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-s8036" xml:space="preserve">
              <pb o="123" file="0141" n="141" rhead=""/>
            buit, ſolertia quadantenus eluceſcere videatur, ſeu ratio quædam aſſig-
              <lb/>
            nari poſſit, cur oculi fundus _Sphær@idicam_ (aut ab hac non multum
              <lb/>
            abludentem) nacta ſit ſiguram. </s>
            <s xml:id="echoid-s8037" xml:space="preserve">quia nimirum illa planorum objecto-
              <lb/>
            rum modicè diſtantium (quibus in diſtinctiùs apprehendendis po-
              <lb/>
            tiſſimus verſatur uſus) excipiendis ſimulachris eſt accommodatiſſima.
              <lb/>
            </s>
            <s xml:id="echoid-s8038" xml:space="preserve">Sed hoc παρεισθδκῶς.</s>
            <s xml:id="echoid-s8039" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8040" xml:space="preserve">V. </s>
            <s xml:id="echoid-s8041" xml:space="preserve">In reliquis reſractionum caſibus paria fermè contingunt, quos
              <lb/>
            ideò tacitus præterlabi poſſem; </s>
            <s xml:id="echoid-s8042" xml:space="preserve">at minuendo veſtro labori, ſeu quò
              <lb/>
            clariùs & </s>
            <s xml:id="echoid-s8043" xml:space="preserve">promptiùs de iis conſtet, non gravabor & </s>
            <s xml:id="echoid-s8044" xml:space="preserve">illos vobis ob
              <lb/>
            oculos ponere: </s>
            <s xml:id="echoid-s8045" xml:space="preserve">nempe</s>
          </p>
          <p>
            <s xml:id="echoid-s8046" xml:space="preserve">Rarioris medii circulo MBN objiciatur recta FAG, cui normalis
              <lb/>
              <note position="right" xlink:label="note-0141-01" xlink:href="note-0141-01a" xml:space="preserve">Fig. 199.</note>
            CA; </s>
            <s xml:id="echoid-s8047" xml:space="preserve">sitque punctum Z puncti cujuſvis F, in FG ſumpti, imago
              <lb/>
            abſoluta; </s>
            <s xml:id="echoid-s8048" xml:space="preserve">& </s>
            <s xml:id="echoid-s8049" xml:space="preserve">ZX ad CA perpendicularis; </s>
            <s xml:id="echoid-s8050" xml:space="preserve">ac CA. </s>
            <s xml:id="echoid-s8051" xml:space="preserve">CR:</s>
            <s xml:id="echoid-s8052" xml:space="preserve">: I. </s>
            <s xml:id="echoid-s8053" xml:space="preserve">R;
              <lb/>
            </s>
            <s xml:id="echoid-s8054" xml:space="preserve">& </s>
            <s xml:id="echoid-s8055" xml:space="preserve">RA. </s>
            <s xml:id="echoid-s8056" xml:space="preserve">CB:</s>
            <s xml:id="echoid-s8057" xml:space="preserve">: RC. </s>
            <s xml:id="echoid-s8058" xml:space="preserve">CE; </s>
            <s xml:id="echoid-s8059" xml:space="preserve">& </s>
            <s xml:id="echoid-s8060" xml:space="preserve">ipſi RE connexæ occurrat XZ pro-
              <lb/>
            tracta ad H; </s>
            <s xml:id="echoid-s8061" xml:space="preserve">eritque rurſus XH = CZ.</s>
            <s xml:id="echoid-s8062" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8063" xml:space="preserve">Nam eſt CA. </s>
            <s xml:id="echoid-s8064" xml:space="preserve">CR:</s>
            <s xml:id="echoid-s8065" xml:space="preserve">: (FC x MZ. </s>
            <s xml:id="echoid-s8066" xml:space="preserve">FM x CZ:</s>
            <s xml:id="echoid-s8067" xml:space="preserve">:) FC x CZ
              <lb/>
            - FC x CM. </s>
            <s xml:id="echoid-s8068" xml:space="preserve">FC x CZ- CM x CZ. </s>
            <s xml:id="echoid-s8069" xml:space="preserve">quare CR x FC x CZ
              <lb/>
            - CR x FC x CM = CA x FC x CZ - CA x CM x CZ = CA x FC x CZ - FC x CM x CX. </s>
            <s xml:id="echoid-s8070" xml:space="preserve">ac indè CR x CZ-
              <lb/>
            CR x CM = CA x CZ - CM x CX. </s>
            <s xml:id="echoid-s8071" xml:space="preserve">tranſponendóque CR x
              <lb/>
            CZ - CA x CZ = CR x CM - CX x CM; </s>
            <s xml:id="echoid-s8072" xml:space="preserve">hoc eſt RX.
