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-s6178" xml:space="preserve">
              <pb o="93" file="0111" n="111" rhead=""/>
            manibus. </s>
            <s xml:id="echoid-s6179" xml:space="preserve">propter alios qui ſimilia volet, ipſeviderit, & </s>
            <s xml:id="echoid-s6180" xml:space="preserve">ſibi para-
              <lb/>
            verit. </s>
            <s xml:id="echoid-s6181" xml:space="preserve">ego jam aliò progredior; </s>
            <s xml:id="echoid-s6182" xml:space="preserve">eò ſcilicet, ut locum definiam
              <lb/>
            imaginis in dato quovis refracto apparentis; </s>
            <s xml:id="echoid-s6183" xml:space="preserve">prætervehemur enim
              <lb/>
            illud in his certè caſibus _intricatiſſimum Problema_ (cujúſque Solutio
              <lb/>
            nullatenus aut laborem quem exigit, aut temporis jacturam compen-
              <lb/>
            ſabit) quo jubetur per datum punctum tranſeuntem refractum deſig-
              <lb/>
            nare. </s>
            <s xml:id="echoid-s6184" xml:space="preserve">poſitione datum igitur refractum accipimus; </s>
            <s xml:id="echoid-s6185" xml:space="preserve">& </s>
            <s xml:id="echoid-s6186" xml:space="preserve">in hoc ima-
              <lb/>
            ginis locum ex hoc uno Theoremate determinamus.</s>
            <s xml:id="echoid-s6187" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6188" xml:space="preserve">XXIV. </s>
            <s xml:id="echoid-s6189" xml:space="preserve">Duorum incidentium ANP, ARS ſibi quàm proximo-
              <lb/>
              <note position="right" xlink:label="note-0111-01" xlink:href="note-0111-01a" xml:space="preserve">Fig. 146.</note>
            rum concipiantur refracti N π, R σ ſeſe puncto Z decuſſantes; </s>
            <s xml:id="echoid-s6190" xml:space="preserve">biſe-
              <lb/>
            centúrque ſubtenſæ NP, N π punctis E, G; </s>
            <s xml:id="echoid-s6191" xml:space="preserve">(à rectis nempe CE,
              <lb/>
            CG ad illas perpendicularibus) dico rationem NZ ad GZ è ratio-
              <lb/>
            nibus CE ad CG (hoc eſt 1. </s>
            <s xml:id="echoid-s6192" xml:space="preserve">R), NG ad NE, ac AN ad AE
              <lb/>
            componi.</s>
            <s xml:id="echoid-s6193" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6194" xml:space="preserve">Ducantur enim CK ad RS, & </s>
            <s xml:id="echoid-s6195" xml:space="preserve">CI ad R σ perpendiculares; </s>
            <s xml:id="echoid-s6196" xml:space="preserve">in
              <lb/>
            que producetis CE, CG capiantur CF = CK; </s>
            <s xml:id="echoid-s6197" xml:space="preserve">& </s>
            <s xml:id="echoid-s6198" xml:space="preserve">CH = CI;
              <lb/>
            </s>
            <s xml:id="echoid-s6199" xml:space="preserve">& </s>
            <s xml:id="echoid-s6200" xml:space="preserve">per F ducatur TV ad NP parallela; </s>
            <s xml:id="echoid-s6201" xml:space="preserve">& </s>
            <s xml:id="echoid-s6202" xml:space="preserve">per H etiam XY ad N π
              <lb/>
            parallela. </s>
            <s xml:id="echoid-s6203" xml:space="preserve">Jam eſt AP. </s>
