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

Page concordance

< >
Scan Original
41 332
42 333
43 334
44 335
45 336
46 337
47 338
48 339
49 340
50
51
52
53
54
55
56 344
57 345
58 346
59 347
60 348
61 349
62 350
63
64
65
66
67
68
69
70 358
< >
page |< < (379) of 568 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div92" type="section" level="1" n="43">
          <p>
            <s xml:id="echoid-s1747" xml:space="preserve">
              <pb o="379" file="0091" n="97" rhead="DE CIRCULI MAGNIT. INVENTA."/>
            oſtendendum eſt primò centrum gravitatis portionis A B di-
              <lb/>
            ſtare à vertice B ultra punctum E; </s>
            <s xml:id="echoid-s1748" xml:space="preserve">nam, quod in diametro
              <lb/>
            ſitum ſit, alibi oſtendimus. </s>
            <s xml:id="echoid-s1749" xml:space="preserve">Ducatur per E recta baſi paral-
              <lb/>
            lela, quæ utrimque circumferentiæ occurrat in punctis F & </s>
            <s xml:id="echoid-s1750" xml:space="preserve">
              <lb/>
            G. </s>
            <s xml:id="echoid-s1751" xml:space="preserve">Per quæ ducantur K I, H L baſi A C ad angulos re-
              <lb/>
            ctos, atque hæ cum ea, quæ portionem in vertice contingit,
              <lb/>
            conſtituant rectangulum K L. </s>
            <s xml:id="echoid-s1752" xml:space="preserve">Quoniam igitur portio ſemi-
              <lb/>
            circulo minor eſt, conſtat rectanguli dicti dimidium F L con-
              <lb/>
            tineri intra ſegmentum A F G C, atque inſuper ſpatia quæ-
              <lb/>
            dam A F I, L G C. </s>
            <s xml:id="echoid-s1753" xml:space="preserve">Alterum vero rectanguli K L ſemiſſem
              <lb/>
            K G complecti ſegmentum F B G unà cum ſpatiis F B K,
              <lb/>
            B G H. </s>
            <s xml:id="echoid-s1754" xml:space="preserve">Quæ ſpatia quum ſint tota ſupra rectam F G, et-
              <lb/>
            iam centrum commune gravitatis eorum ſupra eandem ſitum
              <lb/>
            erit. </s>
            <s xml:id="echoid-s1755" xml:space="preserve">Eſt autem E punctum in ipſa F G centrum grav. </s>
            <s xml:id="echoid-s1756" xml:space="preserve">to-
              <lb/>
            tius rectanguli K L. </s>
            <s xml:id="echoid-s1757" xml:space="preserve">Igitur ſpatii reliqui B F I L G B cen-
              <lb/>
            trum grav. </s>
            <s xml:id="echoid-s1758" xml:space="preserve">erit infra rectam F G. </s>
            <s xml:id="echoid-s1759" xml:space="preserve">Sed & </s>
            <s xml:id="echoid-s1760" xml:space="preserve">ſpatiorum A F I,
              <lb/>
            L G C commune gravitatis centrum eſt infra eandem F G.
              <lb/>
            </s>
            <s xml:id="echoid-s1761" xml:space="preserve">Ergo magnitudinis ex ſpatiis hiſce & </s>
            <s xml:id="echoid-s1762" xml:space="preserve">dicto ſpatio B F I L G B
              <lb/>
            compoſitæ, quæ eſt portio ipſa A B C, centrum gravitatis
              <lb/>
            infra lineam F G reperiri neceſſe eſt, ideoque infra E pun-
              <lb/>
            ctum.</s>
            <s xml:id="echoid-s1763" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1764" xml:space="preserve">Eadem verò diameter B D ſecetur nunc in S, ita ut B S
              <lb/>
              <note position="right" xlink:label="note-0091-01" xlink:href="note-0091-01a" xml:space="preserve">TAB. XL.
                <lb/>
              Fig. 3.</note>
            ſit ſeſquialtera reliquæ S D. </s>
            <s xml:id="echoid-s1765" xml:space="preserve">Dico centrum grav. </s>
            <s xml:id="echoid-s1766" xml:space="preserve">portionis
              <lb/>
            A B C minus diſtare à vertice B quam punctum S. </s>
            <s xml:id="echoid-s1767" xml:space="preserve">Sit enim
              <lb/>
            B D P totius circuli diameter. </s>
            <s xml:id="echoid-s1768" xml:space="preserve">& </s>
            <s xml:id="echoid-s1769" xml:space="preserve">ducatur per S recta baſi
              <lb/>
            parallela quæ circumferentiæ occurrat in F & </s>
            <s xml:id="echoid-s1770" xml:space="preserve">G. </s>
            <s xml:id="echoid-s1771" xml:space="preserve">Et parabo-
              <lb/>
            le intelligatur cujus vertex B, axis B D, rectum vero latus
              <lb/>
            æquale S P. </s>
            <s xml:id="echoid-s1772" xml:space="preserve">Et occurat baſi portionis in H & </s>
            <s xml:id="echoid-s1773" xml:space="preserve">K. </s>
            <s xml:id="echoid-s1774" xml:space="preserve">Quoniam
              <lb/>
            igitur quadratum F S æquale eſt rectangulo B S P, hoc eſt,
              <lb/>
            ei quod ſub B S & </s>
            <s xml:id="echoid-s1775" xml:space="preserve">latere recto parabolæ continetur, tranſibit
              <lb/>
            ea per F punctum, itemque per G. </s>
            <s xml:id="echoid-s1776" xml:space="preserve">Partes autem lineæ pa-
              <lb/>
            rabolicæ B F, B G intra circumferentiam cadent, ſed reli-
              <lb/>
            quæ F H, G K erunt exteriores. </s>
            <s xml:id="echoid-s1777" xml:space="preserve">Hoc enim oſtenditur du-
              <lb/>
            ctâ inter B & </s>
            <s xml:id="echoid-s1778" xml:space="preserve">S ordinatim applicatâ N L, quæ circumfe-
              <lb/>
            rentiæ occurrat in N, parabolæ autem in M. </s>
            <s xml:id="echoid-s1779" xml:space="preserve">Nam quia qua-
              <lb/>
            dratum N L æquale eſt rectangulo B L P, quadratum </s>
          </p>
        </div>
      </text>
    </echo>
Impressum