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

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            <s xml:id="echoid-s1721" xml:space="preserve">
              <pb o="378" file="0090" n="96" rhead="CHRISTIANI HUGENII"/>
            ſimul A G, A B; </s>
            <s xml:id="echoid-s1722" xml:space="preserve">hoc eſt, minor quam C A cum dimidia
              <lb/>
            A G. </s>
            <s xml:id="echoid-s1723" xml:space="preserve">Quare ablatâ utrimque C A, erit C H minor dimi-
              <lb/>
            diâ A G. </s>
            <s xml:id="echoid-s1724" xml:space="preserve">C A vero dimidiâ A G major eſt. </s>
            <s xml:id="echoid-s1725" xml:space="preserve">Ergo ſi adda-
              <lb/>
            tur A C ad A G, erit tota C G major quam tripla ipſius
              <lb/>
            C H. </s>
            <s xml:id="echoid-s1726" xml:space="preserve">Quia autem ut H G ad G E, ita eſt E D ad D K;
              <lb/>
            </s>
            <s xml:id="echoid-s1727" xml:space="preserve">ut autem G E ad G C, ita L D ad D E: </s>
            <s xml:id="echoid-s1728" xml:space="preserve">Erit ex æquo in
              <lb/>
            proportione turbata ut H G ad G C, ita L D ad D K. </s>
            <s xml:id="echoid-s1729" xml:space="preserve">Et
              <lb/>
            per converſionem rationis & </s>
            <s xml:id="echoid-s1730" xml:space="preserve">dividendo, ut G C ad C H,
              <lb/>
            ita D K ad K L. </s>
            <s xml:id="echoid-s1731" xml:space="preserve">Ergo etiam D K major quam tripla K L. </s>
            <s xml:id="echoid-s1732" xml:space="preserve">
              <lb/>
            Erat autem D K exceſſus ipſius E B ſupra E G. </s>
            <s xml:id="echoid-s1733" xml:space="preserve">Ergo K L
              <lb/>
            minor eſt triente dicti exceſſus. </s>
            <s xml:id="echoid-s1734" xml:space="preserve">K B autem æqualis eſt ipſi
              <lb/>
            E B ſubtenſæ. </s>
            <s xml:id="echoid-s1735" xml:space="preserve">Ergo K B unà cum K L, hoc eſt, tota
              <lb/>
            L B omnino minor erit arcu B E . </s>
            <s xml:id="echoid-s1736" xml:space="preserve">Quod erat
              <note symbol="*" position="left" xlink:label="note-0090-01" xlink:href="note-0090-01a" xml:space="preserve">per 7. huj.</note>
            dum.</s>
            <s xml:id="echoid-s1737" xml:space="preserve"/>
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            <s xml:id="echoid-s1738" xml:space="preserve">Perpenſo autem Theoremate præcedenti, liquet non poſſe
              <lb/>
            ſumi punctum aliud in producta B A diametro, quod minus
              <lb/>
            à circulo diſtet quam punctum C, eandemque ſervet proprie-
              <lb/>
            tatem, ut nimirum ductâ C L fiat tangens intercepta B L
              <lb/>
            ſemper minor arcu abſciſſo B E.</s>
            <s xml:id="echoid-s1739" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1740" xml:space="preserve">Porro uſus hujus Theorematis multiplex eſt, cum in inve-
              <lb/>
            niendis triangulorum angulis quorum cognita ſint latera, id-
              <lb/>
            que citra tabularum opem, tum ut latera ex angulis datis
              <lb/>
            inveniantur, vel cuilibet peripheriæ arcui ſubtenſa aſſigne-
              <lb/>
            tur. </s>
            <s xml:id="echoid-s1741" xml:space="preserve">Quæ omnia à Snellio in Cyclometricis diligenter pertra-
              <lb/>
            ctata ſunt.</s>
            <s xml:id="echoid-s1742" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div92" type="section" level="1" n="43">
          <head xml:id="echoid-head66" xml:space="preserve">
            <emph style="sc">Theorema</emph>
          XIV.
            <emph style="sc">Propos</emph>
          . XVII.</head>
          <p style="it">
            <s xml:id="echoid-s1743" xml:space="preserve">
              <emph style="bf">P</emph>
            Ortionis circuli centrum gravitatis diametrum
              <lb/>
            portionis ita dividit, ut pars quæ ad verticem
              <lb/>
            reliquâ major ſit, minor autem quam ejuſdem ſeſ-
              <lb/>
            quialtera.</s>
            <s xml:id="echoid-s1744" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1745" xml:space="preserve">Eſto circuli portio A B C, (ponatur autem ſemicirculo
              <lb/>
              <note position="left" xlink:label="note-0090-02" xlink:href="note-0090-02a" xml:space="preserve">TAB. XL.
                <lb/>
              Fig. 2.</note>
            minor, quoniam cæteræ ad propoſitum non faciunt) & </s>
            <s xml:id="echoid-s1746" xml:space="preserve">dia-
              <lb/>
            meter portionis ſit B D, quæ bifariam ſecetur in E. </s>
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