            <s xml:id="echoid-s6204" xml:space="preserve">AN :</s>
            <s xml:id="echoid-s6205" xml:space="preserve">: arc PS. </s>
            <s xml:id="echoid-s6206" xml:space="preserve">arc NR (ob ſumptam
              <lb/>
            arcuum indefinitam parvitatem). </s>
            <s xml:id="echoid-s6207" xml:space="preserve">ergò {AP ±: </s>
            <s xml:id="echoid-s6208" xml:space="preserve">AN/2}. </s>
            <s xml:id="echoid-s6209" xml:space="preserve">AN :</s>
            <s xml:id="echoid-s6210" xml:space="preserve">:
              <lb/>
            {arc PS ±: </s>
            <s xml:id="echoid-s6211" xml:space="preserve">arc. </s>
            <s xml:id="echoid-s6212" xml:space="preserve">NR/2}. </s>
            <s xml:id="echoid-s6213" xml:space="preserve">arc NR. </s>
            <s xml:id="echoid-s6214" xml:space="preserve">hoc eſt AE. </s>
            <s xml:id="echoid-s6215" xml:space="preserve">AN :</s>
            <s xml:id="echoid-s6216" xml:space="preserve">: arc NT. </s>
            <s xml:id="echoid-s6217" xml:space="preserve">arc
              <lb/>
            NR. </s>
            <s xml:id="echoid-s6218" xml:space="preserve">item eſt NZ. </s>
            <s xml:id="echoid-s6219" xml:space="preserve">Z π :</s>
            <s xml:id="echoid-s6220" xml:space="preserve">: arc NR. </s>
            <s xml:id="echoid-s6221" xml:space="preserve">arc πσ. </s>
            <s xml:id="echoid-s6222" xml:space="preserve">ac indè NZ. </s>
            <s xml:id="echoid-s6223" xml:space="preserve">
              <lb/>
            {NZ ±: </s>
            <s xml:id="echoid-s6224" xml:space="preserve">Z π/2} :</s>
            <s xml:id="echoid-s6225" xml:space="preserve">: arc NR. </s>
            <s xml:id="echoid-s6226" xml:space="preserve">{arc NR ±: </s>
            <s xml:id="echoid-s6227" xml:space="preserve">πσ/2}. </s>
            <s xml:id="echoid-s6228" xml:space="preserve">hoc eſt NZ. </s>
            <s xml:id="echoid-s6229" xml:space="preserve">ZG :</s>
            <s xml:id="echoid-s6230" xml:space="preserve">:
              <note symbol="*" position="right" xlink:label="note-0111-02" xlink:href="note-0111-02a" xml:space="preserve">_Lect. 9._
                <lb/>
              _Num. iI_</note>
            NR. </s>
            <s xml:id="echoid-s6231" xml:space="preserve">arc NX. </s>
            <s xml:id="echoid-s6232" xml:space="preserve">ergò, rationes æquales adjungendo, eſt. </s>
            <s xml:id="echoid-s6233" xml:space="preserve">AE. </s>
            <s xml:id="echoid-s6234" xml:space="preserve">AN
              <lb/>
            + NZ. </s>
            <s xml:id="echoid-s6235" xml:space="preserve">ZG = arc NT. </s>
            <s xml:id="echoid-s6236" xml:space="preserve">arc NR + arc NR. </s>
            <s xml:id="echoid-s6237" xml:space="preserve">arc NX = arc
              <lb/>
            NT. </s>
            <s xml:id="echoid-s6238" xml:space="preserve">arc NX. </s>
            <s xml:id="echoid-s6239" xml:space="preserve">quoniam autem eſt CE. </s>
            <s xml:id="echoid-s6240" xml:space="preserve">CG :</s>
            <s xml:id="echoid-s6241" xml:space="preserve">: (I. </s>
            <s xml:id="echoid-s6242" xml:space="preserve">R :</s>
            <s xml:id="echoid-s6243" xml:space="preserve">: CK.
