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

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          <p>
            <s xml:id="echoid-s1884" xml:space="preserve">
              <pb o="55" file="0079" n="79" rhead=""/>
            verò cum recto, quod excedat CM, eſt quidem maior ipſa ANCO,
              <note symbol="a" position="right" xlink:label="note-0079-01" xlink:href="note-0079-01a" xml:space="preserve">2. Co-
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              roll. 19. h.</note>
            veltota cadit extra ABCDE, cum Hyperbole, cuius regula IG ſit ei
              <note symbol="b" position="right" xlink:label="note-0079-02" xlink:href="note-0079-02a" xml:space="preserve">24. h.</note>
            cumſcripta, & </s>
            <s xml:id="echoid-s1885" xml:space="preserve">eò ampliùs ea, quæ cum recto quod excedat CG; </s>
            <s xml:id="echoid-s1886" xml:space="preserve">vel ſaltem
              <lb/>
            ſecat Hyperbolen ABCD ſupra portionis baſim AE ſi rectum cadat
              <note symbol="c" position="right" xlink:label="note-0079-03" xlink:href="note-0079-03a" xml:space="preserve">1. Co-
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              roll. 19. h.</note>
            M, & </s>
            <s xml:id="echoid-s1887" xml:space="preserve">G. </s>
            <s xml:id="echoid-s1888" xml:space="preserve">Vnde hæc Hyperbolæ portio ANCOE eſt _MAXIMA_ inſcripta
              <lb/>
            quæſita, cum dato tranſuerſo CI. </s>
            <s xml:id="echoid-s1889" xml:space="preserve">Quod erat primò, &</s>
            <s xml:id="echoid-s1890" xml:space="preserve">c.</s>
            <s xml:id="echoid-s1891" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1892" xml:space="preserve">Siautem inſcribẽda ſit _MAXIMA_ Hyperbolæ portio cum dato recto CM,
              <lb/>
            quod ſit minus recto CG (cum æ quali enim, vel maiori ſemper eſſet circum-
              <lb/>
            ſcripta) iuncta LM, & </s>
            <s xml:id="echoid-s1893" xml:space="preserve">producta vſque ad occurſum cum diametro in I; </s>
            <s xml:id="echoid-s1894" xml:space="preserve">cum
              <lb/>
            tranſuerſo latere CI, ac recto CM adſcribatur per C Hyperbole
              <note symbol="d" position="right" xlink:label="note-0079-04" xlink:href="note-0079-04a" xml:space="preserve">6. huius.</note>
            quæ ſecabit Hyperbolæ portionem ABCD in A & </s>
            <s xml:id="echoid-s1895" xml:space="preserve">E, eique erit inſcripta.</s>
            <s xml:id="echoid-s1896" xml:space="preserve">
              <note symbol="e" position="right" xlink:label="note-0079-05" xlink:href="note-0079-05a" xml:space="preserve">1. Co-
                <lb/>
              roll. 19. h.</note>
            Dico hanc eſſe _MAXIMAM_ quæſitam. </s>
            <s xml:id="echoid-s1897" xml:space="preserve">Quoniam quæ adſcribitur per C cum
              <lb/>
            eodem recto CM, ſed cum tranſuerſo, quod excedat CI, minor eſt
              <note symbol="f" position="right" xlink:label="note-0079-06" xlink:href="note-0079-06a" xml:space="preserve">3. Corol.
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              19. huius.</note>
            bola ANCO, quæ verò cum tranſuerſo, quod minus ſit ipſo CI, & </s>
            <s xml:id="echoid-s1898" xml:space="preserve">
              <note symbol="g" position="right" xlink:label="note-0079-07" xlink:href="note-0079-07a" xml:space="preserve">ibidem.</note>
            maior eadem ANCO, ſed omninò ſecat Hyperbolen ABCDE ſupra
              <note symbol="h" position="right" xlink:label="note-0079-08" xlink:href="note-0079-08a" xml:space="preserve">1. Co-
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              roll. 19. h.</note>
            catam AE. </s>
            <s xml:id="echoid-s1899" xml:space="preserve">Eſt igitur huiuſmodi Hyperbolæ portio ANCO _MAXIMA_ in-
              <lb/>
            ſcripta quæſita cum dato recto CM. </s>
            <s xml:id="echoid-s1900" xml:space="preserve">Quod erat ſecundò, &</s>
            <s xml:id="echoid-s1901" xml:space="preserve">c.</s>
            <s xml:id="echoid-s1902" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1903" xml:space="preserve">Ampliùs, ſit data Hyperbolæ portio ANCOE, cuius verſum CI, rectum
              <lb/>
            CM, regula IML, baſis AE, ac diameter CI, cui oporteat per verticem C,
              <lb/>
            cum dato tranſuerſo CF, quod maius ſit CI _MINIMAM_ Hyperbolæ portio-
              <lb/>
            nem circumſcribere.</s>
            <s xml:id="echoid-s1904" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1905" xml:space="preserve">Producatur ſemi-baſis AH conueniens cum regula IM, in L, & </s>
            <s xml:id="echoid-s1906" xml:space="preserve">iungatur
              <lb/>
            FL contingentem CM ſecans in G, & </s>
            <s xml:id="echoid-s1907" xml:space="preserve">cum tranſuerſo CF, ac recto CG ad-
              <lb/>
            ſcribatur per verticem C Hyperbole ABCDE, quæ occurret datæ
              <note symbol="i" position="right" xlink:label="note-0079-09" xlink:href="note-0079-09a" xml:space="preserve">6. huius.</note>
            bolæ ANCO in punctis A, E, eique erit circumſcripta ſupra baſim AE,& </s>
            <s xml:id="echoid-s1908" xml:space="preserve">erit
              <lb/>
            _MINIMA_ Hyperbolæ portio quæſita.</s>
            <s xml:id="echoid-s1909" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1910" xml:space="preserve">Quoniam, quæ adſcribitur cum eodem verſo CF, ſed cum recto maiore
              <lb/>
            ipſo CG, eſt quoque maior Hyperbola ABCD, quę verò cum recto
              <note symbol="l" position="right" xlink:label="note-0079-10" xlink:href="note-0079-10a" xml:space="preserve">1. Corol.
