Viviani, Vincenzo, De maximis et minimis, geometrica divinatio : in qvintvm Conicorvm Apollonii Pergaei

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        <div xml:id="echoid-div103" type="section" level="1" n="60">
          <p>
            <s xml:id="echoid-s1312" xml:space="preserve">
              <pb o="37" file="0057" n="57" rhead=""/>
            mul adſcribi intelligatur, vel SECTIONES SIMVL ADSCRIPTÆ dican-
              <lb/>
            tur, quando cum fuerint æqualiter inclinatæ earum diametri, & </s>
            <s xml:id="echoid-s1313" xml:space="preserve">ordinatim
              <lb/>
            ductæ inter ſe mutuò congruant.</s>
            <s xml:id="echoid-s1314" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1315" xml:space="preserve">Nempe cum duę coni-
              <lb/>
              <figure xlink:label="fig-0057-01" xlink:href="fig-0057-01a" number="34">
                <image file="0057-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0057-01"/>
              </figure>
            ſectiones ABC, DEF æ-
              <lb/>
            qualiter inclinatæ, ita di-
              <lb/>
            ſpoſitę fuerint vt ipſarum
              <lb/>
            diametri BG, EI ſibi mu-
              <lb/>
            tuò congruant, & </s>
            <s xml:id="echoid-s1316" xml:space="preserve">omnes
              <lb/>
            vnius applicatę (quarum
              <lb/>
            vna AG) congruant om-
              <lb/>
            nibus alterius applicatis,
              <lb/>
            (quarum vna ſit DI) ipſæ
              <lb/>
            vocentur ſectiones ſimul
              <lb/>
            adſcriptæ.</s>
            <s xml:id="echoid-s1317" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div105" type="section" level="1" n="61">
          <head xml:id="echoid-head66" xml:space="preserve">III.</head>
          <p>
            <s xml:id="echoid-s1318" xml:space="preserve">Coni-ſectio, vel circulus, coni-ſectioni, vel circulo inſcribi dicatur, vel
              <lb/>
            SECTIO SECTIONI INSCRIPTA vocetur, quando cum fuerit altera al-
              <lb/>
            teri adſcripta, ſit quoque tota intra eandem, nec alicubi ſe mutuò ſecent,
              <lb/>
            licet in infinitum producantur, quæ in infinitum extendi poſſunt.</s>
            <s xml:id="echoid-s1319" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1320" xml:space="preserve">Hoc eſt, ſi vt in prima, & </s>
            <s xml:id="echoid-s1321" xml:space="preserve">ſecunda figura vtriuſque ordinis præcedentis
              <lb/>
            ſchematis duæ coni-ſectiones ABC, DEF fuerint ſimul adſcriptæ, & </s>
            <s xml:id="echoid-s1322" xml:space="preserve">altera
              <lb/>
            ipſarum vt DEF tota cadat intra aliam ABC, tunc dicatur ſectio DEF inſcri-
              <lb/>
            pta ſectioni ABC.</s>
            <s xml:id="echoid-s1323" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div106" type="section" level="1" n="62">
          <head xml:id="echoid-head67" xml:space="preserve">IV.</head>
          <p>
            <s xml:id="echoid-s1324" xml:space="preserve">Coni-ſectio, vel circulus, coni-ſectioni, vel circulo circumſcribi intelli-
              <lb/>
            gatur, vel SECTIO SECTIONI CIRCVMSCRIPTA dicatur, ſi cum fue-
              <lb/>
            rit altera alteri adſcripta, tota quoque cadat extra eandem, nec alicubi ſe
              <lb/>
            mutuò ſecent quamuis in infinitum abeant.</s>
            <s xml:id="echoid-s1325" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1326" xml:space="preserve">Qualis eſt in prædictis figuris ſectio ABC, quæ cum ſit adſcripta ſectioni
              <lb/>
            DEF tota cadit extra eandem DEF.</s>
            <s xml:id="echoid-s1327" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div107" type="section" level="1" n="63">
          <head xml:id="echoid-head68" xml:space="preserve">V.</head>
          <p>
            <s xml:id="echoid-s1328" xml:space="preserve">Coni-ſectio, vel circulus coni-ſectioni, vel circulo per verticem, vel per
              <lb/>
            punctum intra, aut extra ſectionem datum adſcribi, vel inſcribi, aut circum-
              <lb/>
            ſcribi intelligatur, ſiue SECTIO SECTIONI PER VERTICEM, vel PER
              <lb/>
            DATVM PVNCTVM INTRA, aut EXTRA SECTIONEM ADSCRI-
              <lb/>
            PTA, vel INSCRIPTA, aut CIRCVMSCRIPTA dicatur, quando cum
              <lb/>
            fuerit altera alteri adſcripta, vel inſcripta, aut circumſcripta, vnius diameter
              <lb/>
            per datum punctum educta ſit quoque diameter alterius; </s>
            <s xml:id="echoid-s1329" xml:space="preserve">vt videre eſt in
              <lb/>
            præcedentibus figuris.</s>
            <s xml:id="echoid-s1330" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div108" type="section" level="1" n="64">
          <head xml:id="echoid-head69" xml:space="preserve">VI.</head>
          <p>
            <s xml:id="echoid-s1331" xml:space="preserve">HYPERBOLE, & </s>
            <s xml:id="echoid-s1332" xml:space="preserve">ELLIPSES, SIMILES inter ſe dicantur, quando cum
              <lb/>
            fuerint ęqualiter inclinatę ipſarum latera ſint proportionalia, hoc eſt vt tran-
              <lb/>
            ſuerſum vnius ad rectum, ita ſit tranſuerſum ad rectum alterius eiuſdem no-
              <lb/>
            minis.</s>
            <s xml:id="echoid-s1333" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div109" type="section" level="1" n="65">
          <head xml:id="echoid-head70" xml:space="preserve">VII.</head>
          <p>
            <s xml:id="echoid-s1334" xml:space="preserve">CONGRVENTES CONI-SECTIONES dicantur illæ, quæ cum </s>
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