              <lb/>
            </s>
            <s xml:id="echoid-s6244" xml:space="preserve">CI :</s>
            <s xml:id="echoid-s6245" xml:space="preserve">:) CF. </s>
            <s xml:id="echoid-s6246" xml:space="preserve">CH. </s>
            <s xml:id="echoid-s6247" xml:space="preserve">vel permutando CE. </s>
            <s xml:id="echoid-s6248" xml:space="preserve">CF :</s>
            <s xml:id="echoid-s6249" xml:space="preserve">: CG. </s>
            <s xml:id="echoid-s6250" xml:space="preserve">CH; </s>
            <s xml:id="echoid-s6251" xml:space="preserve">erit,
              <lb/>
            juxta præmonſtrata, arc NT. </s>
            <s xml:id="echoid-s6252" xml:space="preserve">arc NX = NG. </s>
            <s xml:id="echoid-s6253" xml:space="preserve">NE + CE. </s>
            <s xml:id="echoid-s6254" xml:space="preserve">CG.</s>
            <s xml:id="echoid-s6255" xml:space="preserve">
              <note symbol="*" position="right" xlink:label="note-0111-03" xlink:href="note-0111-03a" xml:space="preserve">_12 Lect._
                <lb/>
              _Num. 6._</note>
            quapropter erit AE. </s>
            <s xml:id="echoid-s6256" xml:space="preserve">AN + NZ. </s>
            <s xml:id="echoid-s6257" xml:space="preserve">ZG = NG. </s>
            <s xml:id="echoid-s6258" xml:space="preserve">NF + CE.
              <lb/>
            </s>
            <s xml:id="echoid-s6259" xml:space="preserve">CG. </s>
            <s xml:id="echoid-s6260" xml:space="preserve">unde (rationes hinc indè pares ſubducendo) erit NZ. </s>
            <s xml:id="echoid-s6261" xml:space="preserve">ZG :</s>
            <s xml:id="echoid-s6262" xml:space="preserve">:
              <lb/>
            + CE. </s>
            <s xml:id="echoid-s6263" xml:space="preserve">CG + NG. </s>
            <s xml:id="echoid-s6264" xml:space="preserve">NE + AN. </s>
            <s xml:id="echoid-s6265" xml:space="preserve">AE. </s>
            <s xml:id="echoid-s6266" xml:space="preserve">Quod propoſitum fuit
              <lb/>
            oſtendere.</s>
            <s xml:id="echoid-s6267" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s6268" xml:space="preserve">XXV. </s>
            <s xml:id="echoid-s6269" xml:space="preserve">Hinc, ſi fiat CE. </s>
            <s xml:id="echoid-s6270" xml:space="preserve">CG :</s>
            <s xml:id="echoid-s6271" xml:space="preserve">: NE. </s>
            <s xml:id="echoid-s6272" xml:space="preserve">L; </s>
            <s xml:id="echoid-s6273" xml:space="preserve">& </s>
            <s xml:id="echoid-s6274" xml:space="preserve">AN. </s>
            <s xml:id="echoid-s6275" xml:space="preserve">AE :</s>
            <s xml:id="echoid-s6276" xml:space="preserve">: L.
              <lb/>
            </s>
            <s xml:id="echoid-s6277" xml:space="preserve">M; </s>
            <s xml:id="echoid-s6278" xml:space="preserve">erit NZ ZG :</s>
            <s xml:id="echoid-s6279" xml:space="preserve">: NG. </s>
            <s xml:id="echoid-s6280" xml:space="preserve">M. </s>
            <s xml:id="echoid-s6281" xml:space="preserve">Nam NG. </s>
            <s xml:id="echoid-s6282" xml:space="preserve">NE + CE. </s>
            <s xml:id="echoid-s6283" xml:space="preserve">CG
              <lb/>
            + AN. </s>
            <s xml:id="echoid-s6284" xml:space="preserve">AE = NG. </s>
            <s xml:id="echoid-s6285" xml:space="preserve">NE + NE. </s>
            <s xml:id="echoid-s6286" xml:space="preserve">L. </s>
            <s xml:id="echoid-s6287" xml:space="preserve">+ L. </s>
            <s xml:id="echoid-s6288" xml:space="preserve">M = NG. </s>
            <s xml:id="echoid-s6289" xml:space="preserve">M.</s>
            <s xml:id="echoid-s6290" xml:space="preserve"/>
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