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

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          <p>
            <s xml:id="echoid-s2003" xml:space="preserve">
              <pb o="58" file="0082" n="82" rhead=""/>
            ſaltem ſecat portionem ABC ſupra baſim AD, ſi rectum cadat inter M, & </s>
            <s xml:id="echoid-s2004" xml:space="preserve">
              <lb/>
            G, quale eſt CO nam iuncta regula IO, & </s>
            <s xml:id="echoid-s2005" xml:space="preserve">producta omnino ſecat
              <note symbol="a" position="left" xlink:label="note-0082-01" xlink:href="note-0082-01a" xml:space="preserve">1. Co-
                <lb/>
              roll. prop
                <lb/>
              19. huius.</note>
            GL ſupra eandem AD. </s>
            <s xml:id="echoid-s2006" xml:space="preserve">Quare Hyperbolæ portio ANCD eſt _MAXIMA_ in-
              <lb/>
            ſcripta quæſita cum dato tranſuerſo CI. </s>
            <s xml:id="echoid-s2007" xml:space="preserve">Quod erat primò, &</s>
            <s xml:id="echoid-s2008" xml:space="preserve">c.</s>
            <s xml:id="echoid-s2009" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2010" xml:space="preserve">Iam eidem Ellipticæ portioni ABCD inſcribenda ſit _MAXIMA_ Hyperbo-
              <lb/>
            læ portio cum dato recto CM, quod tamen ſit minus latitudine EL, ſemiap-
              <lb/>
            plicatæ AE (ſi enim ei æquale, vel maius eſſet, iuncta regula LM nunquam
              <lb/>
            cum diametro EC conueniret) Supra C.</s>
            <s xml:id="echoid-s2011" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2012" xml:space="preserve">Iungatur I.</s>
            <s xml:id="echoid-s2013" xml:space="preserve">M, quę ideo producta occur-
              <lb/>
              <figure xlink:label="fig-0082-01" xlink:href="fig-0082-01a" number="52">
                <image file="0082-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0082-01"/>
              </figure>
            ret diametro in I, & </s>
            <s xml:id="echoid-s2014" xml:space="preserve">cum tranſuerſo IC,
              <lb/>
            datoq; </s>
            <s xml:id="echoid-s2015" xml:space="preserve">recto CM adſcribatur per C
              <note symbol="b" position="left" xlink:label="note-0082-02" xlink:href="note-0082-02a" xml:space="preserve">6. huius.</note>
            perbolæ portio ANCD, quæ datæ portio-
              <lb/>
            ni ABC occurret in A, & </s>
            <s xml:id="echoid-s2016" xml:space="preserve">D, & </s>
            <s xml:id="echoid-s2017" xml:space="preserve"> erit
              <note symbol="c" position="left" xlink:label="note-0082-03" xlink:href="note-0082-03a" xml:space="preserve">1. Co-
                <lb/>
              roll. 19. h.</note>
            pta; </s>
            <s xml:id="echoid-s2018" xml:space="preserve">quàm dico eſſe _MAXIMAM_: </s>
            <s xml:id="echoid-s2019" xml:space="preserve">nam quę
              <lb/>
            adſcribitur cum eodem recto CM, ſed cum
              <lb/>
            tranſuerſo, quod excedat CI minor
              <note symbol="d" position="left" xlink:label="note-0082-04" xlink:href="note-0082-04a" xml:space="preserve">4. Co-
                <lb/>
              roll. 19. h.</note>
            ipſa ANC; </s>
            <s xml:id="echoid-s2020" xml:space="preserve">quæ verò cum tranſuerſo, quod
              <lb/>
            ſit minus CI, quale eſt CP, eſt
              <note symbol="e" position="left" xlink:label="note-0082-05" xlink:href="note-0082-05a" xml:space="preserve">ibidem.</note>
            maior ipſa ANC, ſed omnino ſecat datam
              <lb/>
            portionem ABC, ſupra baſim AD
              <note symbol="f" position="left" xlink:label="note-0082-06" xlink:href="note-0082-06a" xml:space="preserve">1. Co-
                <lb/>
              roll. 19. h.</note>
            iuncta regula PM, & </s>
            <s xml:id="echoid-s2021" xml:space="preserve">producta, omnino
              <lb/>
            ſecet regulam GL ſupra eandem AD. </s>
            <s xml:id="echoid-s2022" xml:space="preserve">Qua-
              <lb/>
            re huiuſmodi Hyperbolæ portio ANCD,
              <lb/>
            eſt _MAXIMA_ inſcripta cũ dato recto CM.
