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

Page concordance

< >
Scan Original
101 77
102 78
103 79
104 80
105 81
106 82
107 83
108 84
109 85
110 86
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
< >
page |< < (134) of 347 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div436" type="section" level="1" n="184">
          <pb o="134" file="0158" n="158" rhead=""/>
          <p>
            <s xml:id="echoid-s4502" xml:space="preserve">Iam in Parabola, quam exhibet prima huius ſchematis ſigura, cum ſint
              <lb/>
            BC, EF diametri ipſæ erunt inter ſe parallelæ, BA verò eas ſecat,
              <note symbol="a" position="left" xlink:label="note-0158-01" xlink:href="note-0158-01a" xml:space="preserve">cõuerſ.
                <lb/>
              46. pr. co-
                <lb/>
              nic.</note>
            angulus GBF æquatur angulo EFA, ſed eſt GBF obtuſus, cum GBE ſit re-
              <lb/>
            ctus (nam eſt CB axis Parabolæ) ergo angulus quoque EFA obtuſus erit,
              <lb/>
            ſiue maior conſequenti BFE.</s>
            <s xml:id="echoid-s4503" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4504" xml:space="preserve">In Hyperbola verò ſecundæ ſiguræ, cum angulus CBA externus triangu-
              <lb/>
            li DBF ſit acutus, (nam CBE rectus eſt) ſitque maior interno BFE, is quidem
              <lb/>
            acutus erit, & </s>
            <s xml:id="echoid-s4505" xml:space="preserve">qui ei deinceps EFA erit obtuſus, ſiue maior ipſo BFE.</s>
            <s xml:id="echoid-s4506" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4507" xml:space="preserve">In Ellipſi tandem tertiæ ſiguræ iuncta DA, cum in trianguiis DFB, DFA
              <lb/>
            ſit BF ęqualis AF, & </s>
            <s xml:id="echoid-s4508" xml:space="preserve">communis FD baſis verò BD maior DA, erit
              <note symbol="b" position="left" xlink:label="note-0158-02" xlink:href="note-0158-02a" xml:space="preserve">86. h.</note>
            BFD maior angulo DFA, & </s>
            <s xml:id="echoid-s4509" xml:space="preserve">eiad verticẽ EFA maior angulo ad verticẽ BFE.</s>
            <s xml:id="echoid-s4510" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4511" xml:space="preserve">In triangulis itaq; </s>
            <s xml:id="echoid-s4512" xml:space="preserve">AFE, BFE,
              <lb/>
              <figure xlink:label="fig-0158-01" xlink:href="fig-0158-01a" number="124">
                <image file="0158-01" xlink:href="http://echo.mpiwg-berlin.mpg.de/zogilib?fn=/permanent/library/QN4GHYBF/figures/0158-01"/>
              </figure>
            cuiuslibet harum ſigurarum, cum
              <lb/>
            ſit latus A F æqualis FB, & </s>
            <s xml:id="echoid-s4513" xml:space="preserve">FE
              <lb/>
            commune, augulus verò E F A
              <lb/>
            demonſtratus ſit maior angulo
              <lb/>
            BFE, erit baſis A F maior baſi
              <lb/>
            BE. </s>
            <s xml:id="echoid-s4514" xml:space="preserve">Quare contingens B E ex
              <lb/>
            termino maioris axis, minor eſt
              <lb/>
            altera contingente A E. </s>
            <s xml:id="echoid-s4515" xml:space="preserve">Quod
              <lb/>
            primò probandum erat.</s>
            <s xml:id="echoid-s4516" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4517" xml:space="preserve">Si verò, in Ellipſi ABC, quar-
              <lb/>
            tæ ſiguræ, axis BC fuerit minor.
              <lb/>
            </s>
            <s xml:id="echoid-s4518" xml:space="preserve">Poſitis, & </s>
            <s xml:id="echoid-s4519" xml:space="preserve">conſtructis ijſdem. </s>
            <s xml:id="echoid-s4520" xml:space="preserve">Cum in triangulis AFD, BFD ſit latus AF æ-
              <lb/>
            qualle lateri BF, & </s>
            <s xml:id="echoid-s4521" xml:space="preserve">commune FD, baſis verò AD maior baſi DB (cum minor
              <lb/>
            ſemi-axis DB ſit _MINIMA_ ſemi-diametrorum) erit angulus AFD, ſiue
              <note symbol="c" position="left" xlink:label="note-0158-03" xlink:href="note-0158-03a" xml:space="preserve">ibidem.</note>
            maior angulo BFD, hoc eſt AFE, ſuntque in triangulis BFE, AFE latera BF,
              <lb/>
            AF inter ſe æqualia, & </s>
            <s xml:id="echoid-s4522" xml:space="preserve">latus FE commune: </s>
            <s xml:id="echoid-s4523" xml:space="preserve">quare baſis BE, erit maior
              <note symbol="d" position="left" xlink:label="note-0158-04" xlink:href="note-0158-04a" xml:space="preserve">30. ſec.
                <lb/>
              conic.</note>
            AE Quod ſuit vltimò demonſtrandum.</s>
            <s xml:id="echoid-s4524" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div443" type="section" level="1" n="185">
          <head xml:id="echoid-head190" xml:space="preserve">THEOR. XLIII. PROP. LXXXVIII.</head>
          <p>
            <s xml:id="echoid-s4525" xml:space="preserve">Si coni-ſectionem recta linea contingens cum axe conueniat, & </s>
            <s xml:id="echoid-s4526" xml:space="preserve">
              <lb/>
            à tactu erigatur contingenti perpendicularis, hæc neceſſariò cum
              <lb/>
            axe conueniet, in Ellipſi cum vtroque axe, ſed priùs cum maiori;
              <lb/>
            </s>
            <s xml:id="echoid-s4527" xml:space="preserve">parſque ipſius intercepta inter contactum, & </s>
            <s xml:id="echoid-s4528" xml:space="preserve">occurſum cum axe,
              <lb/>
            qui tamen in Ellipſi ſit axis maior, ſemper minor erit eo axis ſe-
              <lb/>
            gmento, quod inter occurſum, & </s>
            <s xml:id="echoid-s4529" xml:space="preserve">verticem intercipitur.</s>
            <s xml:id="echoid-s4530" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4531" xml:space="preserve">Cum autem in Ellipſi, contingens linea minori axi occurret,
              <lb/>
            tunc prædicta perpendicularis inter contactum, & </s>
            <s xml:id="echoid-s4532" xml:space="preserve">minorem axem
              <lb/>
            intercepta, maior ſemper erit ſegmento minoris axis, quod inter
              <lb/>
            occurſum, & </s>
            <s xml:id="echoid-s4533" xml:space="preserve">verticem intercipitur.</s>
            <s xml:id="echoid-s4534" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4535" xml:space="preserve">SIt coni-ſectio ABC, cuius axis BD, & </s>
            <s xml:id="echoid-s4536" xml:space="preserve">prima ſigura Parabolen, aut Hy-
              <lb/>
            perbolen repræſentet, ſecunda verò Ellipſim, cuius axis maior, ſit </s>
          </p>
        </div>
      </text>
    </echo>
Impressum