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-s4809" xml:space="preserve">
              <pb o="76" file="0094" n="94" rhead=""/>
            in axe capiatur CK = CG; </s>
            <s xml:id="echoid-s4810" xml:space="preserve">connectatúrque recta NK, fore NK
              <lb/>
            ipſius MNPrefractum. </s>
            <s xml:id="echoid-s4811" xml:space="preserve">Connectantur enim rectæ FG, BG; </s>
            <s xml:id="echoid-s4812" xml:space="preserve">& </s>
            <s xml:id="echoid-s4813" xml:space="preserve">
              <lb/>
            quoniam eſt BZ. </s>
            <s xml:id="echoid-s4814" xml:space="preserve">CZ:</s>
            <s xml:id="echoid-s4815" xml:space="preserve">: (I.</s>
            <s xml:id="echoid-s4816" xml:space="preserve">R:</s>
            <s xml:id="echoid-s4817" xml:space="preserve">:) FZ. </s>
            <s xml:id="echoid-s4818" xml:space="preserve">FC; </s>
            <s xml:id="echoid-s4819" xml:space="preserve">erit permutando
              <lb/>
            BZ. </s>
            <s xml:id="echoid-s4820" xml:space="preserve">FZ:</s>
            <s xml:id="echoid-s4821" xml:space="preserve">: CZ. </s>
            <s xml:id="echoid-s4822" xml:space="preserve">FC. </s>
            <s xml:id="echoid-s4823" xml:space="preserve">dividendóque BF. </s>
            <s xml:id="echoid-s4824" xml:space="preserve">FZ:</s>
            <s xml:id="echoid-s4825" xml:space="preserve">: FZ.
              <lb/>
            </s>
            <s xml:id="echoid-s4826" xml:space="preserve">
              <note position="left" xlink:label="note-0094-01" xlink:href="note-0094-01a" xml:space="preserve">Fig. 109.</note>
            FC. </s>
            <s xml:id="echoid-s4827" xml:space="preserve">itaque patet triangula BF G, GFC(latera ſcilicet habentia
              <lb/>
            circa communem angulum GFCproportionalia) ſimilia fore.
              <lb/>
            </s>
            <s xml:id="echoid-s4828" xml:space="preserve">quamobrem erit BG. </s>
            <s xml:id="echoid-s4829" xml:space="preserve">GF:</s>
            <s xml:id="echoid-s4830" xml:space="preserve">: GC. </s>
            <s xml:id="echoid-s4831" xml:space="preserve">CF. </s>
            <s xml:id="echoid-s4832" xml:space="preserve">ſeu permutatim BG. </s>
            <s xml:id="echoid-s4833" xml:space="preserve">GC
              <lb/>
            :</s>
            <s xml:id="echoid-s4834" xml:space="preserve">: GF. </s>
            <s xml:id="echoid-s4835" xml:space="preserve">CF. </s>
            <s xml:id="echoid-s4836" xml:space="preserve">hoc eſt BG. </s>
            <s xml:id="echoid-s4837" xml:space="preserve">GC:</s>
            <s xml:id="echoid-s4838" xml:space="preserve">: FZ. </s>
            <s xml:id="echoid-s4839" xml:space="preserve">CF:</s>
            <s xml:id="echoid-s4840" xml:space="preserve">: I. </s>
            <s xml:id="echoid-s4841" xml:space="preserve">R. </s>
            <s xml:id="echoid-s4842" xml:space="preserve">verum in tri-
              <lb/>
            angulis BC G, NCKeſt BC = CN, & </s>
            <s xml:id="echoid-s4843" xml:space="preserve">CG = CK; </s>
            <s xml:id="echoid-s4844" xml:space="preserve">& </s>
            <s xml:id="echoid-s4845" xml:space="preserve">ang. </s>
            <s xml:id="echoid-s4846" xml:space="preserve">
              <lb/>
            BCG = NCK; </s>
            <s xml:id="echoid-s4847" xml:space="preserve">adeóque BG. </s>
            <s xml:id="echoid-s4848" xml:space="preserve">GC:</s>
            <s xml:id="echoid-s4849" xml:space="preserve">: NK. </s>
            <s xml:id="echoid-s4850" xml:space="preserve">CK. </s>
            <s xml:id="echoid-s4851" xml:space="preserve">quare erit quo-
              <lb/>
            que NK. </s>
            <s xml:id="echoid-s4852" xml:space="preserve">CK:</s>
            <s xml:id="echoid-s4853" xml:space="preserve">: I. </s>
            <s xml:id="echoid-s4854" xml:space="preserve">R. </s>
            <s xml:id="echoid-s4855" xml:space="preserve">ergò, ſecundum generatim antehac
              <note symbol="*" position="left" xlink:label="note-0094-02" xlink:href="note-0094-02a" xml:space="preserve">_Lect. 3. nu-_
                <lb/>
              _mero. 10._</note>
            liquet NK ipſius MN refractum exiſtere.</s>
            <s xml:id="echoid-s4856" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4857" xml:space="preserve">_Coroll._ </s>
            <s xml:id="echoid-s4858" xml:space="preserve">Adnotetur eſſe triangula BFG, GFCſimilia; </s>
            <s xml:id="echoid-s4859" xml:space="preserve">ac eſſe
              <lb/>
            BG. </s>
            <s xml:id="echoid-s4860" xml:space="preserve">CC:</s>
            <s xml:id="echoid-s4861" xml:space="preserve">: I. </s>
