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

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            patet quomodo cuilibet horum trilineorum circumſcribi poſſit figura ex
              <lb/>
            æque-altis parallelogrammis, &</s>
            <s xml:id="echoid-s1216" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1217" xml:space="preserve">quæ ſuperet proprium trilineum magni-
              <lb/>
            tudine, quæ minor ſit quacunque magnitudine propoſita.</s>
            <s xml:id="echoid-s1218" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1219" xml:space="preserve">Iam dico huiuſmodi trilinea inter ſe eſſe æqualia. </s>
            <s xml:id="echoid-s1220" xml:space="preserve">Nam ſi ſint inæqualia,
              <lb/>
            alterum ipſorum, vt puta AHBCGA altero AHBE minus erit, & </s>
            <s xml:id="echoid-s1221" xml:space="preserve">defectus ſit
              <lb/>
            ſpacium V
              <unsure/>
            ; </s>
            <s xml:id="echoid-s1222" xml:space="preserve">quo poſito circumſcribatur, vti nuper docuimus, trilineo AHB
              <lb/>
            CGA figura ex parallelogrammis SC, TN, VO, HP, &</s>
            <s xml:id="echoid-s1223" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1224" xml:space="preserve">cuius exceſſus ſupra
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            trilineum ſit minor magnitudine V
              <unsure/>
            . </s>
            <s xml:id="echoid-s1225" xml:space="preserve">quapropter talis figura adhuc minor erit
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            trilinco AEBHA, cui circumſcribatur, item per eaſdem lineas ipſi CB æqui-
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              <figure xlink:label="fig-0054-01" xlink:href="fig-0054-01a" number="31">
                <image file="0054-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0054-01"/>
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            diſtantes, figura ex totidem parallelogrammis EY, 1Z, 2&</s>
            <s xml:id="echoid-s1226" xml:space="preserve">, 3I, &</s>
            <s xml:id="echoid-s1227" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1228" xml:space="preserve">Patet nũc
              <lb/>
            talem circumſcriptam, alteri circumſcriptæ ABD 567, &</s>
            <s xml:id="echoid-s1229" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1230" xml:space="preserve">ęqualem eſſe, cum
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            vtraq; </s>
            <s xml:id="echoid-s1231" xml:space="preserve">ipſarum ex æqualibus numero, & </s>
            <s xml:id="echoid-s1232" xml:space="preserve">magnitudine parallelogrammis cõ-
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            ſtet vtrunq; </s>
            <s xml:id="echoid-s1233" xml:space="preserve">vtrique: </s>
            <s xml:id="echoid-s1234" xml:space="preserve">(parallelogramma enim EY, BD, ſunt inter eaſdem pa-
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            rallelas, & </s>
            <s xml:id="echoid-s1235" xml:space="preserve">ſuper æqualibus baſibus EB, BE; </s>
            <s xml:id="echoid-s1236" xml:space="preserve">& </s>
            <s xml:id="echoid-s1237" xml:space="preserve">parallelogrammum IZ æqua-
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            tur parallelogrãmo Q5, cum inter eaſdem ſint parallelas, & </s>
            <s xml:id="echoid-s1238" xml:space="preserve">ſuper æqualibus
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            baſibus IQ, QN, & </s>
            <s xml:id="echoid-s1239" xml:space="preserve">ſic de ſingulis) ſed circumſcripta ABD 567, &</s>
            <s xml:id="echoid-s1240" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1241" xml:space="preserve">eſt
              <note symbol="a" position="left" xlink:label="note-0054-01" xlink:href="note-0054-01a" xml:space="preserve">3. Co-
                <lb/>
              roll. 13. h.</note>
            nor trilineo AEBHA, vt modò oſtendimus, ergo & </s>
            <s xml:id="echoid-s1242" xml:space="preserve">circumſcripta AEBYZ
              <lb/>
            &</s>
            <s xml:id="echoid-s1243" xml:space="preserve">I, &</s>
            <s xml:id="echoid-s1244" xml:space="preserve">c. </s>
            <s xml:id="echoid-s1245" xml:space="preserve">minor erit eodem trilineo AEBHA; </s>
            <s xml:id="echoid-s1246" xml:space="preserve">totum parte, quod eſt abſurdũ.
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            </s>
            <s xml:id="echoid-s1247" xml:space="preserve">Quare huiuſmodi trilinea inter ſe ſunt æqualia. </s>
            <s xml:id="echoid-s1248" xml:space="preserve">Quod oſtendere propoſi-
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            tum fuit.</s>
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