355" xml:space="preserve">extra ipſum circulum, quem,
              <lb/>
            tangit, cum H A perpendicularis ſit ad circuli radium D A; </s>
            <s xml:id="echoid-s3356" xml:space="preserve">igitur circulus B
              <lb/>
            I L A fertur extra coniſectionem ad partes B I, & </s>
            <s xml:id="echoid-s3357" xml:space="preserve">intra eandem ad partes A
              <lb/>
            H; </s>
            <s xml:id="echoid-s3358" xml:space="preserve">quare neceſſario coniſectionem ſecat.</s>
            <s xml:id="echoid-s3359" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s3360" xml:space="preserve">Patet, vt dictum eſt, quod D L G ſit acutus, &</s>
            <s xml:id="echoid-s3361" xml:space="preserve">c. </s>
            <s xml:id="echoid-s3362" xml:space="preserve">Hoc enim ſequitur ex
              <lb/>
              <note position="right" xlink:label="note-0118-05" xlink:href="note-0118-05a" xml:space="preserve">e</note>
            nono Lemmate præmiſſo, reſpicit enim angulus D L G verticem A; </s>
            <s xml:id="echoid-s3363" xml:space="preserve">& </s>
            <s xml:id="echoid-s3364" xml:space="preserve">ideo eſt
              <lb/>
            acutus, & </s>
            <s xml:id="echoid-s3365" xml:space="preserve">cadit neceſſario recta L G intra circulum B L A radio D L deſcri-
              <lb/>
            ptum ad partes L A; </s>
            <s xml:id="echoid-s3366" xml:space="preserve">& </s>
            <s xml:id="echoid-s3367" xml:space="preserve">portio circuli L H A cadit intra coniſectionem L A;
              <lb/>
            </s>
            <s xml:id="echoid-s3368" xml:space="preserve">igitur recta L G cadit intra coniſectionem L A, ſed cadit extra eandem ſectio-
              <lb/>
              <note position="left" xlink:label="note-0118-06" xlink:href="note-0118-06a" xml:space="preserve">35. 36.
                <lb/>
              lib. 1.</note>
            nem, cum contingat eam in L, quod eſt abſurdum.</s>
            <s xml:id="echoid-s3369" xml:space="preserve"/>
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