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

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        <div xml:id="echoid-div109" type="section" level="1" n="65">
          <p>
            <s xml:id="echoid-s1334" xml:space="preserve">
              <pb o="38" file="0058" n="58" rhead=""/>
            rint æqualiter inclinatæ, ſi ſint per vertices ſimul adſcriptæ, inter ſe mutuò
              <lb/>
            congruant.</s>
            <s xml:id="echoid-s1335" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div110" type="section" level="1" n="66">
          <head xml:id="echoid-head71" xml:space="preserve">VIII.</head>
          <p>
            <s xml:id="echoid-s1336" xml:space="preserve">CONI-SECTIONIS VEL CIRCVLI PORTIO, SIVE SEGMENTVM
              <lb/>
            vocetur ſuperficies à quadam ſectionis ordinatim ducta, & </s>
            <s xml:id="echoid-s1337" xml:space="preserve">curua ſectionis,
              <lb/>
            aut circuli peripheria terminata. </s>
            <s xml:id="echoid-s1338" xml:space="preserve">Et ipſa ordinata dicatur
              <lb/>
            BASIS PORTIONIS, SIVE SEGMENTI.</s>
            <s xml:id="echoid-s1339" xml:space="preserve"/>
          </p>
          <figure number="35">
            <image file="0058-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0058-01"/>
          </figure>
        </div>
        <div xml:id="echoid-div111" type="section" level="1" n="67">
          <head xml:id="echoid-head72" xml:space="preserve">IX.</head>
          <p>
            <s xml:id="echoid-s1340" xml:space="preserve">MENSALIS CONI-SECTIONIS, VEL CIRCVLI
              <lb/>
            dicatur differentia duorum ſegmétorum eiuſdem coni-
              <lb/>
            ſectionis, quorum baſes ſint parallelæ.</s>
            <s xml:id="echoid-s1341" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1342" xml:space="preserve">Vt ſi ex coni-ſectione, vel circulo ABC abſcindan-
              <lb/>
            tur duæ portiones ABC, DBE, quarum baſes AC, DE
              <lb/>
            ſint parallelæ, ipſarum portionum differentia ADEC di-
              <lb/>
            catur menſalis, & </s>
            <s xml:id="echoid-s1343" xml:space="preserve">ipſæ AC, DE baſes, & </s>
            <s xml:id="echoid-s1344" xml:space="preserve">AD, CE late-
              <lb/>
            ra eiuſdem menſalis.</s>
            <s xml:id="echoid-s1345" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div112" type="section" level="1" n="68">
          <head xml:id="echoid-head73" xml:space="preserve">THEOR. XI. PROP. XIX.</head>
          <p>
            <s xml:id="echoid-s1346" xml:space="preserve">Si fuerint duæ quæcunque coni-ſectiones æqualiter inclinatæ
              <lb/>
            per vertices ſimul adſcriptæ, ipſæ vel erunt in totum congruentes,
              <lb/>
            & </s>
            <s xml:id="echoid-s1347" xml:space="preserve">eiuſdem nominis, vel in totum diſiunctæ, præter in vertice, hoc
              <lb/>
            eſt altera alteri inſcripta, vel in duobus tantùm punctis ſe mutuò ſe-
              <lb/>
            cabunt in ipſis tamen verticibus ſe contingentes.</s>
            <s xml:id="echoid-s1348" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1349" xml:space="preserve">SInt in præſenti ſchematiſmo duæ quæcunque coni-ſectiones ABC, DBE
              <lb/>
              <note position="left" xlink:label="note-0058-01" xlink:href="note-0058-01a" xml:space="preserve">Schematif-
                <lb/>
              mus 1. & 2.</note>
            æqualiter inclinatæ pereundem verticem B ſimul adſcriptę, quarum có-
              <lb/>
            munis diameter ſit BF: </s>
            <s xml:id="echoid-s1350" xml:space="preserve">dico has ſectiones, vel eſſe in totum congruentes, vel
              <lb/>
            in totum diſiunctæ, vel in duobus tantùm punctis, ſe mutuò ſecantes.</s>
            <s xml:id="echoid-s1351" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1352" xml:space="preserve">Ducatur ex vertice B cuilibet in altera ſectionum ordinatim applicatæ æ-
              <lb/>
            quidiſtans BGH, quæ vtranq; </s>
            <s xml:id="echoid-s1353" xml:space="preserve">ſectionem continget ſuper qua ſumatur
              <note symbol="a" position="left" xlink:label="note-0058-02" xlink:href="note-0058-02a" xml:space="preserve">32. primi
                <lb/>
              conic.</note>
            rectum latus ſectionis ABC, & </s>
            <s xml:id="echoid-s1354" xml:space="preserve">BG rectum ſectionis DBE, ipſarumque regu-
              <lb/>
            læ, ſectionis videlicet ABC, ſit HPL, & </s>
            <s xml:id="echoid-s1355" xml:space="preserve">ſectionis DBE ſit GOI.</s>
            <s xml:id="echoid-s1356" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1357" xml:space="preserve">Iam, vel regulæ GOI, HPL ſibi mutuò congruunt, vel infra contingen-
              <lb/>
            tem BGH nunquam conueniunt, vel infra eandem ſe mutuò ſecant. </s>
            <s xml:id="echoid-s1358" xml:space="preserve">Si pri-
              <lb/>
            mùm, vt in primis 4. </s>
            <s xml:id="echoid-s1359" xml:space="preserve">figuris; </s>
            <s xml:id="echoid-s1360" xml:space="preserve">dico ſectiones in totum ſimul congruere, & </s>
            <s xml:id="echoid-s1361" xml:space="preserve">eiuſ-
              <lb/>
            dem nominis eſſe.</s>
            <s xml:id="echoid-s1362" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1363" xml:space="preserve">Sumpto enim in ſectione ABC quolibet puncto M, per ipſum ducatur ſe-
              <lb/>
            ctionum communis ordinatim applicata MNFOP, ſectionem ſecans DBE in
              <lb/>
            N, diametrum in F, regulam GI in O, NL in P. </s>
            <s xml:id="echoid-s1364" xml:space="preserve">Et quoniam in 4. </s>
            <s xml:id="echoid-s1365" xml:space="preserve">primis fi-
              <lb/>
            guris, in quibus regulæ ſunt congruentes latitudines FO, FP ſunt æquales,
              <lb/>
            & </s>
            <s xml:id="echoid-s1366" xml:space="preserve">altitudo eadem BF erit rectangulum BFO ſiue quadratum NF in
              <note symbol="b" position="left" xlink:label="note-0058-03" xlink:href="note-0058-03a" xml:space="preserve">Coroll.
                <lb/>
              prop. 1. h.</note>
            DBE, æquale rectangulo BFP ſiue quadrato MF in ſectione ABC,
              <note symbol="c" position="left" xlink:label="note-0058-04" xlink:href="note-0058-04a" xml:space="preserve">Coroll.
                <lb/>
              brop. 1. h.</note>
            & </s>
            <s xml:id="echoid-s1367" xml:space="preserve">ſemi-applicatæ NF, MF æquales erunt, hoc eſt ſectiones DBE, ABC con-
              <lb/>
            ueniunt ſimul in punctis N, & </s>
            <s xml:id="echoid-s1368" xml:space="preserve">M, quæ ſunt extrema communium </s>
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