Huygens, Christiaan, Christiani Hugenii opera varia; Bd. 1: Opera mechanica

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          <pb o="69" file="0105" n="111" rhead="HOROLOG. OSCILLATOR."/>
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        <div xml:id="echoid-div92" type="section" level="1" n="38">
          <head xml:id="echoid-head60" xml:space="preserve">PROPOSITIO XV.</head>
          <note position="right" xml:space="preserve">
            <emph style="sc">De de-</emph>
            <lb/>
            <emph style="sc">SCENSU</emph>
            <lb/>
            <emph style="sc">GRAVIUM</emph>
          .</note>
          <p style="it">
            <s xml:id="echoid-s1477" xml:space="preserve">DAto in Cycloide puncto, rectam per illud du-
              <lb/>
            cere quæ Cycloidem tangat.</s>
            <s xml:id="echoid-s1478" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1479" xml:space="preserve">Sit cyclois A B C, & </s>
            <s xml:id="echoid-s1480" xml:space="preserve">punctum in ea datum B, per quod
              <lb/>
              <note position="right" xlink:label="note-0105-02" xlink:href="note-0105-02a" xml:space="preserve">TAB. VII.
                <lb/>
              Fig. 2.</note>
            tangentem ducere oporteat.</s>
            <s xml:id="echoid-s1481" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1482" xml:space="preserve">Circa axem cycloidis A D deſcribatur circulus genitor
              <lb/>
            A E D, & </s>
            <s xml:id="echoid-s1483" xml:space="preserve">ducatur B E parallela baſi cycloidis, quæ dicto
              <lb/>
            circulo occurrat in E, & </s>
            <s xml:id="echoid-s1484" xml:space="preserve">jungatur A E, cui denique paral-
              <lb/>
            lela per B agatur H B N. </s>
            <s xml:id="echoid-s1485" xml:space="preserve">Dico hanc cycloidem in B con-
              <lb/>
            tingere.</s>
            <s xml:id="echoid-s1486" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1487" xml:space="preserve">Sumatur enim in ea punctum quodlibet, à B diverſum,
              <lb/>
            ac primo verſus ſuperiora velut H, & </s>
            <s xml:id="echoid-s1488" xml:space="preserve">per H ducantur re-
              <lb/>
            cta baſi cycloidis parallela, quæ occurrat cycloidi in L, cir-
              <lb/>
            culo A E D in K, rectæ A E in M. </s>
            <s xml:id="echoid-s1489" xml:space="preserve">Quia ergo K L eſt
              <lb/>
            æqualis arcui K A, recta autem K M minor arcu K E, erit
              <lb/>
            recta M L minor arcu A E, hoc eſt, rectâ E B, ſive M H;
              <lb/>
            </s>
            <s xml:id="echoid-s1490" xml:space="preserve">unde apparet punctum H eſſe extra cycloidem.</s>
            <s xml:id="echoid-s1491" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1492" xml:space="preserve">Deinde in recta H N ſumatur punctum N inferius B, & </s>
            <s xml:id="echoid-s1493" xml:space="preserve">
              <lb/>
            per N agatur, ut ante, baſi parallela, quæ occurrat cycloi-
              <lb/>
            di in Q, circulo A E D in O, rectæ A E productæ in P.
              <lb/>
            </s>
            <s xml:id="echoid-s1494" xml:space="preserve">Quia ergo O Q, æqualis eſt arcui O A; </s>
            <s xml:id="echoid-s1495" xml:space="preserve">O P autem major
              <lb/>
            arcu O E; </s>
            <s xml:id="echoid-s1496" xml:space="preserve">erit P Q minor arcu E A, hoc eſt, rectâ E B,
              <lb/>
            ſive P N. </s>
            <s xml:id="echoid-s1497" xml:space="preserve">Unde apparet rurſus punctum N eſſe extra cycloi-
              <lb/>
            dem. </s>
            <s xml:id="echoid-s1498" xml:space="preserve">Cum igitur quodlibet punctum præter B, in recta
              <lb/>
            H B N ſumptum, ſit extra cycloidem, conſtat illam in
              <lb/>
            puncto B cycloidem contingere; </s>
            <s xml:id="echoid-s1499" xml:space="preserve">quod erat demonſtrandum.</s>
            <s xml:id="echoid-s1500" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1501" xml:space="preserve">Huic demonſtrationi an locum ſuum hic relinquerem dubi-
              <lb/>
            tavi, quod non multum ei abſimilem à clariſſimo Wrennio
              <lb/>
            editam inveniam in libro Walliſii de Cycloide. </s>
            <s xml:id="echoid-s1502" xml:space="preserve">Poteſt autem
              <lb/>
            & </s>
            <s xml:id="echoid-s1503" xml:space="preserve">univerſali conſtructione propoſitum abſolvi, quæ non cy-
              <lb/>
            cloidi tantum ſed & </s>
            <s xml:id="echoid-s1504" xml:space="preserve">aliis curvis, ex cujuſlibet figuræ circum-
              <lb/>
            volutione genitis, conveniat; </s>
            <s xml:id="echoid-s1505" xml:space="preserve">dummodo ſit figura in ean-
              <lb/>
            dem partem cava, & </s>
            <s xml:id="echoid-s1506" xml:space="preserve">ex iis quæ geometricæ vocantur.</s>
            <s xml:id="echoid-s1507" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1508" xml:space="preserve">Sit enim curva N A B, orta ex circumvolutione figuræ
              <lb/>
              <note position="right" xlink:label="note-0105-03" xlink:href="note-0105-03a" xml:space="preserve">TAB. VII.
                <lb/>
              Fig. 3.</note>
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