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

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          <p>
            <s xml:id="echoid-s4903" xml:space="preserve">
              <pb o="77" file="0095" n="95" rhead=""/>
            citeriorem. </s>
            <s xml:id="echoid-s4904" xml:space="preserve">erit enim connexa VY refractus obliquiſſimi radii, ceu
              <lb/>
            T V, circulum refringentem contingentis.</s>
            <s xml:id="echoid-s4905" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4906" xml:space="preserve">VIII. </s>
            <s xml:id="echoid-s4907" xml:space="preserve">Item, in ſecundo caſu ſi recta CVIcirculum EGZtan-
              <lb/>
              <note position="right" xlink:label="note-0095-01" xlink:href="note-0095-01a" xml:space="preserve">Fig. 112.</note>
            gat in I, & </s>
            <s xml:id="echoid-s4908" xml:space="preserve">adſumatur CY = CI, erit punctum Y citimus alter
              <lb/>
            refractorum limes. </s>
            <s xml:id="echoid-s4909" xml:space="preserve">Etenim connexa VY refractus erit incidentis
              <lb/>
            (puta VT) ad BC paralleli; </s>
            <s xml:id="echoid-s4910" xml:space="preserve">qui certè cunctorum obliquiſſimus
              <lb/>
            erit hujuſmodi refractionem patientium. </s>
            <s xml:id="echoid-s4911" xml:space="preserve">quum enim (è
              <note symbol="*" position="right" xlink:label="note-0095-02" xlink:href="note-0095-02a" xml:space="preserve">_Lect. 3. num. 7._</note>
            connexâ FI, ſit FI. </s>
            <s xml:id="echoid-s4912" xml:space="preserve">CF:</s>
            <s xml:id="echoid-s4913" xml:space="preserve">: I. </s>
            <s xml:id="echoid-s4914" xml:space="preserve">R. </s>
            <s xml:id="echoid-s4915" xml:space="preserve">hoc eſt ſinus rectus anguli FCI
              <lb/>
            (vel anguli CV T) ad ſinum totum, ut I ad R; </s>
            <s xml:id="echoid-s4916" xml:space="preserve">nullus ipſo TV
              <lb/>
            obliquior medium BNVpenetrabit; </s>
            <s xml:id="echoid-s4917" xml:space="preserve">at ipſe quicunque talis reper-
              <lb/>
            cutietur; </s>
            <s xml:id="echoid-s4918" xml:space="preserve">velut φ ψ in φ ξ.</s>
            <s xml:id="echoid-s4919" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4920" xml:space="preserve">IX. </s>
            <s xml:id="echoid-s4921" xml:space="preserve">Cæterùm hìc (tametſi præter ordlnem non nihil, extráque
              <lb/>
            ſuum locum) egregiam quandam & </s>
            <s xml:id="echoid-s4922" xml:space="preserve">præſertim notabilem iſtius, quem
              <lb/>
            nuncupavimus, refractarii circuli proprietatem interſeremus: </s>
            <s xml:id="echoid-s4923" xml:space="preserve">Om-
              <lb/>
            nium à puncto B promanantium, & </s>
            <s xml:id="echoid-s4924" xml:space="preserve">à circuli EGZcavis partibus
              <lb/>
            refractionem patentium (juxta caſus prænominatos reſpectivam) re-
              <lb/>
            fracti per punctum C tranſibunt.</s>
            <s xml:id="echoid-s4925" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4926" xml:space="preserve">Nam ejuſmodi quilibet incidat radius BG, & </s>
            <s xml:id="echoid-s4927" xml:space="preserve">(ſtantibus quæ præ-
              <lb/>
              <note position="right" xlink:label="note-0095-03" xlink:href="note-0095-03a" xml:space="preserve">Fig. 113,
                <lb/>
              114.</note>
            ſtructa præmonſtratáque ſunt) triangula BG F, GCFſimilia ſunt;
              <lb/>
            </s>
            <s xml:id="echoid-s4928" xml:space="preserve">angulúſque BGFpar angulo GC F; </s>
            <s xml:id="echoid-s4929" xml:space="preserve">itémque FG. </s>
            <s xml:id="echoid-s4930" xml:space="preserve">CF:</s>
            <s xml:id="echoid-s4931" xml:space="preserve">: I. </s>
            <s xml:id="echoid-s4932" xml:space="preserve">R; </s>
            <s xml:id="echoid-s4933" xml:space="preserve">
              <lb/>
            eſt autem FG ad CF, _ut Sinus anguli_ GCF_hoc eſt anguli BGF)_
              <lb/>
            _ad Sinum anguli CG F. </s>
            <s xml:id="echoid-s4934" xml:space="preserve">ergò Sinus anguli_ BGF_(qui eſt angulus_
              <lb/>
            _incidentiæ) ad Sinum anguli_ CGFſe habet, ut I ad R. </s>
            <s xml:id="echoid-s4935" xml:space="preserve">ergò CG β eſt
              <lb/>
            refractus ipſius BG: </s>
            <s xml:id="echoid-s4936" xml:space="preserve">Q. </s>
            <s xml:id="echoid-s4937" xml:space="preserve">E. </s>
            <s xml:id="echoid-s4938" xml:space="preserve">D.</s>
            <s xml:id="echoid-s4939" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4940" xml:space="preserve">_Nota._ </s>
            <s xml:id="echoid-s4941" xml:space="preserve">Si qui ad convexas hujuſce circuli partes incidunt, ità re-
              <lb/>
            flectantur, ut perpetuo Sinus anguli incidentiæ ad Sinum anguli reflexi
              <lb/>
            ſe habeat ut I ad R; </s>
            <s xml:id="echoid-s4942" xml:space="preserve">etiam reflexi per C tranſibunt.</s>
            <s xml:id="echoid-s4943" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4944" xml:space="preserve">Hinc habetur unum (quoad hos caſus) è præcipuis in _Dioptrica_
              <lb/>
            deſideratum, perquam utile; </s>
            <s xml:id="echoid-s4945" xml:space="preserve">Superficies ſimpliciſſima radios ab uno
              <lb/>
            puncto procedentes ità refringens, ut tanquam ab altero proveniant;
              <lb/>
            </s>
            <s xml:id="echoid-s4946" xml:space="preserve">id quod demonſtrationis adductus commoditate _Corollarii_ loco (licèt
              <lb/>
            ad aliam pertinens hypotheſin) hic apponere non dubitavi, redeamus
              <lb/>
            è diverticulo.</s>
            <s xml:id="echoid-s4947" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4948" xml:space="preserve">X. </s>
            <s xml:id="echoid-s4949" xml:space="preserve">Notandum porrò, quòd diverſos refringentes circulos, iíſque
              <lb/>
            competentes, modo præſtituto determinatos, refractarios adſumendo,
              <lb/>
            rectæ CB, EZ, CE, CZ, CF eaſdem in uno, quas in altero quovis
              <lb/>
            proportiones obſervant; </s>
            <s xml:id="echoid-s4950" xml:space="preserve">id quod facilimè demonſtratur; </s>
            <s xml:id="echoid-s4951" xml:space="preserve">& </s>
            <s xml:id="echoid-s4952" xml:space="preserve">ſatís </s>
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