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-div189" type="section" level="1" n="23">
          <p>
            <s xml:id="echoid-s7470" xml:space="preserve">
              <pb o="114" file="0132" n="132" rhead=""/>
            tamen nonnunquam inverſo) quàm exactiſſimè referant. </s>
            <s xml:id="echoid-s7471" xml:space="preserve">qua de re
              <lb/>
            (tam facili, toties acta) penitùs reticens ad minùs trita me pro-
              <lb/>
            moveo.</s>
            <s xml:id="echoid-s7472" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7473" xml:space="preserve">XI. </s>
            <s xml:id="echoid-s7474" xml:space="preserve">Sit jam _Circulare Speculum convexum_ DMB, cujus centrum C;
              <lb/>
            </s>
            <s xml:id="echoid-s7475" xml:space="preserve">
              <note position="left" xlink:label="note-0132-01" xlink:href="note-0132-01a" xml:space="preserve">Fig. 186.</note>
            & </s>
            <s xml:id="echoid-s7476" xml:space="preserve">per C protendatur recta CBA; </s>
            <s xml:id="echoid-s7477" xml:space="preserve">in qua ſumatur portio quædam AR,
              <lb/>
            fiátque CA. </s>
            <s xml:id="echoid-s7478" xml:space="preserve">AB :</s>
            <s xml:id="echoid-s7479" xml:space="preserve">: CX. </s>
            <s xml:id="echoid-s7480" xml:space="preserve">XB; </s>
            <s xml:id="echoid-s7481" xml:space="preserve">neq; </s>
            <s xml:id="echoid-s7482" xml:space="preserve">non CR. </s>
            <s xml:id="echoid-s7483" xml:space="preserve">RB :</s>
            <s xml:id="echoid-s7484" xml:space="preserve">: CY. </s>
            <s xml:id="echoid-s7485" xml:space="preserve">YB; </s>
            <s xml:id="echoid-s7486" xml:space="preserve">erit YX imago
              <lb/>
            abſoluta rectæ RA; </s>
            <s xml:id="echoid-s7487" xml:space="preserve">quòd ſi CB biſecetur in Z; </s>
            <s xml:id="echoid-s7488" xml:space="preserve">erit BZ totius BA ad
              <lb/>
            infinitum exporrectæ imago abſoluta; </s>
            <s xml:id="echoid-s7489" xml:space="preserve">hoc eſt, illæ tales erunt oculi
              <lb/>
            reſpectu in ipſa AB conſtituti. </s>
            <s xml:id="echoid-s7490" xml:space="preserve">ſecùs autem uſpiam collocato oculo,
              <lb/>
            tanquam ad O, totius AB quod conſpicuum eſt (hoc eſt quod ſupra
              <lb/>
            horizontem OT, ſpeculo contiguum extat) ſupra citráque XB ap-
              <lb/>
            parebit. </s>
            <s xml:id="echoid-s7491" xml:space="preserve">Enimvero tranſeat radii AM reflexus KMO per O; </s>
            <s xml:id="echoid-s7492" xml:space="preserve">ita-
              <lb/>
            que punctum K (quod olim oſtenſum) ſupra punctum X, verſus A,
              <lb/>
            extat. </s>
            <s xml:id="echoid-s7493" xml:space="preserve">quinetiam (ex indidem monftratis) puncti A imagines omnes,
              <lb/>
            oculum O reſpicientes, ex reflexione factæ ad partes BMD, citra
              <lb/>
            CA verſus O, cadunt. </s>
            <s xml:id="echoid-s7494" xml:space="preserve">ejus igitur imago quæ in OK, puta α, in ipſa
              <lb/>
            KM exiſtet (id quod etiam, nè quis dubitet, exertius mox oſten-
              <lb/>
            demus). </s>
            <s xml:id="echoid-s7495" xml:space="preserve">ſimili ratione puncti R imago, cogitaρ, ſupra Y, citráque
              <lb/>
            BY jacet. </s>
            <s xml:id="echoid-s7496" xml:space="preserve">quòd ſi porrò per O tranſeat recta ODLH, quæ reflexa ſit
              <lb/>
            rectæ DS ad CA parallelæ (hæc autem quomodo ducatur, antehac
              <lb/>
            declaratum habetur) erit in ODL imago puncti (quale concipiatur
              <lb/>
            S) in ipſa AB infinitè ſemoti; </s>
            <s xml:id="echoid-s7497" xml:space="preserve">hæc puta ſit ad σ. </s>
            <s xml:id="echoid-s7498" xml:space="preserve">erit itaque curva
              <lb/>
            B ρασ imago totius infinitæ rectæ BAS, ad oculum O relata.</s>
