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-div113" type="section" level="1" n="19">
          <p>
            <s xml:id="echoid-s5237" xml:space="preserve">
              <pb o="82" file="0100" n="100" rhead=""/>
            habeatur determinatus; </s>
            <s xml:id="echoid-s5238" xml:space="preserve">ſuccedit ut breviter etiam ipſiſſimum in ſin-
              <lb/>
            gulo tali refracto punctum oſtendamus, ad quod illa conſiſtit. </s>
            <s xml:id="echoid-s5239" xml:space="preserve">in cu-
              <lb/>
            jus rei gratiam hoc quaſi _Lemma_ præſternemus.</s>
            <s xml:id="echoid-s5240" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5241" xml:space="preserve">VI. </s>
            <s xml:id="echoid-s5242" xml:space="preserve">In circulo AN B, cujus centrum C, ſint Semidiametro CA
              <lb/>
            perpendiculares NE, RF; </s>
            <s xml:id="echoid-s5243" xml:space="preserve">item Semidiametro CB ſint perpendicu-
              <lb/>
            lares NG, XH; </s>
            <s xml:id="echoid-s5244" xml:space="preserve">ſint autem CE, EF ipſis CG, GH proportiona-
              <lb/>
              <note position="left" xlink:label="note-0100-01" xlink:href="note-0100-01a" xml:space="preserve">Fig. 122.</note>
            les; </s>
            <s xml:id="echoid-s5245" xml:space="preserve">& </s>
            <s xml:id="echoid-s5246" xml:space="preserve">arcus NR, NX indefinitè parvi; </s>
            <s xml:id="echoid-s5247" xml:space="preserve">ſeu quaſi minimi dictâ
              <lb/>
            conditione præditi; </s>
            <s xml:id="echoid-s5248" xml:space="preserve">dicimus arcum NR ad arcum NX rationem ha-
              <lb/>
            bere conflatam è rationibus ipſarum CE ad CG, & </s>
            <s xml:id="echoid-s5249" xml:space="preserve">NG ad NE; </s>
            <s xml:id="echoid-s5250" xml:space="preserve">vel eſſe
              <lb/>
            arc. </s>
            <s xml:id="echoid-s5251" xml:space="preserve">NR, NX:</s>
            <s xml:id="echoid-s5252" xml:space="preserve">: CE x NG. </s>
            <s xml:id="echoid-s5253" xml:space="preserve">CG x NE. </s>
            <s xml:id="echoid-s5254" xml:space="preserve">Nam per N ducatur VT
              <lb/>
            tangens circulum, ipſiſque FR, HX occurrens punctis T, V. </s>
            <s xml:id="echoid-s5255" xml:space="preserve">eſt
              <lb/>
            itaque (propter Summam ex Hypotheſi parvitatem dictorum arcuum)
              <lb/>
            arc NR. </s>
            <s xml:id="echoid-s5256" xml:space="preserve">CN:</s>
            <s xml:id="echoid-s5257" xml:space="preserve">: NT. </s>
            <s xml:id="echoid-s5258" xml:space="preserve">CN:</s>
            <s xml:id="echoid-s5259" xml:space="preserve">: EF. </s>
            <s xml:id="echoid-s5260" xml:space="preserve">EN. </s>
            <s xml:id="echoid-s5261" xml:space="preserve">item CN. </s>
            <s xml:id="echoid-s5262" xml:space="preserve">arc NX:</s>
            <s xml:id="echoid-s5263" xml:space="preserve">:
              <lb/>
            CN. </s>
            <s xml:id="echoid-s5264" xml:space="preserve">NV:</s>
            <s xml:id="echoid-s5265" xml:space="preserve">: NG. </s>
            <s xml:id="echoid-s5266" xml:space="preserve">GH. </s>
            <s xml:id="echoid-s5267" xml:space="preserve">quapropter erit arc NR. </s>
            <s xml:id="echoid-s5268" xml:space="preserve">CN+ CN.
