Barrow, Isaac, Lectiones opticae & geometricae : in quibus phaenomenon opticorum genuinae rationes investigantur, ac exponuntur: et generalia curvarum linearum symptomata declarantur

Table of contents

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[61.] _Probl_. IV.
Page: 317 (124)
[62.] _Probl_. V.
Page: 317 (124)
[63.] _Probl_. VI.
Page: 318 (125)
[64.] _Probl_. VII
Page: 318 (125)
[65.] _Probl_. VIII.
Page: 319 (126)
[66.] _Probl_. IX.
Page: 319 (126)
[67.] _Probl_. X.
Page: 320 (127)
[68.] _Corol. Theor_. I.
Page: 321 (128)
[69.] _Theor_. II.
Page: 321 (128)
[70.] _Theor_. III.
Page: 321 (128)
[71.] _Theor_. IV.
Page: 321 (128)
[72.] _Theor_. V.
Page: 322 (129)
[73.] _Theor_. VI.
Page: 323 (130)
[74.] _Theor_. VII.
Page: 323 (130)
[75.] Lect. XIII.
Page: 324 (131)
[76.] Æquationum Series prima.
Page: 324 (131)
[77.] _Notetur autem_,
Page: 325 (132)
[78.] Series ſecunda.
Page: 325 (132)
[79.] Not.
Page: 326 (133)
[80.] Series tertia.
Page: 326 (133)
[81.] Not.
Page: 327 (134)
[82.] Not.
Page: 328 (135)
[83.] Series quarta.
Page: 329 (136)
[84.] Not.
Page: 329 (136)
[85.] Series quinta.
Page: 330 (137)
[86.] Series ſexta.
Page: 331 (138)
[87.] Not.
Page: 331 (138)
[88.] Series ſeptima.
Page: 332 (139)
[89.] Not.
Page: 332 (139)
[90.] Series octava.
Page: 333 (140)
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            <s xml:id="echoid-s2641" xml:space="preserve">
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            CN Π, angulo CNP æquari. </s>
            <s xml:id="echoid-s2642" xml:space="preserve">z 2. </s>
            <s xml:id="echoid-s2643" xml:space="preserve">Accepto quovis in NM puncto
              <lb/>
            (puta M) centro C per M deſcribatur circulus MQH; </s>
            <s xml:id="echoid-s2644" xml:space="preserve">item centro
              <lb/>
              <note position="left" xlink:label="note-0066-01" xlink:href="note-0066-01a" xml:space="preserve">Fig. 63.</note>
            N per M deſcribatur circulus MRH, qui priorem MQH ſecet
              <lb/>
            in H; </s>
            <s xml:id="echoid-s2645" xml:space="preserve">erit HN Π reflexus ipſius MN P. </s>
            <s xml:id="echoid-s2646" xml:space="preserve">Etenim connexis CM,
              <lb/>
            CH; </s>
            <s xml:id="echoid-s2647" xml:space="preserve">& </s>
            <s xml:id="echoid-s2648" xml:space="preserve">NM, NH, ex conſtructione liquet triangula CMN, CHN,
              <lb/>
            invicem æquilatera fore; </s>
            <s xml:id="echoid-s2649" xml:space="preserve">proindéque angulos CNM, CNH (& </s>
            <s xml:id="echoid-s2650" xml:space="preserve">
              <lb/>
            indè relìquos MNR, HNR) æquari 3. </s>
            <s xml:id="echoid-s2651" xml:space="preserve">protenſà CNR, à quovis
              <lb/>
            in MN puncto, puta M ducatur MG ad CR perpendicularis, & </s>
            <s xml:id="echoid-s2652" xml:space="preserve">
              <lb/>
            in hac producta ſumatur GH = GM; </s>
            <s xml:id="echoid-s2653" xml:space="preserve">erit conjuncta HN Π iterum
              <lb/>
            reflexus. </s>
            <s xml:id="echoid-s2654" xml:space="preserve">Nam connexis NH, NM patet angulos GNM, GNH
              <lb/>
            æquari. </s>
            <s xml:id="echoid-s2655" xml:space="preserve">verum hi modi ſufficiunt huic conficiendo perfacili negotio.</s>
            <s xml:id="echoid-s2656" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2657" xml:space="preserve">IV. </s>
            <s xml:id="echoid-s2658" xml:space="preserve">Nocetur ſi fuerit HN P reflexus ipſius MN P fore N Π =
              <lb/>
            N P.</s>
            <s xml:id="echoid-s2659" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2660" xml:space="preserve">V. </s>
            <s xml:id="echoid-s2661" xml:space="preserve">Diſpiciamus jam primò quid ex hujuſmodi reflectione contingat
              <lb/>
            puncto ab infinitâ quo ad ſenſum diſtantiâ radianti, ſeu parallelos
              <lb/>
            projicienti radios. </s>
            <s xml:id="echoid-s2662" xml:space="preserve">quorſum, per circuli reflectentis centrum C
