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-s584" xml:space="preserve">
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            tardiùs in medio contumaciore delatum minorem arcum B β delineet;
              <lb/>
            </s>
            <s xml:id="echoid-s585" xml:space="preserve">quibus peractis recta BD tenebit ſitum β δ. </s>
            <s xml:id="echoid-s586" xml:space="preserve">Cùm verò jam punctum
              <lb/>
            D denſius quoque medium interet ad δ; </s>
            <s xml:id="echoid-s587" xml:space="preserve">proindéque pariter & </s>
            <s xml:id="echoid-s588" xml:space="preserve">ipſum
              <lb/>
            retardetur; </s>
            <s xml:id="echoid-s589" xml:space="preserve">motus iſti circulares protinus extinguantur oportet (nec
              <lb/>
            enim jam punctum D velociùs feretur quàm B; </s>
            <s xml:id="echoid-s590" xml:space="preserve">nec ideò majorem ut
              <lb/>
            priùs ſimul arcum deſcribet.) </s>
            <s xml:id="echoid-s591" xml:space="preserve">Itaque prius iter, quàm poterunt proxi-
              <lb/>
            mè, deſerentia tendent utrumque per horum arcuum tangentes δ κ,
              <lb/>
            β α; </s>
            <s xml:id="echoid-s592" xml:space="preserve">radiúſque totus ABCD hoc modo detortus, & </s>
            <s xml:id="echoid-s593" xml:space="preserve">ſitum α β δ κ
              <lb/>
            nactus per hanc poſteà ſemitam rectà decnrret Adnotandum eſt au-
              <lb/>
            tem quæcunque ſit rectæ AB ad rectam EF inclinatio arcus D δ, B β
              <lb/>
            (vel ſemidiametros ZD, ZB) eandem ſemper habere proportionem
              <lb/>
            inter ſe; </s>
            <s xml:id="echoid-s594" xml:space="preserve">talem nempe, qualem in denſitate, ſeu reſiſtentia peculiare
              <lb/>
            diſcrimen exigit. </s>
            <s xml:id="echoid-s595" xml:space="preserve">Etenim ſupponatur in quovis ſuperficiei pellucidæ
              <lb/>
              <note position="right" xlink:label="note-0033-01" xlink:href="note-0033-01a" xml:space="preserve">Fig. 7.</note>
            loco poſitum nobile punctum B; </s>
            <s xml:id="echoid-s596" xml:space="preserve">cùm medium hoc ex hypotheſi ſit
              <lb/>
            homogeneum (hoc eſt ubique pariter obſiſtens) nulla poteſt, opinor
              <lb/>
            aſſignari ratio cur hoc mobile non in quaſvis partes æ quâ velocitate de-
              <lb/>
            ferri poſſit; </s>
            <s xml:id="echoid-s597" xml:space="preserve">nimirum æquè celeriter ad Q tendet, (impetum modò
              <lb/>
            ceperit iſthàc dirigentem) per rectam OBQ, ac in N per rectam
              <lb/>
            ABN. </s>
            <s xml:id="echoid-s598" xml:space="preserve">Adeóque radii lucidi AB, OB utcunque differenter inclinati
              <lb/>
              <note position="right" xlink:label="note-0033-02" xlink:href="note-0033-02a" xml:space="preserve">Fig. 8.</note>
            parem omnino reſiſtentiam invenient; </s>
            <s xml:id="echoid-s599" xml:space="preserve">punctum, inquam, B, ſeu verſus
              <lb/>
            Q, ſeu verſus N nitatur, æqualiter, eodémque modo retardabitur.
              <lb/>
            </s>
            <s xml:id="echoid-s600" xml:space="preserve">Quinetiam cùm punctum D in primo medio ſemper eâdem, quæcunque
              <lb/>
            fuerit ejus poſitio, celeritate promoveatur, ſatis apparet motus iſtos,
              <lb/>
            aut motuum ſemitas eodem tempore decurſas, arcus nempe circulares
              <lb/>
            D δ, B β ſemper eandem inter ſe proportionem ſervare; </s>
            <s xml:id="echoid-s601" xml:space="preserve">nimirum il-
              <lb/>
            lam, quam habent ſemidiametri ZD, ZB, vel Z δ, ZB; </s>
            <s xml:id="echoid-s602" xml:space="preserve">quæ idcir-
              <lb/>
            co proportio, principaliter ac primariò, radiorum refractiones, ad
              <lb/>
            eadem duo media factas, determinat atque metitur. </s>
            <s xml:id="echoid-s603" xml:space="preserve">Hanc autem ean-
              <lb/>
            dem eſſe patet cum illa, quam habent recti ſinus angulorum ipſis Zδ,
              <lb/>
            ZB in triangulo Z δ B oppoſitorum, ipſorum ſcilicet ZB δ (vel
              <lb/>
            ZBE) & </s>
            <s xml:id="echoid-s604" xml:space="preserve">Z δ B. </s>
            <s xml:id="echoid-s605" xml:space="preserve">Eſt autem angulus ZBE complementum anguli
              <lb/>
            ABE, (hoc eſt angulus inclinationis rectæ AB ad EF) & </s>
            <s xml:id="echoid-s606" xml:space="preserve">angulus
              <lb/>
            Z δ B eſt complementum anguli F δ κ, vel inclinatio rectæ δ κ ad ean-
              <lb/>
            dem EF. </s>
            <s xml:id="echoid-s607" xml:space="preserve">Igitur abunde liquet propoſitum. </s>
            <s xml:id="echoid-s608" xml:space="preserve">Patet vero, quod in hoc
              <lb/>
            caſu, angulus EBZ major eſt angulo B δ Z; </s>
            <s xml:id="echoid-s609" xml:space="preserve">vel, ductis BM, δ N
              <lb/>
            ad EF perpendicularibus, quòd angulus MBG major eſt angulo
              <lb/>
            N δ κ; </s>
            <s xml:id="echoid-s610" xml:space="preserve">adeóque quòd hic refractio verſus perpendicularem, quod ai-
              <lb/>
            unt. </s>
            <s xml:id="echoid-s611" xml:space="preserve">contingit. </s>
            <s xml:id="echoid-s612" xml:space="preserve">Ac ità quidem quando radius radius in medium tranſit,
              <lb/>
            ipſi magis obſiſtens, ſen denſiùs. </s>
            <s xml:id="echoid-s613" xml:space="preserve">At ſi medio incurrit faciliorem tran-
              <lb/>
            ſitum præbenti, ſeu rariori, planè ſimili modo, ſed inverſè ſe res habet.</s>
            <s xml:id="echoid-s614" xml:space="preserve"/>
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