              <lb/>
            </s>
            <s xml:id="echoid-s5269" xml:space="preserve">arc NX = (EF. </s>
            <s xml:id="echoid-s5270" xml:space="preserve">EN + NG. </s>
            <s xml:id="echoid-s5271" xml:space="preserve">GH = EF. </s>
            <s xml:id="echoid-s5272" xml:space="preserve">GH+ NG. </s>
            <s xml:id="echoid-s5273" xml:space="preserve">EN
              <lb/>
            = ) CE. </s>
            <s xml:id="echoid-s5274" xml:space="preserve">CG + NG. </s>
            <s xml:id="echoid-s5275" xml:space="preserve">EN. </s>
            <s xml:id="echoid-s5276" xml:space="preserve">hoc eſt arc NR. </s>
            <s xml:id="echoid-s5277" xml:space="preserve">arc NX = CE. </s>
            <s xml:id="echoid-s5278" xml:space="preserve">
              <lb/>
            CG + NG. </s>
            <s xml:id="echoid-s5279" xml:space="preserve">EN: </s>
            <s xml:id="echoid-s5280" xml:space="preserve">Q. </s>
            <s xml:id="echoid-s5281" xml:space="preserve">E. </s>
            <s xml:id="echoid-s5282" xml:space="preserve">D. </s>
            <s xml:id="echoid-s5283" xml:space="preserve">(vel arc NR. </s>
            <s xml:id="echoid-s5284" xml:space="preserve">NX = CE x NG. </s>
            <s xml:id="echoid-s5285" xml:space="preserve">
              <lb/>
            CG x EN.)</s>
            <s xml:id="echoid-s5286" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5287" xml:space="preserve">VII. </s>
            <s xml:id="echoid-s5288" xml:space="preserve">Sit jam radii cujuſvis talis MNP, refringentem interſecantis
              <lb/>
            punctis N, P, refractus N π (refringentem nempe denuò ſecans
              <lb/>
            in π) huic autem indeſinitè vicinus (& </s>
            <s xml:id="echoid-s5289" xml:space="preserve">quaſi proximus) adjaceat
              <lb/>
            radius QR S, cujus itidem refractus R σ (refringenti nempe rurſus
              <lb/>
            occurrens in σ), priorem N π decuſſans in Z; </s>
            <s xml:id="echoid-s5290" xml:space="preserve">biſecentur autem
              <lb/>
            ſubtenſæ NP, N π punctis G, E: </s>
            <s xml:id="echoid-s5291" xml:space="preserve">Dico rationem NZ ad GZ com-
              <lb/>
            poni è rationibus NG ad NE, & </s>
            <s xml:id="echoid-s5292" xml:space="preserve">CE ad CG.</s>
            <s xml:id="echoid-s5293" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">Fig. 123,
            <lb/>
          124.</note>
          <p>
            <s xml:id="echoid-s5294" xml:space="preserve">Nam ducantur rectæ CE (hæc ipſam RS quoque ſecans in F) & </s>
            <s xml:id="echoid-s5295" xml:space="preserve">
              <lb/>
            C G; </s>
            <s xml:id="echoid-s5296" xml:space="preserve">nec non CI ad R σ perpendicularis, & </s>
            <s xml:id="echoid-s5297" xml:space="preserve">in protracta CG ſu-
              <lb/>
            @@@@@r CH = CI; </s>
            <s xml:id="echoid-s5298" xml:space="preserve">& </s>
            <s xml:id="echoid-s5299" xml:space="preserve">per H ducatur XY ad N π parallela, ſeu per-
              <lb/>
            pendicularis ad CH; </s>
            <s xml:id="echoid-s5300" xml:space="preserve">unde eſt XY = R π; </s>
            <s xml:id="echoid-s5301" xml:space="preserve">& </s>
            <s xml:id="echoid-s5302" xml:space="preserve">arc NX = Y π & </s>
            <s xml:id="echoid-s5303" xml:space="preserve">
              <lb/>
            arc XY = arc R σ adeóque arc NR ±: </s>
            <s xml:id="echoid-s5304" xml:space="preserve">σ π = 2 arc NX. </s>
            <s xml:id="echoid-s5305" xml:space="preserve">Eſt-
              <lb/>
            que prætereà CG. </s>
            <s xml:id="echoid-s5306" xml:space="preserve">CE:</s>
            <s xml:id="echoid-s5307" xml:space="preserve">: R. </s>
            <s xml:id="echoid-s5308" xml:space="preserve">I:</s>
            <s xml:id="echoid-s5309" xml:space="preserve">: CI. </s>
            <s xml:id="echoid-s5310" xml:space="preserve">CF:</s>
            <s xml:id="echoid-s5311" xml:space="preserve">: CH. </s>
            <s xml:id="echoid-s5312" xml:space="preserve">CF; </s>
            <s xml:id="echoid-s5313" xml:space="preserve">adeóque
              <lb/>
            permutatim CG. </s>
            <s xml:id="echoid-s5314" xml:space="preserve">CH:</s>
            <s xml:id="echoid-s5315" xml:space="preserve">: CE. </s>
            <s xml:id="echoid-s5316" xml:space="preserve">CF. </s>
            <s xml:id="echoid-s5317" xml:space="preserve">ergò (juxta præcedentem) eſt
              <lb/>
            arc. </s>
            <s xml:id="echoid-s5318" xml:space="preserve">NR. </s>
            <s xml:id="echoid-s5319" xml:space="preserve">NX = NG. </s>
            <s xml:id="echoid-s5320" xml:space="preserve">NE + CE. </s>
            <s xml:id="echoid-s5321" xml:space="preserve">CG. </s>
            <s xml:id="echoid-s5322" xml:space="preserve">ad hæc ob illam (quæ
              <lb/>
            ponitur) arcuum NR, SP, π σ exiquitatem, erit arc NR. </s>
            <s xml:id="echoid-s5323" xml:space="preserve">π σ :</s>
            <s xml:id="echoid-s5324" xml:space="preserve">:
              <lb/>
            ſubtenſa NR. </s>
            <s xml:id="echoid-s5325" xml:space="preserve">π σ :</s>
            <s xml:id="echoid-s5326" xml:space="preserve">: NZ. </s>
            <s xml:id="echoid-s5327" xml:space="preserve">Zσ :</s>
            <s xml:id="echoid-s5328" xml:space="preserve">: NZ. </s>
            <s xml:id="echoid-s5329" xml:space="preserve">Zπ. </s>
            <s xml:id="echoid-s5330" xml:space="preserve">ergò (inverſè compo-
              <lb/>
            nendo, vel dividendo, tum & </s>
            <s xml:id="echoid-s5331" xml:space="preserve">conſequentes ſubduplando) arc NR.
              <lb/>
            </s>
            <s xml:id="echoid-s5332" xml:space="preserve">{arc NR±:</s>
            <s xml:id="echoid-s5333" xml:space="preserve">π σ/2}:</s>
            <s xml:id="echoid-s5334" xml:space="preserve">: NZ.</s>
            <s xml:id="echoid-s5335" xml:space="preserve">{NZ±Zπ/2}. </s>
            <s xml:id="echoid-s5336" xml:space="preserve">atqui velut modò </s>
          </p>
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