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

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            <s xml:id="echoid-s614" xml:space="preserve">
              <pb o="16" file="0034" n="34" rhead=""/>
            Quod (licèt breviùs) conficenetur negotium adſumendo ſicut eadem
              <lb/>
            _Tbebis Atbenas, ac Atbenis Tbebas_ eſt via, ità radium de raro tranſe-
              <lb/>
            untem in denſius, pérque denſius veſtigia ſua replicantem in rarum
              <lb/>
            nil aliud quàm eandem ſemitam repetere; </s>
            <s xml:id="echoid-s615" xml:space="preserve">ut nempe ſi radius ABDC
              <lb/>
            de raro tranſiens in denſius refringatur in α β κ δ; </s>
            <s xml:id="echoid-s616" xml:space="preserve">quòd etiam hic ra-
              <lb/>
            dius α β κ δ è denſiori recidens in rarum viciſſimin ABDC refringe-
              <lb/>
            tur; </s>
            <s xml:id="echoid-s617" xml:space="preserve">quia tamen aſſumptum illud non nemini demonſtrationis & </s>
            <s xml:id="echoid-s618" xml:space="preserve">ip-
              <lb/>
            ſum indigere videatur; </s>
            <s xml:id="echoid-s619" xml:space="preserve">Et univerſim, extremóque rigore ſumptum for-
              <lb/>
            ſan haud adeò verum ſit; </s>
            <s xml:id="echoid-s620" xml:space="preserve">majoris etiam evidentiæ cauſa; </s>
            <s xml:id="echoid-s621" xml:space="preserve">preſertîmq;
              <lb/>
            </s>
            <s xml:id="echoid-s622" xml:space="preserve">demùm quoniam huic caſui nonnulla quodammodò peculiaria ſunt no-
              <lb/>
            tatu non indigna; </s>
            <s xml:id="echoid-s623" xml:space="preserve">quin addo quia præſtare videtur effectum unum-
              <lb/>
            quemque propriis è cauſis deduci) ſeparatim oſtendemus. </s>
            <s xml:id="echoid-s624" xml:space="preserve">Rurſum
              <lb/>
            igitur radius ABDC, quâ priùs figurâ donatus rarioris medii ſuper-
              <lb/>
            ficiem EF incurrat. </s>
            <s xml:id="echoid-s625" xml:space="preserve">Cùm igitur punctum B velociùs procedere jam va-
              <lb/>
            leat quàm anteà (medio ſcilicet illapſum promptiùs cedenti) hoc eſt
              <lb/>
            quàm punctum D, neceſſariò commutabitur rectus utriuſque, quem
              <lb/>
            affectant, motus in ei proximum circularem, circa punctum aliquod
              <lb/>
            in recta BD, puta circa Z; </s>
            <s xml:id="echoid-s626" xml:space="preserve">itâ ut ZD, ZB talem inter ſe proportio-
              <lb/>
              <note position="left" xlink:label="note-0034-01" xlink:href="note-0034-01a" xml:space="preserve">Fig. 9.</note>
            nem obſervent, qualem ſingularis exigit horum in reſiſtentia mediorum
              <lb/>
            diverſitas; </s>
            <s xml:id="echoid-s627" xml:space="preserve">utique ſicut in quæ præceſſerunt; </s>
            <s xml:id="echoid-s628" xml:space="preserve">cùm verò punctum B
              <lb/>
            ità circumductum deſcripſerit arcum B β, & </s>
            <s xml:id="echoid-s629" xml:space="preserve">punctum D arcum D δ;
              <lb/>
            </s>
            <s xml:id="echoid-s630" xml:space="preserve">puncto D ad δ tunc medium rarius ingredienti, ceſſabit iſta motuum
              <lb/>
            inæqualitas; </s>
            <s xml:id="echoid-s631" xml:space="preserve">adeóque ſimul neceſſariò deſinet rotatus circa punctum
              <lb/>
            Z; </s>
            <s xml:id="echoid-s632" xml:space="preserve">ambóque puncta B, D per dictorum arcuum tangentes β α, δ κ (re-
              <lb/>
            ctæ Z β perpendiculares) quod proximum eſt iter arripient. </s>
            <s xml:id="echoid-s633" xml:space="preserve">Rurſus
              <lb/>
            autem, pariter ac in caſu præ cedente, rectæ ZD, ZB (vel Z δ, ZB)
              <lb/>
            proportionem exhibent, quæ refractiones hujuſmodi dimetitur; </s>
            <s xml:id="echoid-s634" xml:space="preserve">ha-
              <lb/>
            bent autem Z δ, ZB ſeipſas, ut recti ſinus angulorum ZB δ, Z δ E; </s>
            <s xml:id="echoid-s635" xml:space="preserve">
              <lb/>
            hoc eſt ut ſinus inclinationis rectæ AB ad ſinum inclinationis rectæ δ κ; </s>
            <s xml:id="echoid-s636" xml:space="preserve">
              <lb/>
            quod propoſitum fuit oſtendere. </s>
            <s xml:id="echoid-s637" xml:space="preserve">Liquet autem quòd hîc ang. </s>
            <s xml:id="echoid-s638" xml:space="preserve">Z δ F
              <lb/>
            major eſt angulo ZB δ, adeóque quod refractus divergit à per-
              <lb/>
            pendiculari.</s>
            <s xml:id="echoid-s639" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s640" xml:space="preserve">V. </s>
            <s xml:id="echoid-s641" xml:space="preserve">Advertendum eſt porrò quoad priorem hypotheſin, ſeu caſum
              <lb/>
            radii de medio rariori contendentis in denſius, eum femper, qualiſcunq;
              <lb/>
            </s>
            <s xml:id="echoid-s642" xml:space="preserve">fit ejus obliquitas, medium denſius ſubire; </s>
            <s xml:id="echoid-s643" xml:space="preserve">& </s>
            <s xml:id="echoid-s644" xml:space="preserve">per ipſum incedere; </s>
            <s xml:id="echoid-s645" xml:space="preserve">
              <lb/>
            modo commonſtratotrato. </s>
            <s xml:id="echoid-s646" xml:space="preserve">[Simpliciter autem hoc, & </s>
            <s xml:id="echoid-s647" xml:space="preserve">abſtractè debet in-
              <lb/>
            telligi, necut accidentarium quicquam interveniat, qualia ſunt, opaci-
              <lb/>
            tas perſpicuitati immiſta, figura diaphanum terminans, ejus craſſities
              <lb/>
            inæqualis, aliud quid poſt poſitum diaphani reſiſtentiam promovens;</s>
            <s xml:id="echoid-s648" xml:space="preserve"/>
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