Huygens, Christiaan, Christiani Hugenii opera varia; Bd. 2: Opera geometrica. Opera astronomica. Varia de optica

Page concordance

< >
Scan Original
121
122
123 399
124 400
125 401
126 402
127 403
128 404
129
130
131
132
133
134
135
136
137
138
139
140 413
141 414
142 415
143 416
144 417
145 418
146 419
147 420
148 421
149 422
150 423
< >
page |< < (417) of 568 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div149" type="section" level="1" n="66">
          <pb o="417" file="0135" n="144" rhead="ET HYPERBOLÆ QUADRATURA."/>
        </div>
        <div xml:id="echoid-div150" type="section" level="1" n="67">
          <head xml:id="echoid-head100" xml:space="preserve">PROP. III. THEOREMA.</head>
          <head xml:id="echoid-head101" style="it" xml:space="preserve">Dico triangulum B A P, & trapezium A B I P ſimul,
            <lb/>
          eſſe ad trapezium A B I P, ut duplum trapezii A B I P ad polygonum A B D L P.</head>
          <note position="right" xml:space="preserve">TAB. XLIII.
            <lb/>
          Fig. 1. 2. 3.</note>
          <p>
            <s xml:id="echoid-s2831" xml:space="preserve">In antecedente demonſtratum eſt trapezia A B F P, A B I P
              <lb/>
            ſimul, eſſe ad duplum trapezii A B I P, ſicut trapezium
              <lb/>
            A B F P ad polygonum A B D L P: </s>
            <s xml:id="echoid-s2832" xml:space="preserve">& </s>
            <s xml:id="echoid-s2833" xml:space="preserve">permutando tra-
              <lb/>
            pezia A B F P, A B I P ſimul, ſunt ad trapezium A B F P,
              <lb/>
            ut duplum trapezii A B I P ad polygonum A B D L P. </s>
            <s xml:id="echoid-s2834" xml:space="preserve">& </s>
            <s xml:id="echoid-s2835" xml:space="preserve">
              <lb/>
            quoniam trapezium A B F P, trapezium A B I P & </s>
            <s xml:id="echoid-s2836" xml:space="preserve">trian-
              <lb/>
            gulum A B P, ſunt continuè proportionalia; </s>
            <s xml:id="echoid-s2837" xml:space="preserve">erit trape-
              <lb/>
            zium A B I P ad trapezium A B F P, ut triangulum A B P
              <lb/>
            ad trapezium A B I P; </s>
            <s xml:id="echoid-s2838" xml:space="preserve">& </s>
            <s xml:id="echoid-s2839" xml:space="preserve">componendo, ut trapezia A B I P,
              <lb/>
            A B F P ſimul, ad trapezium A B F P, ita triangulum
              <lb/>
            A B P & </s>
            <s xml:id="echoid-s2840" xml:space="preserve">trapezium A B I P ſimul, ad trapezium A B I P:
              <lb/>
            </s>
            <s xml:id="echoid-s2841" xml:space="preserve">erat autem, ut trapezia A B I P, A B F P, ſimul, ad tra-
              <lb/>
            pezium A B F P, ita duplum trapezii A B I P ad polygo-
              <lb/>
            num A B D L P; </s>
            <s xml:id="echoid-s2842" xml:space="preserve">& </s>
            <s xml:id="echoid-s2843" xml:space="preserve">igitur ut triangulum A B P & </s>
            <s xml:id="echoid-s2844" xml:space="preserve">trape-
              <lb/>
            zium A B I P ſimul, ad trapezium A B I P, ita duplum
              <lb/>
            trapezii A B I P ad polygonum A B D L P, quod demon-
              <lb/>
            ſtrare oportuit.</s>
            <s xml:id="echoid-s2845" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2846" xml:space="preserve">Producantur (ſi opus ſit) rectæ A D, A L, ſegmentum
              <lb/>
            ſecantes in punctis E & </s>
            <s xml:id="echoid-s2847" xml:space="preserve">O, & </s>
            <s xml:id="echoid-s2848" xml:space="preserve">rectas B I, I P, in H & </s>
            <s xml:id="echoid-s2849" xml:space="preserve">M:
              <lb/>
            </s>
            <s xml:id="echoid-s2850" xml:space="preserve">deinde jungantur rectæ B E, E I, I O, O P, ut complea-
              <lb/>
            tur polygonum A B E I O P.</s>
            <s xml:id="echoid-s2851" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div151" type="section" level="1" n="68">
          <head xml:id="echoid-head102" xml:space="preserve">PROP. IV. THEOREMA.</head>
          <head xml:id="echoid-head103" style="it" xml:space="preserve">Dico polygonum A B E I O P eſſe medium pro-
            <lb/>
          portionale inter polygonum A B D L & trapezium A B I P.</head>
          <note position="right" xml:space="preserve">TAB. XLIII.
            <lb/>
          Fig. 1. 2. 3.</note>
          <p>
            <s xml:id="echoid-s2852" xml:space="preserve">Ex hujus prima manifeſtum eſt trapezium A I L P, tra-
              <lb/>
            pezium A I O P & </s>
            <s xml:id="echoid-s2853" xml:space="preserve">triangulum A I P eſſe </s>
          </p>
        </div>
      </text>
    </echo>
Impressum