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

Page concordance

< >
Scan Original
111 87
112 88
113 89
114 90
115 91
116 92
117 93
118 94
119 95
120 96
121 97
122 98
123 99
124 100
125 101
126 102
127 103
128 104
129 105
130 106
131 107
132 108
133 109
134 110
135 111
136 112
137 113
138 114
139 115
140 116
< >
page |< < (130) of 347 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div424" type="section" level="1" n="177">
          <pb o="130" file="0154" n="154" rhead=""/>
        </div>
        <div xml:id="echoid-div425" type="section" level="1" n="178">
          <head xml:id="echoid-head183" xml:space="preserve">PROBL. XXXIII. PROP. LXXXIV.</head>
          <p>
            <s xml:id="echoid-s4359" xml:space="preserve">Datæ Ellipſi, vel circulo, per terminos cuiuſcunque in ipſo ap-
              <lb/>
            plicatę MINIMAM Ellipſim circumſcribere, cuius tranſuerſum la-
              <lb/>
            tus æquale ſit dato, quod tamen maius ſit tranſuerſa diametro datæ
              <lb/>
            Ellipſis.</s>
            <s xml:id="echoid-s4360" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4361" xml:space="preserve">SIt data Ellipſis, vel circulus ABCO, cuius tranſuerſa diameter BO, & </s>
            <s xml:id="echoid-s4362" xml:space="preserve">
              <lb/>
            quædam ad eam applicata AC: </s>
            <s xml:id="echoid-s4363" xml:space="preserve">oportet per terminos A, C, cum tranſ-
              <lb/>
            uerſo DE, quod excedat BO _MINIMAM_ Ellipſim circumſcribere.</s>
            <s xml:id="echoid-s4364" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4365" xml:space="preserve">Ducatur ex A contingens AK productæ
              <lb/>
              <figure xlink:label="fig-0154-01" xlink:href="fig-0154-01a" number="121">
                <image file="0154-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0154-01"/>
              </figure>
            diametro occurrens in K, & </s>
            <s xml:id="echoid-s4366" xml:space="preserve">KF bifariam
              <lb/>
            ſecetur in puncto G, quod cadet iuter B, & </s>
            <s xml:id="echoid-s4367" xml:space="preserve">
              <lb/>
            K, vt in 83. </s>
            <s xml:id="echoid-s4368" xml:space="preserve">h. </s>
            <s xml:id="echoid-s4369" xml:space="preserve">oſtenſum fuit; </s>
            <s xml:id="echoid-s4370" xml:space="preserve">& </s>
            <s xml:id="echoid-s4371" xml:space="preserve">ad datam
              <lb/>
            lineam DE applicetur parallelogrammum,
              <lb/>
            æquale quadrato GF, excedens figura
              <lb/>
            quadrata, ſitque rectangulum DHE, & </s>
            <s xml:id="echoid-s4372" xml:space="preserve">
              <lb/>
            ſumpta HI media proportionali inter DH,
              <lb/>
            HE, erit rectangulum DHI, ſiue quadra-
              <lb/>
            tum GF, ęquale quadrato HI, hoc eſt linea
              <lb/>
            GF æqualis HI: </s>
            <s xml:id="echoid-s4373" xml:space="preserve">ſumpta ergo GL æquali
              <lb/>
            HE, erit reliqua LF æqualis EI, & </s>
            <s xml:id="echoid-s4374" xml:space="preserve">pũctum
              <lb/>
            L cadet extra B: </s>
            <s xml:id="echoid-s4375" xml:space="preserve">quoniam cum ſit OK ad
              <lb/>
            KB, vt AF ad FB, ſitque KF bifariam
              <note symbol="a" position="left" xlink:label="note-0154-01" xlink:href="note-0154-01a" xml:space="preserve">36. pri-
                <lb/>
              mi conic.</note>
            cta in G, erit rectangulum OGB æquale quadrato GF, ſiue quadrato
              <note symbol="b" position="left" xlink:label="note-0154-02" xlink:href="note-0154-02a" xml:space="preserve">79. h.</note>
            ſiue rectangulo DHE; </s>