              <lb/>
            protendatur indefinitè recta ABC (hoc autem in ſequentibus evitandæ
              <lb/>
            repetitioni perpetuò factum intelligatur; </s>
            <s xml:id="echoid-s2663" xml:space="preserve">quin ejuſmodi recta nomi-
              <lb/>
            netur axis; </s>
            <s xml:id="echoid-s2664" xml:space="preserve">hîc _Speculi,_ poſteà _Diapbani_) biſecetur autem Semidiame-
              <lb/>
            ter CB in Z; </s>
            <s xml:id="echoid-s2665" xml:space="preserve">& </s>
            <s xml:id="echoid-s2666" xml:space="preserve">per Z tranſeat recta ZY ad CB perpendicularis,
              <lb/>
            indeſinitéque protenſa ; </s>
            <s xml:id="echoid-s2667" xml:space="preserve">tum quilibet incidat axi parallelus radius
              <lb/>
            MN P ad N; </s>
            <s xml:id="echoid-s2668" xml:space="preserve">(convexo circuli nil refert, an cavo; </s>
            <s xml:id="echoid-s2669" xml:space="preserve">nam in utroque
              <lb/>
            caſu reflexus quoad directionem idem erit; </s>
            <s xml:id="echoid-s2670" xml:space="preserve">vel ejus qui in hoc, iſte qui
              <lb/>
            in illo productus erit) connexáque CN ipſam ZY interſecet in V;
              <lb/>
            </s>
            <s xml:id="echoid-s2671" xml:space="preserve">ſiátque CK = CV; </s>
            <s xml:id="echoid-s2672" xml:space="preserve">ducatúrque NK; </s>
            <s xml:id="echoid-s2673" xml:space="preserve">erit NK ipſius MN reflex-
              <lb/>
            us (vel reflexi productus) Nam ducatur NQ ad CB perpendicu-
              <lb/>
            laris, & </s>
            <s xml:id="echoid-s2674" xml:space="preserve">connectatur CP. </s>
            <s xml:id="echoid-s2675" xml:space="preserve">éſtque CZ . </s>
            <s xml:id="echoid-s2676" xml:space="preserve">CK :</s>
            <s xml:id="echoid-s2677" xml:space="preserve">: (CZ. </s>
            <s xml:id="echoid-s2678" xml:space="preserve">CV :</s>
            <s xml:id="echoid-s2679" xml:space="preserve">: )
              <lb/>
            CQ. </s>
            <s xml:id="echoid-s2680" xml:space="preserve">CN . </s>
            <s xml:id="echoid-s2681" xml:space="preserve">quapropter antecedentes duplicando CN . </s>
            <s xml:id="echoid-s2682" xml:space="preserve">CK :</s>
            <s xml:id="echoid-s2683" xml:space="preserve">:
              <lb/>
            PN. </s>
            <s xml:id="echoid-s2684" xml:space="preserve">CN. </s>
            <s xml:id="echoid-s2685" xml:space="preserve">item angulus KCN æquatur alterno CNP. </s>
            <s xml:id="echoid-s2686" xml:space="preserve">ergò tri-
              <lb/>
            angula CKN, NCP ſimilia ſunt; </s>
            <s xml:id="echoid-s2687" xml:space="preserve">adeoque KN = KC. </s>
            <s xml:id="echoid-s2688" xml:space="preserve">igitur è
              <lb/>
            ſuprà generatim oſtenſis patet fore KN, ipſius MN reflexum.</s>
            <s xml:id="echoid-s2689" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2690" xml:space="preserve">VI. </s>
            <s xml:id="echoid-s2691" xml:space="preserve">Hinc particularis emergit methodus hujuſmodi quotcunque
              <lb/>
            reflexos quàm expeditiſſime deſignandi; </s>
            <s xml:id="echoid-s2692" xml:space="preserve">quin & </s>
            <s xml:id="echoid-s2693" xml:space="preserve">ipſorum erga ſe ra-
              <lb/>
            tiones ac reſpectus; </s>
            <s xml:id="echoid-s2694" xml:space="preserve">nec non pleraque primaria _Symptomata_ facilè
              <lb/>
            diluceſcunt; </s>
            <s xml:id="echoid-s2695" xml:space="preserve">corollariis nempe ſubjectis comprehenſa.</s>
            <s xml:id="echoid-s2696" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2697" xml:space="preserve">VII. </s>
            <s xml:id="echoid-s2698" xml:space="preserve">I. </s>
            <s xml:id="echoid-s2699" xml:space="preserve">Patet punctum Z, Semidiametrum CB biſecans, </s>
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