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

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          <p>
            <s xml:id="echoid-s2087" xml:space="preserve">
              <pb o="60" file="0084" n="84" rhead=""/>
            A D. </s>
            <s xml:id="echoid-s2088" xml:space="preserve">Quave
              <unsure/>
            Ellipſis portio A M C eſt _MAXIMA_ inſcripta cum dato recto C L.
              <lb/>
            </s>
            <s xml:id="echoid-s2089" xml:space="preserve">Quod ſecundò, &</s>
            <s xml:id="echoid-s2090" xml:space="preserve">c.</s>
            <s xml:id="echoid-s2091" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2092" xml:space="preserve">SIt verò data Ellipſis portio AMCD, cuius tranſuerſum CH, rectum C L, re-
              <lb/>
            gula LH, baſis A D, & </s>
            <s xml:id="echoid-s2093" xml:space="preserve">diameter C E: </s>
            <s xml:id="echoid-s2094" xml:space="preserve">oportet per verticem C _MINIMAM_
              <lb/>
            Ellipſis portionem circumſcribere, cum dato tranſuerſo C F, quod minus ſit
              <lb/>
            verſo CH datæ portionis, maius verò eius diametro C E.</s>
            <s xml:id="echoid-s2095" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2096" xml:space="preserve">Producta ſemi - applicata A E, occurrat regulæ
              <lb/>
              <figure xlink:label="fig-0084-01" xlink:href="fig-0084-01a" number="54">
                <image file="0084-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0084-01"/>
              </figure>
            LH in I, & </s>
            <s xml:id="echoid-s2097" xml:space="preserve">iuncta F I occurrat contingenti C L in
              <lb/>
            G, & </s>
            <s xml:id="echoid-s2098" xml:space="preserve">cum tranſuerſo dato C F, cumque recto C G
              <lb/>
            adſcribatur per C Ellipſis portio A B C D,
              <note symbol="a" position="left" xlink:label="note-0084-01" xlink:href="note-0084-01a" xml:space="preserve">7. hu.</note>
            item per A, & </s>
            <s xml:id="echoid-s2099" xml:space="preserve">D tranſibit, & </s>
            <s xml:id="echoid-s2100" xml:space="preserve"> portioni AMC
              <note symbol="b" position="left" xlink:label="note-0084-02" xlink:href="note-0084-02a" xml:space="preserve">1. Co-
                <lb/>
              roll. 19. h.</note>
            circumſcripta, quàm dico eſſe _MINIMAM_. </s>
            <s xml:id="echoid-s2101" xml:space="preserve">Quæ-
              <lb/>
            libet enim adſcripta Ellipſis cum eodem tranſuerſo
              <lb/>
            C F, ſed cum recto, quod maius ſit ipſo C G, eſt
              <lb/>
            maior eadem ABCD; </s>
            <s xml:id="echoid-s2102" xml:space="preserve">quæ verò cum recto,
              <note symbol="c" position="left" xlink:label="note-0084-03" xlink:href="note-0084-03a" xml:space="preserve">2. Co-
                <lb/>
              roll. 19. h.</note>
            minus ſit CG eſt quidem minor eadem A B C,
              <note symbol="d" position="left" xlink:label="note-0084-04" xlink:href="note-0084-04a" xml:space="preserve">ibid.</note>
            vel tota cadit intra datam AMCD, tum, cum rectũ
              <lb/>
            idem fuerit cum recto CL, aut ipſo minus; </s>
            <s xml:id="echoid-s2103" xml:space="preserve">vel
              <note symbol="e" position="left" xlink:label="note-0084-05" xlink:href="note-0084-05a" xml:space="preserve">1. Co-
                <lb/>
              roll. 19. h.</note>
            tem ſecat portionem AMC ſupra baſim AD, quan-
              <lb/>
            do nempe illius rectum cadat inter C L, & </s>
            <s xml:id="echoid-s2104" xml:space="preserve">C G,
              <lb/>
            quale eſt C O, nam iuncta regula O F, omnino ſe-
              <lb/>
            cat regulam L H ſupra eandem applicatam A D.