            <s xml:id="echoid-s4376" xml:space="preserve">ſed eſt OB minor DE, ex conſtructione, quare GB
              <lb/>
            erit maior HE, ſiue maior GL; </s>
            <s xml:id="echoid-s4377" xml:space="preserve">itaque punctum L cadet extra Ellipſim
              <note symbol="c" position="left" xlink:label="note-0154-03" xlink:href="note-0154-03a" xml:space="preserve">80. h.</note>
            CO. </s>
            <s xml:id="echoid-s4378" xml:space="preserve">Sumatur ampliùs FN æqualis ID, & </s>
            <s xml:id="echoid-s4379" xml:space="preserve">erit tota LN æqualis datæ ED,
              <lb/>
            itemque punctum N cadet extra Ellipſim ABCO: </s>
            <s xml:id="echoid-s4380" xml:space="preserve">Nam cum ſit rectangulum
              <lb/>
            DHE, ſiue NGL æquale quadrato HI, ſiue GF, ſitque rectangulum OGB,
              <lb/>
            æquale eidem quadrato GF, vt ſupra oſtendimus, erunt rectangula OGB,
              <lb/>
            NGL inter ſe æqualia, & </s>
            <s xml:id="echoid-s4381" xml:space="preserve">ideo vt OG ad GN, ita LG ad GB, ſed eſt LG mi-
              <lb/>
            nor GB, vt ſuperiùs demonſtrauimus, vnde, & </s>
            <s xml:id="echoid-s4382" xml:space="preserve">OG minor erit GN, nempe
              <lb/>
            punctum N cadet extra Ellipſim ABCO. </s>
            <s xml:id="echoid-s4383" xml:space="preserve">Poſtremò cum tranſuerſo latere
              <lb/>
            NL, quod æquale eſt datæ lineæ DE, circa applicatam AC
              <note symbol="d" position="left" xlink:label="note-0154-04" xlink:href="note-0154-04a" xml:space="preserve">Coroll.
                <lb/>
              57. h.</note>
            Ellipſis ALCN. </s>
            <s xml:id="echoid-s4384" xml:space="preserve">Dico hanc eſſe _MINIMAM_ circumſcriptam quæſitam.</s>
            <s xml:id="echoid-s4385" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4386" xml:space="preserve">Quoniam cum ſit rectangulum NGL æquale quadrato GF, erit NG ad
              <lb/>
            GF, vt GF ad GL, & </s>
            <s xml:id="echoid-s4387" xml:space="preserve">componendo, NG cum GF, ſiue NK, erit ad GF, vt
              <lb/>
            FG cum GL, ſiue vt KL ad GL, & </s>
            <s xml:id="echoid-s4388" xml:space="preserve">permutando NK ad KL, vt GF ad GL,
              <lb/>
            vel vt NG ad GF, vel vt NF ad FL, ergo recta KAM Ellipſim ALCN
              <note symbol="e" position="left" xlink:label="note-0154-05" xlink:href="note-0154-05a" xml:space="preserve">Coroll.
                <lb/>
              12. h.</note>
            tingit in A, ſed eadem KAM contingit quoque ad idem punctum A
              <note symbol="f" position="left" xlink:label="note-0154-06" xlink:href="note-0154-06a" xml:space="preserve">4. h.</note>
            pſim ABCO: </s>
            <s xml:id="echoid-s4389" xml:space="preserve">quapropter Ellipſis ALCN datæ ABCO erit circumſcripta.</s>
            <s xml:id="echoid-s4390" xml:space="preserve">
              <note symbol="g" position="left" xlink:label="note-0154-07" xlink:href="note-0154-07a" xml:space="preserve">61. h.</note>
            At ipſa erit _MINIMA_: </s>
            <s xml:id="echoid-s4391" xml:space="preserve">nam quælibet alia, quæ ipſi adſcribitur per eoſdem
              <lb/>
            terminos communis applicatæ AC, & </s>
            <s xml:id="echoid-s4392" xml:space="preserve">cum tranſuerſa diametro æquali ipſi
              <lb/>
            LN, _licet maior ſuerit eadem ALCN_, inſcriptam ABCO omnino ſecat; </s>
            <s xml:id="echoid-s4393" xml:space="preserve">
              <note symbol="b" position="left" xlink:label="note-0154-08" xlink:href="note-0154-08a" xml:space="preserve">83. h.</note>
            </s>
          </p>
        </div>
      </text>
    </echo>
Impressum