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

Page concordance

< >
Scan Original
91 376
92
93
94
95 377
96 378
97 379
98 380
99 381
100 382
101 383
102 384
103 385
104 386
105
106 386
107
108 387
109
110 389
111 390
112 391
113 392
114 393
115 394
116 395
117 396
118 397
119 398
120
< >
page |< < (377) of 568 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div88" type="section" level="1" n="41">
          <pb o="377" file="0089" n="95" rhead="DE CIRCULI MAGNIT. INVENTA."/>
          <p>
            <s xml:id="echoid-s1693" xml:space="preserve">Hoc Theorema alterum eſt ex iis quibus Cyclometria
              <lb/>
            Willebrordi Snellii tota innititur, quæque demonſtraſſe ipſe
              <lb/>
            videri voluit, argumentatione uſus quæ meram quæſiti pe-
              <lb/>
            titionem continet. </s>
            <s xml:id="echoid-s1694" xml:space="preserve">Sed & </s>
            <s xml:id="echoid-s1695" xml:space="preserve">alterum ſubjungemus, quod utile
              <lb/>
            eſt imprimis & </s>
            <s xml:id="echoid-s1696" xml:space="preserve">contemplatione digniſſimum.</s>
            <s xml:id="echoid-s1697" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div90" type="section" level="1" n="42">
          <head xml:id="echoid-head65" xml:space="preserve">
            <emph style="sc">Theor</emph>
          . XIII.
            <emph style="sc">Prop</emph>
          . XVI.</head>
          <p style="it">
            <s xml:id="echoid-s1698" xml:space="preserve">
              <emph style="bf">S</emph>
            I diametro circuli ſemidiameter in directum adji-
              <lb/>
            ciatur, & </s>
            <s xml:id="echoid-s1699" xml:space="preserve">ab adjectæ termino recta ducatur quæ
              <lb/>
            circulum ſecet, occurr atque tangenti circulum ad ter-
              <lb/>
            minum diametri oppoſitum: </s>
            <s xml:id="echoid-s1700" xml:space="preserve">Intercipiet eapartem tan-
              <lb/>
            gentis arcu adjacente abſciſſo minorem.</s>
            <s xml:id="echoid-s1701" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1702" xml:space="preserve">Eſto circulus, cujus diameter A B; </s>
            <s xml:id="echoid-s1703" xml:space="preserve">quæ producatur, & </s>
            <s xml:id="echoid-s1704" xml:space="preserve">
              <lb/>
              <note position="right" xlink:label="note-0089-01" xlink:href="note-0089-01a" xml:space="preserve">TAB. XL.
                <lb/>
              Fig. 1.</note>
            ſit A C ſemidiametro æqualis. </s>
            <s xml:id="echoid-s1705" xml:space="preserve">Et ducatur recta C L,
              <lb/>
            quæ circumferentiam ſecundò ſecet in E; </s>
            <s xml:id="echoid-s1706" xml:space="preserve">occurratque tan-
              <lb/>
            genti in L, ei nimirum quæ circulum contingit in termino
              <lb/>
            diametri B. </s>
            <s xml:id="echoid-s1707" xml:space="preserve">Dico interceptam B L arcu B E minorem eſſe.
              <lb/>
            </s>
            <s xml:id="echoid-s1708" xml:space="preserve">Jungantur enim A E, E B, poſitâque A H ipſi A E æqua-
              <lb/>
            li ducatur H E & </s>
            <s xml:id="echoid-s1709" xml:space="preserve">producatur, occurratque tangenti in K. </s>
            <s xml:id="echoid-s1710" xml:space="preserve">
              <lb/>
            Denique ſit E G diametro A B ad angulos rectos, E D ve-
              <lb/>
            ro tangenti B L. </s>
            <s xml:id="echoid-s1711" xml:space="preserve">Quoniam igitur iſoſceles eſt triangulus
              <lb/>
            H A E, erunt anguli inter ſe æquales H & </s>
            <s xml:id="echoid-s1712" xml:space="preserve">H E A. </s>
            <s xml:id="echoid-s1713" xml:space="preserve">Quia
              <lb/>
            autem angulus A E B rectus eſt, etiam recto æquales erunt
              <lb/>
            duo ſimul H E A, K E B. </s>
            <s xml:id="echoid-s1714" xml:space="preserve">Verùm duo quoque iſti H & </s>
            <s xml:id="echoid-s1715" xml:space="preserve">
              <lb/>
            H K B uni recto æquantur, quoniam in triangulo H K B
              <lb/>
            rectus eſt angulus B. </s>
            <s xml:id="echoid-s1716" xml:space="preserve">Ergo demptis utrimque æqualibus,
              <lb/>
            hinc nimirum angulo H, inde angulo H E A, relinquen-
              <lb/>
            tur inter ſe æquales anguli K E B, H K B. </s>
            <s xml:id="echoid-s1717" xml:space="preserve">Triangulus
              <lb/>
            igitur iſoſceles eſt K B E, ejuſque latera æqualia E B, B K. </s>
            <s xml:id="echoid-s1718" xml:space="preserve">
              <lb/>
            Eſt autem B D æqualis E G. </s>
            <s xml:id="echoid-s1719" xml:space="preserve">Ergo D K differentia eſt quâ
              <lb/>
            B E excedit E G. </s>
            <s xml:id="echoid-s1720" xml:space="preserve">Porro quoniam eſt A G ad A E, ut A E
              <lb/>
            ad A B, erunt duæ ſimul A G, A B majores duplâ A E .</s>
            <s xml:id="echoid-s1721" xml:space="preserve">
              <note symbol="*" position="right" xlink:label="note-0089-02" xlink:href="note-0089-02a" xml:space="preserve">25.5. Elem.</note>
            Ideoque A E, hoc eſt, A H minor quam dimidia </s>
          </p>
        </div>
      </text>
    </echo>
Impressum