              <lb/>
            </s>
            <s xml:id="echoid-s2023" xml:space="preserve">Quod ſecundò, &</s>
            <s xml:id="echoid-s2024" xml:space="preserve">c.</s>
            <s xml:id="echoid-s2025" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2026" xml:space="preserve">Ampliùs ſit data Hyperbolę portio AN
              <lb/>
            CD, cuius tranſuerſum CI, rectum CM, regula IM, diameter CE, baſis
              <lb/>
            AD: </s>
            <s xml:id="echoid-s2027" xml:space="preserve">oportet per verticem C _MINIMAM_ Ellipſis portionem circumſcribere
              <lb/>
            cum dato tranſuerſo CF, quod tamen excedat diametrum CE.</s>
            <s xml:id="echoid-s2028" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2029" xml:space="preserve">Producatur item AE occurrens regulæ IM in L, & </s>
            <s xml:id="echoid-s2030" xml:space="preserve">iungatur FL, quæ pro-
              <lb/>
            ducta conueniat cum contingente CM in G, & </s>
            <s xml:id="echoid-s2031" xml:space="preserve">cum dato tranſuerſo CF, ac
              <lb/>
            recto CG adſcribatur per C Ellipſis portio ABCD, quæ datæ
              <note symbol="g" position="left" xlink:label="note-0082-07" xlink:href="note-0082-07a" xml:space="preserve">7. huius.</note>
            occurret in A, D, eritque circumſcripta, & </s>
            <s xml:id="echoid-s2032" xml:space="preserve">erit _MINIMA_: </s>
            <s xml:id="echoid-s2033" xml:space="preserve">Nam quæ adſcri-
              <lb/>
            bitur cum eodem tranſuerſo CF, ſed cum recto, quod excedat CG eſt
              <note symbol="h" position="left" xlink:label="note-0082-08" xlink:href="note-0082-08a" xml:space="preserve">1. Co-
                <lb/>
              roll. 19. h.</note>
            ior ipſa ABC, quæ verò cum recto, quod minus ſit CG; </s>
            <s xml:id="echoid-s2034" xml:space="preserve">vel tota cadit intra
              <lb/>
            ANCD, tùm cum rectum æquet ipſum CM, & </s>
            <s xml:id="echoid-s2035" xml:space="preserve"> eò magis ſi ipſo ſit minus;</s>
            <s xml:id="echoid-s2036" xml:space="preserve">
              <note symbol="i" position="left" xlink:label="note-0082-09" xlink:href="note-0082-09a" xml:space="preserve">1. Co-
                <lb/>
              rol. 19. h.</note>
            vel ſaltem ſecat portionem ANC ſupra baſim AD, quando nempe rectum cadat inter CM, & </s>
            <s xml:id="echoid-s2037" xml:space="preserve">CG, quale eſt CO, nam iuncta regula FO, omnino ſecat
              <lb/>
              <note symbol="l" position="left" xlink:label="note-0082-10" xlink:href="note-0082-10a" xml:space="preserve">20. h.</note>
            Hyperbolæ regulam ML ſupra eandem AD. </s>
            <s xml:id="echoid-s2038" xml:space="preserve">Quapropter Ellipſis portio
              <lb/>
            ABCD, erit _MINIMA_ circumſcripta cũ dato tranſuerſo CI. </s>
            <s xml:id="echoid-s2039" xml:space="preserve">Quod tertiò, &</s>
            <s xml:id="echoid-s2040" xml:space="preserve">c.</s>
            <s xml:id="echoid-s2041" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2042" xml:space="preserve">Poſtremò, datis ijſdem, ſit circumſcribenda _MINIMA_ Ellipſis portio, cum
              <lb/>
            dato recto CG, quod tamen excedat latitudinem EL (ad hoc vt iuncta re-
              <lb/>
            gula GL cum diametro CE poſſit conuenire infra E) & </s>
            <s xml:id="echoid-s2043" xml:space="preserve">ipſa GL occurrat CE
              <lb/>
            in F, & </s>
            <s xml:id="echoid-s2044" xml:space="preserve">cum dato recto CG, ac tranſuerſo CF adſcribatur per C
              <note symbol="m" position="left" xlink:label="note-0082-11" xlink:href="note-0082-11a" xml:space="preserve">7. h.</note>
            portio ABCD, quæ item datæ portioni occurret in A, & </s>
            <s xml:id="echoid-s2045" xml:space="preserve">D, eritq; </s>
            <s xml:id="echoid-s2046" xml:space="preserve">
              <note symbol="n" position="left" xlink:label="note-0082-12" xlink:href="note-0082-12a" xml:space="preserve">1. Co-
                <lb/>
              roll. 19. h.</note>
            ſcripta; </s>
            <s xml:id="echoid-s2047" xml:space="preserve">quàm dico eſſe _MINIMAM_: </s>
            <s xml:id="echoid-s2048" xml:space="preserve">quæ enim adſcribitur cum codem recto
              <lb/>
              <note symbol="o" position="left" xlink:label="note-0082-13" xlink:href="note-0082-13a" xml:space="preserve">4. Co-
                <lb/>
              roll. prop.
                <lb/>
              19. huius.</note>
            CG, ſed cum tranſuerſo, quod ſit maius CF, eſt etiam maior ipſa ABC;</s>
            <s xml:id="echoid-s2049" xml:space="preserve"/>
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