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

Page concordance

< >
Scan Original
11
12
13
14
15
16 316
17 317
18 318
19 319
20 320
21 321
22 322
23 323
24 324
25
26
27
28 325
29 326
30
31
32
33 327
34 328
35
36
37
38 329
39 330
40 331
< >
page |< < (316) of 568 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div9" type="section" level="1" n="9">
          <p>
            <s xml:id="echoid-s53" xml:space="preserve">
              <pb o="316" file="0016" n="16" rhead="THEOR. DE QUADRAT."/>
            minor erit dato ſpatio; </s>
            <s xml:id="echoid-s54" xml:space="preserve">ſit ea parallelogrammum B F, & </s>
            <s xml:id="echoid-s55" xml:space="preserve">di-
              <lb/>
            vidatur baſis A C in partes æquales ipſi D F, punctis
              <lb/>
            G, H, K &</s>
            <s xml:id="echoid-s56" xml:space="preserve">c. </s>
            <s xml:id="echoid-s57" xml:space="preserve">atque inde ducantur ad ſectionem rectæ
              <lb/>
            G L, H M, K N &</s>
            <s xml:id="echoid-s58" xml:space="preserve">c. </s>
            <s xml:id="echoid-s59" xml:space="preserve">diametro B D parallelæ, & </s>
            <s xml:id="echoid-s60" xml:space="preserve">perfi-
              <lb/>
            ciantur parallelogramma D O, G P, H Q, K R &</s>
            <s xml:id="echoid-s61" xml:space="preserve">c. </s>
            <s xml:id="echoid-s62" xml:space="preserve">Di-
              <lb/>
            co figuram ex omnibus iſtis parallelogrammis compoſitam
              <lb/>
            (quæ impoſterum ordinatè circumſcripta vocabitur) ſupera-
              <lb/>
            re portionem A B C minori quàm datum ſit ſpatio.</s>
            <s xml:id="echoid-s63" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s64" xml:space="preserve">Jungantur enim A N, N M, M L, L B, B S, &</s>
            <s xml:id="echoid-s65" xml:space="preserve">c.
              <lb/>
            </s>
            <s xml:id="echoid-s66" xml:space="preserve">eritque hac ratione inſcripta quoque portioni figura quædam
              <lb/>
            rectilinea; </s>
            <s xml:id="echoid-s67" xml:space="preserve">majorque erit exceſſus figuræ circumſcriptæ quæ
              <lb/>
            ex parallelogrammis compoſita eſt, ſuper inſcriptam, quàm
              <lb/>
            ſupra portionem A B C. </s>
            <s xml:id="echoid-s68" xml:space="preserve">Exceſſus autem circumſcriptæ ſuper
              <lb/>
            inſcriptam ex triangulis conſtat, quorum quæ ſunt ab una
              <lb/>
            diametri parte, ut A R N, N Q M, M P L, L O B,
              <lb/>
            æquantur dimidio parallelogrammi O D vel B F, quia ſin-
              <lb/>
            gulorum baſes baſi D F æquales ſunt, & </s>
            <s xml:id="echoid-s69" xml:space="preserve">omnium ſimul al-
              <lb/>
            titudo, parallelogrammi B F altitudini. </s>
            <s xml:id="echoid-s70" xml:space="preserve">Eâdem ratione trian-
              <lb/>
            gula qu& </s>
            <s xml:id="echoid-s71" xml:space="preserve">ſunt ab altera diametri parte, æquantur dimidio
              <lb/>
            parallelogrammi B F: </s>
            <s xml:id="echoid-s72" xml:space="preserve">Ergo omnia ſimul triangula ſive di-
              <lb/>
            ctus exceſſus æqualis eſt parallelogrammo B F, eóque mi-
              <lb/>
            nor ſpatio dato. </s>
            <s xml:id="echoid-s73" xml:space="preserve">Sed eodem exceſſu adhuc minor erat ex-
              <lb/>
            ceſſus figuræ circumſcriptæ ſupra portionem A B C: </s>
            <s xml:id="echoid-s74" xml:space="preserve">igitur
              <lb/>
            hic exceſſus dato ſpatio multo minor eſt. </s>
            <s xml:id="echoid-s75" xml:space="preserve">Et apparet fieri
              <lb/>
            poſſe quod proponebatur.</s>
            <s xml:id="echoid-s76" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div11" type="section" level="1" n="10">
          <head xml:id="echoid-head22" xml:space="preserve">
            <emph style="sc">Theorema</emph>
          II.</head>
          <p style="it">
            <s xml:id="echoid-s77" xml:space="preserve">DAtâ portione hyperboles, vel ellipſis vel circuli
              <lb/>
            portione, dimidiâ ellipſi dimidiove circulo non
              <lb/>
            majore, & </s>
            <s xml:id="echoid-s78" xml:space="preserve">dato triangulo qui baſin habeat baſi por-
              <lb/>
            tionis æqualem; </s>
            <s xml:id="echoid-s79" xml:space="preserve">poteſt utrique figura circumſcribi ex
              <lb/>
            parallelogrammis quorum ſit omnium eadem latitu-
              <lb/>
            do, ita ut uterque ſimulexceſſus quo figuræ circum-
              <lb/>
            ſcriptæ portionem & </s>
            <s xml:id="echoid-s80" xml:space="preserve">triangulum ſuperant, ſit minor
              <lb/>
            ſpatio quovis dato.</s>
            <s xml:id="echoid-s81" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum