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

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              <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>
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