              <lb/>
            </s>
            <s xml:id="echoid-s8073" xml:space="preserve">CZ:</s>
            <s xml:id="echoid-s8074" xml:space="preserve">: AR. </s>
            <s xml:id="echoid-s8075" xml:space="preserve">CM:</s>
            <s xml:id="echoid-s8076" xml:space="preserve">: RC. </s>
            <s xml:id="echoid-s8077" xml:space="preserve">CE:</s>
            <s xml:id="echoid-s8078" xml:space="preserve">: RX. </s>
            <s xml:id="echoid-s8079" xml:space="preserve">XH. </s>
            <s xml:id="echoid-s8080" xml:space="preserve">quapropter eſt CZ = XH.</s>
            <s xml:id="echoid-s8081" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8082" xml:space="preserve">VI. </s>
            <s xml:id="echoid-s8083" xml:space="preserve">Hinc dilucidè rurſus apparet rectæ FA Gimaginem abſolu-
              <lb/>
            tam (vel ad oculum in centro C ſitum relatam) ſi RC &</s>
            <s xml:id="echoid-s8084" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s8085" xml:space="preserve">CE, _el-_
              <lb/>
            _lipticam_ fore; </s>
            <s xml:id="echoid-s8086" xml:space="preserve">ſin RC = CE, fore _parabolicam_ (quarum ſectio-
              <lb/>
            num pars anterior ETE ad convexam circuli refringentis partem
              <lb/>
              <note position="right" xlink:label="note-0141-02" xlink:href="note-0141-02a" xml:space="preserve">Fig. 200.</note>
            MBN pertinet, poſterior YEEY ad cavam LDL). </s>
            <s xml:id="echoid-s8087" xml:space="preserve">Quòd ſi
              <lb/>
            fuerit RC &</s>
            <s xml:id="echoid-s8088" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s8089" xml:space="preserve">RE, _ejus image hyperbolica erit_; </s>
            <s xml:id="echoid-s8090" xml:space="preserve">& </s>
            <s xml:id="echoid-s8091" xml:space="preserve">quidem _hyperbolæ_
              <lb/>
            YTY pars ſuperior ETE ad circuli partem NBN referenda eſt;
              <lb/>
            </s>
            <s xml:id="echoid-s8092" xml:space="preserve">pars autem inferior YEEY unà cum tota hyperbola ζ V ζ ad partes
              <lb/>
            concavas LDL pertinebit. </s>
            <s xml:id="echoid-s8093" xml:space="preserve">nempe ſi fuerint rectæ CK æquales ipſi
              <lb/>
            CE, tota hyperbola ζ V ζ interceptam punctis K rectæ FG portio-
              <lb/>
            nem referet, ejúſque quod hinc indè protenſum ſupereſt ab ipſa YEEY
              <lb/>
            repræſentabitur.</s>
            <s xml:id="echoid-s8094" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s8095" xml:space="preserve">VII. </s>
            <s xml:id="echoid-s8096" xml:space="preserve">Porrò, quoad omnes hoſce caſus animadvertere licet poſſe
              <lb/>
            ſectionem eandem conicam innumeris rectis lineis ad diverſos </s>
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