            <s xml:id="echoid-s7499" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7500" xml:space="preserve">XII. </s>
            <s xml:id="echoid-s7501" xml:space="preserve">Iſta verò linea tali pacto delineatur: </s>
            <s xml:id="echoid-s7502" xml:space="preserve">Super diametrum CO
              <lb/>
            deſcribatur circulus OTC; </s>
            <s xml:id="echoid-s7503" xml:space="preserve">& </s>
            <s xml:id="echoid-s7504" xml:space="preserve">ab O ducatur recta quæpiam OMF,
              <lb/>
            cujus reflexa ſit MA; </s>
            <s xml:id="echoid-s7505" xml:space="preserve">in qua ſumatur ME = MF; </s>
            <s xml:id="echoid-s7506" xml:space="preserve">tum ſecetur
              <lb/>
            FM in α, ut ſit F α. </s>
            <s xml:id="echoid-s7507" xml:space="preserve">α M :</s>
            <s xml:id="echoid-s7508" xml:space="preserve">: AE. </s>
            <s xml:id="echoid-s7509" xml:space="preserve">AM; </s>
            <s xml:id="echoid-s7510" xml:space="preserve">erit (è pridem demonſtra-
              <lb/>
            tis) punctum α puncti A imago. </s>
            <s xml:id="echoid-s7511" xml:space="preserve">ſimili modo quotcunque lineæ
              <lb/>
            B αρσ puncta reperiuntur.</s>
            <s xml:id="echoid-s7512" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7513" xml:space="preserve">XIII. </s>
            <s xml:id="echoid-s7514" xml:space="preserve">Quòd autem ſit punctum α citra K (verſus oculum) ità con-
              <lb/>
            ſtabit. </s>
            <s xml:id="echoid-s7515" xml:space="preserve">Ducatur FQ ad AM parallela. </s>
            <s xml:id="echoid-s7516" xml:space="preserve">eſt ergo angulus FQA
              <lb/>
            par angulo CAM. </s>
            <s xml:id="echoid-s7517" xml:space="preserve">aſt angulus FCA angulo ACE minor eſt. </s>
            <s xml:id="echoid-s7518" xml:space="preserve">ergò
              <lb/>
            eſt CF. </s>
            <s xml:id="echoid-s7519" xml:space="preserve">FQ &</s>
            <s xml:id="echoid-s7520" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s7521" xml:space="preserve">CE. </s>
            <s xml:id="echoid-s7522" xml:space="preserve">AE. </s>
            <s xml:id="echoid-s7523" xml:space="preserve">atqui CF = CE; </s>
            <s xml:id="echoid-s7524" xml:space="preserve">quare FQ &</s>
            <s xml:id="echoid-s7525" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s7526" xml:space="preserve">AE.
              <lb/>
            </s>
            <s xml:id="echoid-s7527" xml:space="preserve">ergò eſt FQ. </s>
            <s xml:id="echoid-s7528" xml:space="preserve">AM &</s>
            <s xml:id="echoid-s7529" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s7530" xml:space="preserve">AE. </s>
            <s xml:id="echoid-s7531" xml:space="preserve">AM. </s>
            <s xml:id="echoid-s7532" xml:space="preserve">hoc eſt FK. </s>
            <s xml:id="echoid-s7533" xml:space="preserve">KM &</s>
            <s xml:id="echoid-s7534" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s7535" xml:space="preserve">F α. </s>
            <s xml:id="echoid-s7536" xml:space="preserve">αM. </s>
            <s xml:id="echoid-s7537" xml:space="preserve">
              <lb/>
            componendóque FM. </s>
            <s xml:id="echoid-s7538" xml:space="preserve">KM &</s>
            <s xml:id="echoid-s7539" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s7540" xml:space="preserve">FM. </s>
            <s xml:id="echoid-s7541" xml:space="preserve">αM. </s>
            <s xml:id="echoid-s7542" xml:space="preserve">unde KM &</s>
            <s xml:id="echoid-s7543" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s7544" xml:space="preserve">αM. </s>
            <s xml:id="echoid-s7545" xml:space="preserve">adeó-
              <lb/>
            que punctum αcitra K verſus O jacet: </s>
            <s xml:id="echoid-s7546" xml:space="preserve">Q. </s>
            <s xml:id="echoid-s7547" xml:space="preserve">E. </s>
            <s xml:id="echoid-s7548" xml:space="preserve">D.</s>
            <s xml:id="echoid-s7549" xml:space="preserve"/>
          </p>
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