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-div395" type="section" level="1" n="123">
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            <s xml:id="echoid-s4301" xml:space="preserve">
              <pb o="107" file="0145" n="145" rhead="Conicor. Lib. V."/>
            culum Z A γ, qui coniſectionem in puncto A ſecat.</s>
            <s xml:id="echoid-s4302" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s4303" xml:space="preserve">Sumatur enim quodlibet punctum G in productione breuiſsimæ A I ſupra,
              <lb/>
            vel infra punctum D: </s>
            <s xml:id="echoid-s4304" xml:space="preserve">manifeſtum eſt (ex 8. </s>
            <s xml:id="echoid-s4305" xml:space="preserve">præcedentium propoſit.) </s>
            <s xml:id="echoid-s4306" xml:space="preserve">à puncto
              <lb/>
            G duci poſſe duos breuiſecantes ramos, quorum A G erit infimus, ſi punctum G
              <lb/>
            cadit ſupra punctum D, & </s>
            <s xml:id="echoid-s4307" xml:space="preserve">tunc circulus radio G A deſcriptus continget coniſe-
              <lb/>
              <note position="right" xlink:label="note-0145-01" xlink:href="note-0145-01a" xml:space="preserve">11.
                <lb/>
              Additarũ.</note>
            ctionem intrinſecus in A: </s>
            <s xml:id="echoid-s4308" xml:space="preserve">ſi vero punctum g cadat infra punctum D, tunc pa-
              <lb/>
              <note position="right" xlink:label="note-0145-02" xlink:href="note-0145-02a" xml:space="preserve">8.
                <lb/>
              Additarũ.</note>
            riter ex g duo breuiſecantes duci poſſunt ad ſectionem, quorum ſupremus erit
              <lb/>
            g A; </s>
            <s xml:id="echoid-s4309" xml:space="preserve">& </s>
            <s xml:id="echoid-s4310" xml:space="preserve">propterea circulus radio g A deſcriptus continget coniſectionem B AC
              <lb/>
              <note position="right" xlink:label="note-0145-03" xlink:href="note-0145-03a" xml:space="preserve">11.
                <lb/>
              Additarũ.</note>
            extrinſecus in A; </s>
            <s xml:id="echoid-s4311" xml:space="preserve">quaproptcr circulus radio D A deſcriptus (quem contingit
              <lb/>
            eadem recta linea X A quæ tangebat ſectionem in A) vnicus erit, qui ſectionem
              <lb/>
            B C ſecet in A, quod erat oſtendendum.</s>
            <s xml:id="echoid-s4312" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s4313" xml:space="preserve">Circulorum omnium intrinſecus tangentium coniſectionem non in axis
              <lb/>
              <note position="right" xlink:label="note-0145-04" xlink:href="note-0145-04a" xml:space="preserve">PROP.
                <lb/>
              13.
                <lb/>
              Addit.</note>
            vertice, aſsignari non poteſt maximus: </s>
            <s xml:id="echoid-s4314" xml:space="preserve">tangentium vero intrinſecus ſe-
              <lb/>
            ctionem in termino axis maximus erit, cuius radius æqualis eſt ſemie-
              <lb/>
            recto.</s>
            <s xml:id="echoid-s4315" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s4316" xml:space="preserve">Repetatur figura, & </s>
            <s xml:id="echoid-s4317" xml:space="preserve">
              <lb/>
              <figure xlink:label="fig-0145-01" xlink:href="fig-0145-01a" number="132">
                <image file="0145-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/xxxxxxxx/figures/0145-01"/>
              </figure>
            hypotheſis præcedẽtis pro
              <lb/>
            poſitionis. </s>
            <s xml:id="echoid-s4318" xml:space="preserve">Quoniã qui-
              <lb/>
            libet circulus radio G A
              <lb/>
            minori, quàm D A de-
              <lb/>
            ſcriptus ſemper intrin-
              <lb/>
            ſecus tangit coniſectio-
              <lb/>
            nem in A (vt in præce-
              <lb/>
            dẽti propoſitione dictum
              <lb/>
            eſt) vbicumque ponatur
              <lb/>
            centrum G ſupra punctũ
              <lb/>
            D; </s>
            <s xml:id="echoid-s4319" xml:space="preserve">neque augendo ra-
              <lb/>
            dium G A efſicitur alius
              <lb/>
            contactus circuli, & </s>
            <s xml:id="echoid-s4320" xml:space="preserve">ſe-
              <lb/>
            ctionis, quàm intrinſe-
              <lb/>
            cus, & </s>
            <s xml:id="echoid-s4321" xml:space="preserve">tunc primo cir-
              <lb/>
            culus deſinit intrinſecus
              <lb/>
            tangere ſectionem in A,
              <lb/>
            quando D A efſicitur
              <lb/>
            radius, ſcilicet quando
              <lb/>
            non amplius intrinſecus ſectionem tangit, ſed eam ſecat in A; </s>
            <s xml:id="echoid-s4322" xml:space="preserve">quapropter aſsi-
              <lb/>
            gnari non poteſt maximus circulorum tangentium intrinſecus ſectionem in A.
              <lb/>
            </s>
            <s xml:id="echoid-s4323" xml:space="preserve">Quod verò circulorum intrinſecus tangentium eandem ſectionem in vertice axis
              <lb/>
            B, ille, cuius radius B K æqualis eſt ſemierecto B H ſit maximus, oſtenſum eſt
              <lb/>
            à Maurolico propoſ: </s>
            <s xml:id="echoid-s4324" xml:space="preserve">5. </s>
            <s xml:id="echoid-s4325" xml:space="preserve">8. </s>
            <s xml:id="echoid-s4326" xml:space="preserve">& </s>
            <s xml:id="echoid-s4327" xml:space="preserve">11. </s>
            <s xml:id="echoid-s4328" xml:space="preserve">libri 5. </s>
            <s xml:id="echoid-s4329" xml:space="preserve">Conicorum. </s>
            <s xml:id="echoid-s4330" xml:space="preserve">Patet ergo propoſitum.</s>
            <s xml:id="echoid-s4331" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s4332" xml:space="preserve">Iiſdem poſitis: </s>
            <s xml:id="echoid-s4333" xml:space="preserve">dico circulorum omnium extrinſecus tangentium coni-
              <lb/>
              <note position="right" xlink:label="note-0145-05" xlink:href="note-0145-05a" xml:space="preserve">PROP.
                <lb/>
              14.
                <lb/>
              Addit.</note>
            ſectionem minimum aſsignari non poſſe.</s>
            <s xml:id="echoid-s4334" xml:space="preserve"/>
          </p>
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