              <lb/>
            </s>
            <s xml:id="echoid-s2105" xml:space="preserve">Quare huiuſmodi portio Elliptica ABCD erit _MI-_
              <lb/>
            _NIMA_ cir cumſcripta cum dato tranſuerſo CF. </s>
            <s xml:id="echoid-s2106" xml:space="preserve">Quod tertiò, &</s>
            <s xml:id="echoid-s2107" xml:space="preserve">c.</s>
            <s xml:id="echoid-s2108" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2109" xml:space="preserve">Sit tandem circumſcribenda portioni AMC _MINIMA_ Ellipſis portio cum
              <lb/>
            dato recto C G, quod tamen ſuperet rectum C L.</s>
            <s xml:id="echoid-s2110" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2111" xml:space="preserve">Iungatur G I, & </s>
            <s xml:id="echoid-s2112" xml:space="preserve">producatur, donec conueniat cum diametro in F, & </s>
            <s xml:id="echoid-s2113" xml:space="preserve">cum
              <lb/>
            tranſuerſo C F, datoque recto C G adſcribatur per C, Elliptica portio
              <note symbol="f" position="left" xlink:label="note-0084-06" xlink:href="note-0084-06a" xml:space="preserve">7. h.</note>
            quæ pariter per A, & </s>
            <s xml:id="echoid-s2114" xml:space="preserve">D tranſibit eritque datæ portioni circumſcripta: </s>
            <s xml:id="echoid-s2115" xml:space="preserve">
              <note symbol="g" position="left" xlink:label="note-0084-07" xlink:href="note-0084-07a" xml:space="preserve">1. Co-
                <lb/>
              roll. 19. h.</note>
            dico hanc eſſe _MINIMAM_ quæſitam.</s>
            <s xml:id="echoid-s2116" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2117" xml:space="preserve">Ellipſis enim, quæ adſcribitur per C cum eodem recto C G, ſed cum tranſ-
              <lb/>
              <note symbol="h" position="left" xlink:label="note-0084-08" xlink:href="note-0084-08a" xml:space="preserve">4. Co-
                <lb/>
              roll. 19. h.</note>
            uerſo, quod excedat versũ CF eſt maior ipſa ABCD, quæ verò cum trãſuerſo, quod minus ſit ipſo CF, quale eſt CR, eſt quidem minor eadem A B C D, ſed
              <note symbol="i" position="left" xlink:label="note-0084-09" xlink:href="note-0084-09a" xml:space="preserve">ibidem.</note>
            omnino ſecat portionem AMCD ſupra baſim A D cum & </s>
            <s xml:id="echoid-s2118" xml:space="preserve">iuncta regula CR
              <note symbol="l" position="left" xlink:label="note-0084-10" xlink:href="note-0084-10a" xml:space="preserve">1. Co-
                <lb/>
              roll. 19. h.</note>
            cet datæ portionis regulam L I ſupra eandem baſim AD. </s>
            <s xml:id="echoid-s2119" xml:space="preserve">Quare Ellipſis portio
              <lb/>
            ABCD eſt _MINIMA_ circumſcripta cum dato recto CG. </s>
            <s xml:id="echoid-s2120" xml:space="preserve">Quod vltimò, &</s>
            <s xml:id="echoid-s2121" xml:space="preserve">c.</s>
            <s xml:id="echoid-s2122" xml:space="preserve"/>
          </p>
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        <div xml:id="echoid-div195" type="section" level="1" n="92">
          <head xml:id="echoid-head97" xml:space="preserve">THEOR. XIII. PROP. XXXII.</head>
          <p>
            <s xml:id="echoid-s2123" xml:space="preserve">Parabolæ, vel Hyperbolę cum earum diametris, iuxta ordinatim ſe-
              <lb/>
            mi - applicatas ſunt ſemper ſimul recedentes, & </s>
            <s xml:id="echoid-s2124" xml:space="preserve">ad interuallum per-
              <lb/>
            ueniunt maius quolibet dato interuallo.</s>
            <s xml:id="echoid-s2125" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2126" xml:space="preserve">PRimum facilè conſtat ex 20. </s>
            <s xml:id="echoid-s2127" xml:space="preserve">ac 21. </s>
            <s xml:id="echoid-s2128" xml:space="preserve">primi Conic. </s>
            <s xml:id="echoid-s2129" xml:space="preserve">Secundum verò ſic.</s>
            <s xml:id="echoid-s2130" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2131" xml:space="preserve">Ducta enim cõtingente ex ſectionis vertice, quę quodam dato interuallo
              <lb/>
            ſit maior, atq; </s>
            <s xml:id="echoid-s2132" xml:space="preserve">ex eius termino ducta alia, quæ ipſi diametro ſit æquidiſtans, hæc
              <lb/>
              <note symbol="m" position="left" xlink:label="note-0084-11" xlink:href="note-0084-11a" xml:space="preserve">26. pr.
                <lb/>
              Conic.</note>
            omnino in vno tantùm puncto cum ſectione cõueniet, à quo ſi agatur </s>
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