            <s xml:id="echoid-s4862" xml:space="preserve">R; </s>
            <s xml:id="echoid-s4863" xml:space="preserve">& </s>
            <s xml:id="echoid-s4864" xml:space="preserve">ang. </s>
            <s xml:id="echoid-s4865" xml:space="preserve">BG F = GC F; </s>
            <s xml:id="echoid-s4866" xml:space="preserve">& </s>
            <s xml:id="echoid-s4867" xml:space="preserve">eſſe BF, FG,
              <lb/>
            FC {.</s>
            <s xml:id="echoid-s4868" xml:space="preserve">./.</s>
            <s xml:id="echoid-s4869" xml:space="preserve">.}&</s>
            <s xml:id="echoid-s4870" xml:space="preserve">c.</s>
            <s xml:id="echoid-s4871" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4872" xml:space="preserve">III. </s>
            <s xml:id="echoid-s4873" xml:space="preserve">Ex hoc (ſanè pulchro, perutilíque _Theoremate_) cùm particu-
              <lb/>
            laris exoritur methodus hujuſmodi quotcunque refractos expeditiſſimè
              <lb/>
            ſeu delineandi, ſeu computandi; </s>
            <s xml:id="echoid-s4874" xml:space="preserve">tum ipſorum præcipua _ſymptomata_
              <lb/>
            facilimè diſcernuntur ac demonſtrantur. </s>
            <s xml:id="echoid-s4875" xml:space="preserve">qualia ſunt, quæ in ſubjectis
              <lb/>
            exhibentur _Corollariis._</s>
            <s xml:id="echoid-s4876" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4877" xml:space="preserve">IV. </s>
            <s xml:id="echoid-s4878" xml:space="preserve">Patet hinc punctum Z eſſe limitem ultra quem (reſpectu cen-
              <lb/>
            tri) nullus axem interſecat refractus; </s>
            <s xml:id="echoid-s4879" xml:space="preserve">ſeu perpendicularis ipſius AB
              <lb/>
            (vel ei ſaltem quàm proximè adjacentis radii) refractum ad Z termi-
              <lb/>
              <note position="left" xlink:label="note-0094-03" xlink:href="note-0094-03a" xml:space="preserve">Fig. 110.</note>
            nari. </s>
            <s xml:id="echoid-s4880" xml:space="preserve">quia nimirum eſt CZ &</s>
            <s xml:id="echoid-s4881" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s4882" xml:space="preserve">CG, vel CR.</s>
            <s xml:id="echoid-s4883" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4884" xml:space="preserve">V. </s>
            <s xml:id="echoid-s4885" xml:space="preserve">Conſequitur etiam, ſi duorum incidentium MN, QR (quorum
              <lb/>
            QR ſit obliquior) refracti conveniant cum axe punctis K, L, fore
              <lb/>
            CK&</s>
            <s xml:id="echoid-s4886" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s4887" xml:space="preserve">CL. </s>
            <s xml:id="echoid-s4888" xml:space="preserve">Etenim ſi rectæ NC, RC ad circulum refractarium
              <lb/>
              <note position="left" xlink:label="note-0094-04" xlink:href="note-0094-04a" xml:space="preserve">Fig. 111.</note>
            (itâ circulum EGZmeritò ſubinde nominabimus) producantur, ut
              <lb/>
            ipſum ſecent punctis G, H; </s>
            <s xml:id="echoid-s4889" xml:space="preserve">liquet eſſe CG &</s>
            <s xml:id="echoid-s4890" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s4891" xml:space="preserve">CH; </s>
            <s xml:id="echoid-s4892" xml:space="preserve">adeóque CK
              <lb/>
            &</s>
            <s xml:id="echoid-s4893" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s4894" xml:space="preserve">CL. </s>
            <s xml:id="echoid-s4895" xml:space="preserve">Hinc</s>
          </p>
          <p>
            <s xml:id="echoid-s4896" xml:space="preserve">VI. </s>
            <s xml:id="echoid-s4897" xml:space="preserve">Ad eaſdem partes incidentium refracti ſeſe priùs interſecant
              <lb/>
            quàm axem; </s>
            <s xml:id="echoid-s4898" xml:space="preserve">(veluti puta refracti NK, RL ſeſe decuſſant in X.)</s>
            <s xml:id="echoid-s4899" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4900" xml:space="preserve">VII. </s>
            <s xml:id="echoid-s4901" xml:space="preserve">Quinetiam, ſi in primo caſu per centrum C dueatur recta
              <lb/>
              <note position="left" xlink:label="note-0094-05" xlink:href="note-0094-05a" xml:space="preserve">Fig. 111.</note>
            VI ad BZ perpendicularis, dictóque circulo refractario occurrens
              <lb/>
            ad I; </s>
            <s xml:id="echoid-s4902" xml:space="preserve">& </s>
            <s xml:id="echoid-s4903" xml:space="preserve">fiat CY = CI, patet punctum Y eſſe limitem </s>
          </p>
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