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-s5336" xml:space="preserve">
              <pb o="83" file="0101" n="101" rhead=""/>
            arc {NR & </s>
            <s xml:id="echoid-s5337" xml:space="preserve">+ -;</s>
            <s xml:id="echoid-s5338" xml:space="preserve">: πσ/2} = NX; </s>
            <s xml:id="echoid-s5339" xml:space="preserve">item eſt {NZ & </s>
            <s xml:id="echoid-s5340" xml:space="preserve">+ -;</s>
            <s xml:id="echoid-s5341" xml:space="preserve">: Z π/2} = GZ. </s>
            <s xml:id="echoid-s5342" xml:space="preserve">eri@ ergòarc
              <lb/>
              <note position="right" xlink:label="note-0101-01" xlink:href="note-0101-01a" xml:space="preserve">Fig. 124.</note>
            NR. </s>
            <s xml:id="echoid-s5343" xml:space="preserve">NX :</s>
            <s xml:id="echoid-s5344" xml:space="preserve">: NZ. </s>
            <s xml:id="echoid-s5345" xml:space="preserve">GZ. </s>
            <s xml:id="echoid-s5346" xml:space="preserve">quapropter erit (juxta præcedentem)
              <lb/>
            NZ. </s>
            <s xml:id="echoid-s5347" xml:space="preserve">GZ = NG. </s>
            <s xml:id="echoid-s5348" xml:space="preserve">NE + CE. </s>
            <s xml:id="echoid-s5349" xml:space="preserve">CG.</s>
            <s xml:id="echoid-s5350" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5351" xml:space="preserve">VIII. </s>
            <s xml:id="echoid-s5352" xml:space="preserve">Porrò liquet punctum Z eſſe locum imaginis, quem expe-
              <lb/>
            timus, oculo conſpicuæ in recta N π conſtituto; </s>
            <s xml:id="echoid-s5353" xml:space="preserve">utpote circa quod
              <lb/>
            viciniorum ipſi NP radiorum refracti ipſam N π interſecant; </s>
            <s xml:id="echoid-s5354" xml:space="preserve">qua de
              <lb/>
            re multoties egimus, ut pigeat eò plura βαττλγ{εĩ}ν.</s>
            <s xml:id="echoid-s5355" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5356" xml:space="preserve">IX. </s>
            <s xml:id="echoid-s5357" xml:space="preserve">Facilè verò, Secundum _Theorema pramiſſum_, deſignatur
              <lb/>
            punctum Z. </s>
            <s xml:id="echoid-s5358" xml:space="preserve">Ducatur nempe CG ad refractum NK perpendicula-
              <lb/>
            ris; </s>
            <s xml:id="echoid-s5359" xml:space="preserve">& </s>
            <s xml:id="echoid-s5360" xml:space="preserve">ad connexam CN ducatur perpendicularis GV; </s>
            <s xml:id="echoid-s5361" xml:space="preserve">& </s>
            <s xml:id="echoid-s5362" xml:space="preserve">per V
              <lb/>
            ducatur VZ ad CK parallela, ſecans ipſam NK in Z. </s>
            <s xml:id="echoid-s5363" xml:space="preserve">factum erit.
              <lb/>
            </s>
            <s xml:id="echoid-s5364" xml:space="preserve">Nam, connexâ GE, liquet angulos GEC, GNC(circumducti
              <lb/>
              <note position="right" xlink:label="note-0101-02" xlink:href="note-0101-02a" xml:space="preserve">Fig. 125.</note>
            nempe per N, E, G, C circuli ſubtenfæ GE inſiſtentes ambos) æqua-
              <lb/>
            ri; </s>
            <s xml:id="echoid-s5365" xml:space="preserve">hoc eſt angulos GEC, VGCæquari. </s>
            <s xml:id="echoid-s5366" xml:space="preserve">quapropter (utrique
              <lb/>
            rectum adjiciendo) toti NEG, ZGVæquantur. </s>
            <s xml:id="echoid-s5367" xml:space="preserve">item alterni
              <lb/>
            GNE, VZGæquantur. </s>
            <s xml:id="echoid-s5368" xml:space="preserve">ergò triangula GN E, VZGſimilia ſunt,
              <lb/>
            unde NG. </s>
            <s xml:id="echoid-s5369" xml:space="preserve">NE :</s>
            <s xml:id="echoid-s5370" xml:space="preserve">: ZV. </s>
            <s xml:id="echoid-s5371" xml:space="preserve">ZG. </s>
            <s xml:id="echoid-s5372" xml:space="preserve">itaque. </s>
            <s xml:id="echoid-s5373" xml:space="preserve">CE. </s>
            <s xml:id="echoid-s5374" xml:space="preserve">CG + NG. </s>
            <s xml:id="echoid-s5375" xml:space="preserve">NE =
              <lb/>
            CE. </s>
            <s xml:id="echoid-s5376" xml:space="preserve">CG + ZV. </s>
            <s xml:id="echoid-s5377" xml:space="preserve">ZG. </s>
            <s xml:id="echoid-s5378" xml:space="preserve">verùm (ob refractionem) eſt NK. </s>
            <s xml:id="echoid-s5379" xml:space="preserve">KC
              <lb/>
            :</s>
            <s xml:id="echoid-s5380" xml:space="preserve">: I. </s>
            <s xml:id="echoid-s5381" xml:space="preserve">R :</s>
            <s xml:id="echoid-s5382" xml:space="preserve">: CE. </s>
            <s xml:id="echoid-s5383" xml:space="preserve">CG; </s>
            <s xml:id="echoid-s5384" xml:space="preserve">hoc eſt NZ. </s>
            <s xml:id="echoid-s5385" xml:space="preserve">ZV :</s>
            <s xml:id="echoid-s5386" xml:space="preserve">: CE. </s>
            <s xml:id="echoid-s5387" xml:space="preserve">CG. </s>
            <s xml:id="echoid-s5388" xml:space="preserve">eſt igitur
              <lb/>
            CE. </s>
            <s xml:id="echoid-s5389" xml:space="preserve">CG + NG. </s>
            <s xml:id="echoid-s5390" xml:space="preserve">NE = NZ. </s>
            <s xml:id="echoid-s5391" xml:space="preserve">ZV + ZV. </s>
            <s xml:id="echoid-s5392" xml:space="preserve">ZG; </s>
            <s xml:id="echoid-s5393" xml:space="preserve">hoc eſt CE.