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              19. huius.</note>
            re ipſo CG, eſt quidem minor eadem ABCD, ſed veltota cadit intra
              <note symbol="m" position="right" xlink:label="note-0079-11" xlink:href="note-0079-11a" xml:space="preserve">2. Co-
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              roll. 19. h.</note>
            tam ANCO ſi nempe rectum æquale fuerit ipſo CM, & </s>
            <s xml:id="echoid-s1911" xml:space="preserve">eò magis ſi
              <note symbol="n" position="right" xlink:label="note-0079-12" xlink:href="note-0079-12a" xml:space="preserve">ibidem.</note>
            eſſet CM; </s>
            <s xml:id="echoid-s1912" xml:space="preserve">vel ſaltem ſecat Hyperbolen ANCO ſupra baſim AE,
              <note symbol="o" position="right" xlink:label="note-0079-13" xlink:href="note-0079-13a" xml:space="preserve">3. Corol.
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              19. huius.</note>
            rectum cadat inter CM, & </s>
            <s xml:id="echoid-s1913" xml:space="preserve">CG; </s>
            <s xml:id="echoid-s1914" xml:space="preserve">tunc enim harum regulæ ſe mutuò ſecarent,
              <lb/>
            ſupra eandem baſim AE. </s>
            <s xml:id="echoid-s1915" xml:space="preserve">Vnde Hyperbolæ portio ABCDE, eſt _MINIMA_
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            circumſcripta quæſita cum dato tranſuerſo CF. </s>
            <s xml:id="echoid-s1916" xml:space="preserve">Quod tertiò, &</s>
            <s xml:id="echoid-s1917" xml:space="preserve">c.</s>
            <s xml:id="echoid-s1918" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1919" xml:space="preserve">Demùm eidem datæ Hyperbolæ ANCO, ſit circumſcribenda _MINIMA_
              <lb/>
            Hyperbole cum dato recto CG, quod excedat datæ rectum CM. </s>
            <s xml:id="echoid-s1920" xml:space="preserve">Facta ea-
              <lb/>
            dem conſtructione, iungatur LG diametro occurrens in F, & </s>
            <s xml:id="echoid-s1921" xml:space="preserve">cum tranſuerſo
              <lb/>
            CF, ac dato recto CG adſcribatur per C Hyperbole ABCDE, quæ
              <note symbol="p" position="right" xlink:label="note-0079-14" xlink:href="note-0079-14a" xml:space="preserve">1. Co-
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              roll. 19. h.</note>
            ſecabit in A, & </s>
            <s xml:id="echoid-s1922" xml:space="preserve">E eique erit circumſcripta, & </s>
            <s xml:id="echoid-s1923" xml:space="preserve">erit _MINIMA_ quæſita. </s>
            <s xml:id="echoid-s1924" xml:space="preserve">
              <note symbol="q" position="right" xlink:label="note-0079-15" xlink:href="note-0079-15a" xml:space="preserve">6. huius.</note>
            quæ cum eodem recto CG, ſed cum tranſuerſo, quod minus ſit CF, maior
              <lb/>
            eſt ipſa ABCD, quę verò cum tranſuerſo, quod maius ſit ipſo CF, quale
              <note symbol="r" position="right" xlink:label="note-0079-16" xlink:href="note-0079-16a" xml:space="preserve">1. Co-
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              roll. 19. h.</note>
            CP, eſt quidem minor, ſed omnino ſecat, portionem ANCO ſupra
              <note symbol="s" position="right" xlink:label="note-0079-17" xlink:href="note-0079-17a" xml:space="preserve">3. Corol.
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              19. huius.</note>
            AE, cum iuncta regula PG, & </s>
            <s xml:id="echoid-s1925" xml:space="preserve">producta, ſecet regulam IL ſupra ipſam baſim
              <lb/>
            AE. </s>
            <s xml:id="echoid-s1926" xml:space="preserve">Quare Hyperbolæ portio ABCD eſt _MINIMA_ circumſcripta quæſita
              <lb/>
            cum dato recto CG. </s>
            <s xml:id="echoid-s1927" xml:space="preserve">Quod tandem faciendum erat.</s>
            <s xml:id="echoid-s1928" xml:space="preserve"/>
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