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

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            <s xml:id="echoid-s1637" xml:space="preserve">
              <pb o="75" file="0113" n="120" rhead="HOROLOG. OSCILLATOR."/>
            traque parte centri Z, & </s>
            <s xml:id="echoid-s1638" xml:space="preserve">ſit G H, earum quæ ſunt à parte
              <lb/>
              <note position="right" xlink:label="note-0113-01" xlink:href="note-0113-01a" xml:space="preserve">
                <emph style="sc">De motu</emph>
                <lb/>
                <emph style="sc">IN</emph>
                <emph style="sc">Cy-</emph>
                <lb/>
                <emph style="sc">CLOIDE</emph>
              .</note>
            B, centro proxima, vel per ipſum centrum tranſeat. </s>
            <s xml:id="echoid-s1639" xml:space="preserve">Itaque
              <lb/>
            tangentes omnes inter G H & </s>
            <s xml:id="echoid-s1640" xml:space="preserve">B O comprehenſæ, ut H K,
              <lb/>
            L M, N O, ſingulæ ſuis arcubus minores ſunt . </s>
            <s xml:id="echoid-s1641" xml:space="preserve">
              <note symbol="*" position="right" xlink:label="note-0113-02" xlink:href="note-0113-02a" xml:space="preserve">Prop. 16.
                <lb/>
              huj.</note>
            autem & </s>
            <s xml:id="echoid-s1642" xml:space="preserve">tangens G F, arcu ſequente F D minor eſt , &</s>
            <s xml:id="echoid-s1643" xml:space="preserve">
              <note symbol="*" position="right" xlink:label="note-0113-03" xlink:href="note-0113-03a" xml:space="preserve">Prop. 17.
                <lb/>
              huj.</note>
            ſimiliter tangens E D arcu D A. </s>
            <s xml:id="echoid-s1644" xml:space="preserve">Itaque tangentes omnes
              <lb/>
            inter B O & </s>
            <s xml:id="echoid-s1645" xml:space="preserve">C D interjectæ, minores ſunt arcubus B H & </s>
            <s xml:id="echoid-s1646" xml:space="preserve">
              <lb/>
            F A, ac proinde omnino minores arcubus B H, H A, ſive
              <lb/>
            arcu B A, quod erat primo oſtendendum.</s>
            <s xml:id="echoid-s1647" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1648" xml:space="preserve">Porro jam demonſtrabimus tangentes omnes inter B O & </s>
            <s xml:id="echoid-s1649" xml:space="preserve">A
              <lb/>
            majores eſſe arcu A N. </s>
            <s xml:id="echoid-s1650" xml:space="preserve">Enimvero parallela G H, vel pro-
              <lb/>
            pius centrum Z tranſit quam parallela E F, quam pono
              <lb/>
            proximam eſſe earum quæ à parte A tranſeunt, vel erit re-
              <lb/>
            motior, vel æque diſtabit.</s>
            <s xml:id="echoid-s1651" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1652" xml:space="preserve">Quod ſi E F longius à centro vel æque remota eſt ac G H,
              <lb/>
            erit tangens F G major arcu ſuo F H, & </s>
            <s xml:id="echoid-s1653" xml:space="preserve">reliquæ tangen-
              <lb/>
            tes verſus A, nimirum E D, C A majores ſingulæ arcubus
              <lb/>
              <note symbol="*" position="right" xlink:label="note-0113-04" xlink:href="note-0113-04a" xml:space="preserve">Prop. 15.
                <lb/>
              huj.</note>
            ſuis ; </s>
            <s xml:id="echoid-s1654" xml:space="preserve">adeo ut omnes ſimul G F, E D, C A majores ſint arcu H A. </s>
            <s xml:id="echoid-s1655" xml:space="preserve">ſed & </s>
            <s xml:id="echoid-s1656" xml:space="preserve">arcu H L major erit tangens L M , &</s>
            <s xml:id="echoid-s1657" xml:space="preserve">
              <note symbol="*" position="right" xlink:label="note-0113-05" xlink:href="note-0113-05a" xml:space="preserve">Prop. 19.
                <lb/>
              huj.</note>
            arcu L N tangens N O; </s>
            <s xml:id="echoid-s1658" xml:space="preserve">itaque tangentes omnes, præter
              <lb/>
            H K, majores ſimul erunt arcu A N; </s>
            <s xml:id="echoid-s1659" xml:space="preserve">multoque magis, ac-
              <lb/>
            cedente ipſa H K, tangentes omnes inter A & </s>
            <s xml:id="echoid-s1660" xml:space="preserve">B compre-
              <lb/>
            henſæ arcu eodem A N majores erunt.</s>
            <s xml:id="echoid-s1661" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1662" xml:space="preserve">Si vero G H à centro longius diſtat quam E F, erit tan-
              <lb/>
            gens K H major arcu H F , & </s>
            <s xml:id="echoid-s1663" xml:space="preserve">tangens M L ut ante
              <note symbol="*" position="right" xlink:label="note-0113-06" xlink:href="note-0113-06a" xml:space="preserve">Prop. 19.
                <lb/>
              huj.</note>
            jor arcu L H, & </s>
            <s xml:id="echoid-s1664" xml:space="preserve">tangens O N major arcu N L, & </s>
            <s xml:id="echoid-s1665" xml:space="preserve">omnes
              <lb/>
            proinde tangentes O N, M L, K H majores arcu N F.
              <lb/>
            </s>
            <s xml:id="echoid-s1666" xml:space="preserve">Sed & </s>
            <s xml:id="echoid-s1667" xml:space="preserve">tangens E D major eſt arcu ſuo F D , & </s>
            <s xml:id="echoid-s1668" xml:space="preserve">
              <note symbol="*" position="right" xlink:label="note-0113-07" xlink:href="note-0113-07a" xml:space="preserve">Prop. 11.
                <lb/>
              huj.</note>
            C A major ſimiliter arcu ſuo D A. </s>
            <s xml:id="echoid-s1669" xml:space="preserve">Itaque tangentes omnes
              <lb/>
            inter B O & </s>
            <s xml:id="echoid-s1670" xml:space="preserve">A, præter G F, majores erunt arcu N A;
              <lb/>
            </s>
            <s xml:id="echoid-s1671" xml:space="preserve">multoque magis tangentes eædem, accedente G F, hoc eſt,
              <lb/>
            omnes quæ inter B O & </s>
            <s xml:id="echoid-s1672" xml:space="preserve">A interjiciuntur, eodem arcu N A
              <lb/>
            majores erunt.</s>
            <s xml:id="echoid-s1673" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s1674" xml:space="preserve">Ex his vero etiam demonſtratio manifeſta eſt in caſibus
              <lb/>
            aliis, qualiscunque ſemicircumferentiæ arcus accipiatur,
              <lb/>
            quippe cum vel eadem ſit ubique, vel pars tantum præce-
              <lb/>
            dentis demonſtrationis.</s>
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