Barrow, Isaac, Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur

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        <div xml:id="echoid-div99" type="section" level="1" n="18">
          <head xml:id="echoid-head21" xml:space="preserve">
            <emph style="sc">Lect.</emph>
          IX.</head>
          <p>
            <s xml:id="echoid-s3797" xml:space="preserve">I. </s>
            <s xml:id="echoid-s3798" xml:space="preserve">Q Ualiter in obverſum Speculi circularis convexum finitè di-
              <lb/>
            ſtans punctum radiat, & </s>
            <s xml:id="echoid-s3799" xml:space="preserve">ubi loci adparet oculo in recta con-
              <lb/>
            ſtituto per ipſum radians & </s>
            <s xml:id="echoid-s3800" xml:space="preserve">ſpeculi centrum trajecta poſtremo con-
              <lb/>
            niſi demonſtrare; </s>
            <s xml:id="echoid-s3801" xml:space="preserve">nunc idem quoad aſpectum aliàs ubicunque ſitum
              <lb/>
            aggredimur expiſcari. </s>
            <s xml:id="echoid-s3802" xml:space="preserve">quò primum attinet ut rectam inveſtigemus,
              <lb/>
            in qua conſiſtet Imago; </s>
            <s xml:id="echoid-s3803" xml:space="preserve">tum ut punctum ejus in iſta recta præciſum
              <lb/>
            determinemus. </s>
            <s xml:id="echoid-s3804" xml:space="preserve">& </s>
            <s xml:id="echoid-s3805" xml:space="preserve">primo quidem negotio ſatisfactum erit hujuſmodi
              <lb/>
            _Prob@ema_ conficiendo; </s>
            <s xml:id="echoid-s3806" xml:space="preserve">quod (ſequentium quoque gratiâ) genera-
              <lb/>
            tim proponimus.</s>
            <s xml:id="echoid-s3807" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3808" xml:space="preserve">II. </s>
            <s xml:id="echoid-s3809" xml:space="preserve">_Dato circulo reflectente_ (cujus centrum C) _datiſque binis pun-_
              <lb/>
            _ctis; </s>
            <s xml:id="echoid-s3810" xml:space="preserve">ab horum uno recta ducatur, cujus rtflexus per alterum tran-_
              <lb/>
            _ſeat._</s>
            <s xml:id="echoid-s3811" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3812" xml:space="preserve">1. </s>
            <s xml:id="echoid-s3813" xml:space="preserve">Si data puncta (puta A, X) ſint ambo in circuli peripheria,
              <lb/>
              <note position="right" xlink:label="note-0081-01" xlink:href="note-0081-01a" xml:space="preserve">Fig. 86.</note>
            manifeſtum eſt biſecto arcu AX in N, connexiſque ſubtenſis NA,
              <lb/>
            N X, rectas NA, NX ſibi mutuò reflexas fore; </s>
            <s xml:id="echoid-s3814" xml:space="preserve">ſeu, junctâ CN,
              <lb/>
            angulum CNXangulo CNA æquari.</s>
            <s xml:id="echoid-s3815" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3816" xml:space="preserve">2. </s>
            <s xml:id="echoid-s3817" xml:space="preserve">Etiam ſi datorum unum (X) in circumferentia ponatur; </s>
            <s xml:id="echoid-s3818" xml:space="preserve">liquet,
              <lb/>
              <note position="right" xlink:label="note-0081-02" xlink:href="note-0081-02a" xml:space="preserve">Fig. 87.</note>
            connexis AX, CX, factóque angulo CXH = CXA, ſore XA,
              <lb/>
            XH alterum alterius reflexum.</s>
            <s xml:id="echoid-s3819" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3820" xml:space="preserve">3. </s>
            <s xml:id="echoid-s3821" xml:space="preserve">Item ſi data puncta (A, X) æqualiter à centro diſtent; </s>
            <s xml:id="echoid-s3822" xml:space="preserve">con-
              <lb/>
              <note position="right" xlink:label="note-0081-03" xlink:href="note-0081-03a" xml:space="preserve">Fig. 83.</note>
            nexis rectis AC, XC, biſectóque angulo XCA à recta CN circu-
              <lb/>
            lum reflectentem interſecante ad N; </s>
            <s xml:id="echoid-s3823" xml:space="preserve">perſpicuum eſt conjunctas rectas
              <lb/>
            AN, XN, invicem in ſe reflecti; </s>
            <s xml:id="echoid-s3824" xml:space="preserve">vel angulum CNXipſi CNA
              <lb/>
            æquari.</s>
            <s xml:id="echoid-s3825" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3826" xml:space="preserve">III. </s>
            <s xml:id="echoid-s3827" xml:space="preserve">4. </s>
            <s xml:id="echoid-s3828" xml:space="preserve">Si puncta data (puta jam A, K) ambo exiſtant in recta per
              <lb/>
            reflectentis centrum tranſeunte (nempe AB KC.)</s>
            <s xml:id="echoid-s3829" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3830" xml:space="preserve">I. </s>
            <s xml:id="echoid-s3831" xml:space="preserve">Fiat CK. </s>
            <s xml:id="echoid-s3832" xml:space="preserve">AC:</s>
            <s xml:id="echoid-s3833" xml:space="preserve">: CB. </s>
            <s xml:id="echoid-s3834" xml:space="preserve">T. </s>
            <s xml:id="echoid-s3835" xml:space="preserve">ac inter CB, & </s>
            <s xml:id="echoid-s3836" xml:space="preserve">T ſit proportione
              <lb/>
              <note position="right" xlink:label="note-0081-04" xlink:href="note-0081-04a" xml:space="preserve">Fig. 8@.</note>
            media V (unde CBq. </s>
            <s xml:id="echoid-s3837" xml:space="preserve">Vq:</s>
            <s xml:id="echoid-s3838" xml:space="preserve">: CB. </s>
            <s xml:id="echoid-s3839" xml:space="preserve">T:</s>
            <s xml:id="echoid-s3840" xml:space="preserve">: CK. </s>
            <s xml:id="echoid-s3841" xml:space="preserve">AC). </s>
            <s xml:id="echoid-s3842" xml:space="preserve">tum centro A,
              <lb/>
            intervallo √:</s>
            <s xml:id="echoid-s3843" xml:space="preserve">: ACq - Vq. </s>
            <s xml:id="echoid-s3844" xml:space="preserve">deſcribatur circulus </s>
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