              <lb/>
            </s>
            <s xml:id="echoid-s5394" xml:space="preserve">CG + NG. </s>
            <s xml:id="echoid-s5395" xml:space="preserve">NE = NZ. </s>
            <s xml:id="echoid-s5396" xml:space="preserve">ZG. </s>
            <s xml:id="echoid-s5397" xml:space="preserve">ergò punctum Z conditionem
              <lb/>
            obtinet, imaginis loco congruentem, è mox oſtenſis. </s>
            <s xml:id="echoid-s5398" xml:space="preserve">adeò liquet
              <lb/>
            propoſitum.</s>
            <s xml:id="echoid-s5399" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5400" xml:space="preserve">X. </s>
            <s xml:id="echoid-s5401" xml:space="preserve">Quin ſubnotamus rectam NK ad punctum Z ità dividi, ut ſit
              <lb/>
            NZ. </s>
            <s xml:id="echoid-s5402" xml:space="preserve">ZK :</s>
            <s xml:id="echoid-s5403" xml:space="preserve">: NGq. </s>
            <s xml:id="echoid-s5404" xml:space="preserve">CGq. </s>
            <s xml:id="echoid-s5405" xml:space="preserve">Etenim eſt NZ. </s>
            <s xml:id="echoid-s5406" xml:space="preserve">ZK :</s>
            <s xml:id="echoid-s5407" xml:space="preserve">: NV. </s>
            <s xml:id="echoid-s5408" xml:space="preserve">VC
              <lb/>
            :</s>
            <s xml:id="echoid-s5409" xml:space="preserve">: NVq. </s>
            <s xml:id="echoid-s5410" xml:space="preserve">VGq :</s>
            <s xml:id="echoid-s5411" xml:space="preserve">: NGq. </s>
            <s xml:id="echoid-s5412" xml:space="preserve">CGq.</s>
            <s xml:id="echoid-s5413" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5414" xml:space="preserve">XI. </s>
            <s xml:id="echoid-s5415" xml:space="preserve">Subjiciam & </s>
            <s xml:id="echoid-s5416" xml:space="preserve">hoc è dictis conſectarium _Theorema:_</s>
            <s xml:id="echoid-s5417" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5418" xml:space="preserve">Fiat √ 3 Rq. </s>
            <s xml:id="echoid-s5419" xml:space="preserve">√ Iq - Rq :</s>
            <s xml:id="echoid-s5420" xml:space="preserve">: CB. </s>
            <s xml:id="echoid-s5421" xml:space="preserve">CQ; </s>
            <s xml:id="echoid-s5422" xml:space="preserve">ductáque QN ad
              <lb/>
            CB perpendicularis circumferentiæ occurrat ad N; </s>
            <s xml:id="echoid-s5423" xml:space="preserve">radii verò MN
              <lb/>
            ad CB paralleli refractus ſit NK, circuli peripheriæ denuò occur-
              <lb/>
              <note position="right" xlink:label="note-0101-03" xlink:href="note-0101-03a" xml:space="preserve">Fig. 126.</note>
            rens in Z; </s>
            <s xml:id="echoid-s5424" xml:space="preserve">dico punctum Z eſſe imaginem, qualem mox definivimus,
              <lb/>
            oculo conſpicuam in ipſa NK ſito.</s>
            <s xml:id="echoid-s5425" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5426" xml:space="preserve">Nam (ductis CE ad MN, & </s>
            <s xml:id="echoid-s5427" xml:space="preserve">CG ad NZ perpendicularibus,
              <lb/>
            ac junctâ CN) ob 3 Rq. </s>
            <s xml:id="echoid-s5428" xml:space="preserve">Iq - Rq :</s>
            <s xml:id="echoid-s5429" xml:space="preserve">: CNq. </s>
            <s xml:id="echoid-s5430" xml:space="preserve">NEq. </s>
            <s xml:id="echoid-s5431" xml:space="preserve">hoc eſt
              <lb/>
            3 CGq. </s>
            <s xml:id="echoid-s5432" xml:space="preserve">CEq - CGq :</s>
            <s xml:id="echoid-s5433" xml:space="preserve">: CN q. </s>
            <s xml:id="echoid-s5434" xml:space="preserve">NE q; </s>
            <s xml:id="echoid-s5435" xml:space="preserve">erit dividendo 4 CG </s>
          </p>
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