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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[101.] Addenda Lectionibus Geometricis.
Page: 342 (149)
[102.] _Probl_. I.
Page: 342 (149)
[103.] _Probl_. II.
Page: 342 (149)
[104.] _Probl_. III.
Page: 342 (149)
[105.] Addenda Lectionibus Geometricis.
Page: 343 (150)
[106.] _Theor_. I.
Page: 343 (150)
[107.] _Theor_. II.
Page: 343 (150)
[108.] _Theor_. III.
Page: 343 (150)
[109.] _Theor_. IV.
Page: 344 (151)
[110.] _Theor_. V.
Page: 344 (151)
[111.] _Theor_. VI.
Page: 344 (151)
[112.] FINIS.
Page: 344 (151)
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            <s xml:id="echoid-s5604" xml:space="preserve">1._</s>
            <s xml:id="echoid-s5605" xml:space="preserve">Tranſactis iis quœ refractioni conveniunt iſti, quam ad ctr_-
              <lb/>
            _culi peripberiam ſubeunt radii ſibimet paralleli; </s>
            <s xml:id="echoid-s5606" xml:space="preserve">quid iis. </s>
            <s xml:id="echoid-s5607" xml:space="preserve">ob_-
              <lb/>
            _venit proximè diſpicien ſxm venit, qui a puncto qu@piam ſenſibiliter_
              <lb/>
            _diver gentes itidem circulo ſe objiciunt refringendos._ </s>
            <s xml:id="echoid-s5608" xml:space="preserve">cum autem in hac
              <lb/>
            Hypotheſi multa reperiatur caſuum varietus è pluribus cauſis oriunda
              <lb/>
            (nedum enim à mediorum ſpecie differentium ordine, vel ſitu verſus
              <lb/>
            ſe diverſo; </s>
            <s xml:id="echoid-s5609" xml:space="preserve">quinetiam circuli refringentis alia ac alia, convexa nem-
              <lb/>
            pe vel concava, facie radiationi obverſa; </s>
            <s xml:id="echoid-s5610" xml:space="preserve">ſed ab ipſius quoque radi-
              <lb/>
            antis magìs aut minùs à refringente ſemoti poſitione concluſionum
              <lb/>
            emergit nonnulla diſcrepantia) nobis incumbet ità rem, quâ poſſu-
              <lb/>
            mus, moderari, ſimul ut cùm ex abſtractione nimia proveniens con-
              <lb/>
            fuſio, tum è repetitione faſtidium aliquouſque devitentur. </s>
            <s xml:id="echoid-s5611" xml:space="preserve">id autem
              <lb/>
            non aliàs, opinor, commodiùs aſſequemur quàm imprimìs generalia
              <lb/>
            quædam attingendo, cuidam uni caſui (illi nempe, ubi I &</s>
            <s xml:id="echoid-s5612" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s5613" xml:space="preserve">R, & </s>
            <s xml:id="echoid-s5614" xml:space="preserve">
              <lb/>
            radii convexis circuli partibus incidunt). </s>
            <s xml:id="echoid-s5615" xml:space="preserve">Sic applicata, ut ſatì; </s>
            <s xml:id="echoid-s5616" xml:space="preserve">faci-
              <lb/>
            lè poſſint ad alios quoque transferri; </s>
            <s xml:id="echoid-s5617" xml:space="preserve">tum peculiaria nonnulla ſingulis
              <lb/>
            congruentia ſubnotando. </s>
            <s xml:id="echoid-s5618" xml:space="preserve">ad rem.</s>
            <s xml:id="echoid-s5619" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5620" xml:space="preserve">II. </s>
            <s xml:id="echoid-s5621" xml:space="preserve">In circulum refringentem BN (cujus centrum C) radiet pun-
              <lb/>
              <note position="right" xlink:label="note-0105-01" xlink:href="note-0105-01a" xml:space="preserve">Fig. 129.</note>
            ctum A; </s>
            <s xml:id="echoid-s5622" xml:space="preserve">& </s>
            <s xml:id="echoid-s5623" xml:space="preserve">connexa A @ protendatur ad utraſque partcs indefinitè;
              <lb/>
            </s>
            <s xml:id="echoid-s5624" xml:space="preserve">tum cujuſvis incidentis AN ſit refractus NK, cum axe nimirum in K
              <lb/>
            conveniens; </s>
            <s xml:id="echoid-s5625" xml:space="preserve">dico compoſitas rationes AC ad CK, & </s>
            <s xml:id="echoid-s5626" xml:space="preserve">NK ad NA
              <lb/>
            æquari rationi I ad R. </s>
            <s xml:id="echoid-s5627" xml:space="preserve">Conjungatur enim CN, & </s>
            <s xml:id="echoid-s5628" xml:space="preserve">ducatur KH ad
              <lb/>
            CN parallela; </s>
            <s xml:id="echoid-s5629" xml:space="preserve">erit igitur (ut generatim antehac habetur oſtenſum)
              <lb/>
            I. </s>
            <s xml:id="echoid-s5630" xml:space="preserve">R :</s>
            <s xml:id="echoid-s5631" xml:space="preserve">: NK. </s>
            <s xml:id="echoid-s5632" xml:space="preserve">NH = NK. </s>
            <s xml:id="echoid-s5633" xml:space="preserve">NA + NA. </s>
            <s xml:id="echoid-s5634" xml:space="preserve">NH = NK. </s>
            <s xml:id="echoid-s5635" xml:space="preserve">NA +
              <lb/>
              <note position="right" xlink:label="note-0105-02" xlink:href="note-0105-02a" xml:space="preserve">3 Lect. num. 9@</note>
            AC. </s>
            <s xml:id="echoid-s5636" xml:space="preserve">CK: </s>
            <s xml:id="echoid-s5637" xml:space="preserve">Q. </s>
            <s xml:id="echoid-s5638" xml:space="preserve">E. </s>
            <s xml:id="echoid-s5639" xml:space="preserve">D.</s>
            <s xml:id="echoid-s5640" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s5641" xml:space="preserve">III. </s>
            <s xml:id="echoid-s5642" xml:space="preserve">Hinc ſi fuerit CA. </s>
            <s xml:id="echoid-s5643" xml:space="preserve">CR :</s>
            <s xml:id="echoid-s5644" xml:space="preserve">: I. </s>
            <s xml:id="echoid-s5645" xml:space="preserve">R. </s>
            <s xml:id="echoid-s5646" xml:space="preserve">erit CK, CR :</s>
            <s xml:id="echoid-s5647" xml:space="preserve">: NK.
              <lb/>
            </s>
            <s xml:id="echoid-s5648" xml:space="preserve">NA.</s>
            <s xml:id="echoid-s5649" xml:space="preserve"/>
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