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

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          <p>
            <s xml:id="echoid-s4122" xml:space="preserve">IX Adnotabimus tantùm quòd ex _Problematis_ hujuſce natura con-
              <lb/>
            ftructioneque propoſita ſatìs attendenti conſtabit (utique ſicut in _H@-_
              <lb/>
            _potheſibus_ antehac tractatis uberiùs eſt declaratum) duorum tantùm
              <lb/>
            ad eaſdem axis partes incidentium reflexosad unum ſeſe punctum de-
              <lb/>
            cuſſare. </s>
            <s xml:id="echoid-s4123" xml:space="preserve">nam aliorum unius (qui ſubinde poteſt dari) vel alterius re-
              <lb/>
            flexi per ejuſmodi punctum tranſeuntes ad alteris partibus incidentes
              <unsure/>
              <lb/>
            pertinebunt.</s>
            <s xml:id="echoid-s4124" xml:space="preserve">‖ Ex his quadantenus eluceſcit datis puncti radiantis,
              <lb/>
            oculíque poſitione deſignari poteſt linea quævis, in qua dicti puncti
              <lb/>
            ſpecies apparebit; </s>
            <s xml:id="echoid-s4125" xml:space="preserve">incumbit proximè punctum in ea præciſum deter-
              <lb/>
            minare, ad quo eadem conſiſtit. </s>
            <s xml:id="echoid-s4126" xml:space="preserve">eo ſpectat hoc Theoremation.</s>
            <s xml:id="echoid-s4127" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4128" xml:space="preserve">X. </s>
            <s xml:id="echoid-s4129" xml:space="preserve">Ab eodem quocunque puncto A manantes duo radii AN, AR
              <lb/>
              <note position="right" xlink:label="note-0085-01" xlink:href="note-0085-01a" xml:space="preserve">Fig. 95, 96.</note>
            in circuli reflectentis peripheria præter illum arcum NR (qui inci-
              <lb/>
            dentiæ punctis interjacent) intercipiant arcum PS; </s>
            <s xml:id="echoid-s4130" xml:space="preserve">eorum verò re-
              <lb/>
            flexi intercipiant arcum π σ; </s>
            <s xml:id="echoid-s4131" xml:space="preserve">erit arcus π σ æqualis Summæ vel diffe-
              <lb/>
            rentiæ dupli arcûs NR, & </s>
            <s xml:id="echoid-s4132" xml:space="preserve">arcûs PS. </s>
            <s xml:id="echoid-s4133" xml:space="preserve">Nam (1) in prima figura;
              <lb/>
            </s>
            <s xml:id="echoid-s4134" xml:space="preserve">eſt PS + SR + RN = PN = N π = π σ + σ R - RN; </s>
            <s xml:id="echoid-s4135" xml:space="preserve">er-
              <lb/>
            gò, pares hinc indè SR, & </s>
            <s xml:id="echoid-s4136" xml:space="preserve">σ R ſubducendo, erit PS + RN =
              <lb/>
            π σ - RN. </s>
            <s xml:id="echoid-s4137" xml:space="preserve">proindéque PS + 2 RN = π σ. </s>
            <s xml:id="echoid-s4138" xml:space="preserve">(2). </s>
            <s xml:id="echoid-s4139" xml:space="preserve">in altera figura; </s>
            <s xml:id="echoid-s4140" xml:space="preserve">
              <lb/>
            erit PS + SR - RN = PN = N π = RN + R σ - σ π. </s>
            <s xml:id="echoid-s4141" xml:space="preserve">qua-
              <lb/>
            rè rurſus æquales auferendo SR, R σ manebit PS - RN = RN
              <lb/>
            - σ π unde tranſponendo erit σ π = 2 RN - PS.</s>
            <s xml:id="echoid-s4142" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4143" xml:space="preserve">XI. </s>
            <s xml:id="echoid-s4144" xml:space="preserve">Etiam hoc _Lemmation_ adſcribemus: </s>
            <s xml:id="echoid-s4145" xml:space="preserve">Biſecetur recta NP in E;
              <lb/>
            </s>
            <s xml:id="echoid-s4146" xml:space="preserve">
              <note position="right" xlink:label="note-0085-02" xlink:href="note-0085-02a" xml:space="preserve">Fig. 94.</note>
            & </s>
            <s xml:id="echoid-s4147" xml:space="preserve">ubivis ſumatur punctum A; </s>
            <s xml:id="echoid-s4148" xml:space="preserve">erit EA = {PA ±: </s>
            <s xml:id="echoid-s4149" xml:space="preserve">NA.</s>
            <s xml:id="echoid-s4150" xml:space="preserve">/2.</s>
            <s xml:id="echoid-s4151" xml:space="preserve">} Nam
              <lb/>
            EA = {P N/2} ±: </s>
            <s xml:id="echoid-s4152" xml:space="preserve">AN = {PN ±: </s>
            <s xml:id="echoid-s4153" xml:space="preserve">2 AN / 2} = {PA ±: </s>
            <s xml:id="echoid-s4154" xml:space="preserve">AN.</s>
            <s xml:id="echoid-s4155" xml:space="preserve">/2}</s>
          </p>
          <p>
            <s xml:id="echoid-s4156" xml:space="preserve">XII. </s>
            <s xml:id="echoid-s4157" xml:space="preserve">Exhinc, ut propoſitum citiùs attingamus, Suppoſito radios
              <lb/>
              <note position="right" xlink:label="note-0085-03" xlink:href="note-0085-03a" xml:space="preserve">Fig. 95, 96.</note>
            A N, AR (quoad caſum præſentem) ſibi quàm proximos incidere,
              <lb/>
            punctum deſignabimus ad quod ipſorum reflexi N π, R σ concurrunt;
              <lb/>
            </s>
            <s xml:id="echoid-s4158" xml:space="preserve">dicimus utique ſi dicti reflexi concurrant ad Z; </s>
            <s xml:id="echoid-s4159" xml:space="preserve">bifectis ſubtenſis NP,
              <lb/>
            N π in E, & </s>
            <s xml:id="echoid-s4160" xml:space="preserve">F; </s>
            <s xml:id="echoid-s4161" xml:space="preserve">fore FZ. </s>
            <s xml:id="echoid-s4162" xml:space="preserve">ZN:</s>
            <s xml:id="echoid-s4163" xml:space="preserve">: EA. </s>
            <s xml:id="echoid-s4164" xml:space="preserve">NA. </s>
            <s xml:id="echoid-s4165" xml:space="preserve">‖ Nam quoniam
              <lb/>
            arcus NR, PS ex hypotheſi ſunt indefinitè parvi (ſeu minimi) ſe ha-
              <lb/>
            bebunt ut ſuæ ſubtenſæ; </s>
            <s xml:id="echoid-s4166" xml:space="preserve">nec non idem de arcubus NR, π σ dici poteſt. </s>
            <s xml:id="echoid-s4167" xml:space="preserve">
              <lb/>
            igitur arc. </s>
            <s xml:id="echoid-s4168" xml:space="preserve">PS. </s>
            <s xml:id="echoid-s4169" xml:space="preserve">RN :</s>
            <s xml:id="echoid-s4170" xml:space="preserve">: PS. </s>
            <s xml:id="echoid-s4171" xml:space="preserve">RN:</s>
            <s xml:id="echoid-s4172" xml:space="preserve">: PA. </s>
            <s xml:id="echoid-s4173" xml:space="preserve">RA. </s>
            <s xml:id="echoid-s4174" xml:space="preserve">(hoc eſt ob RA,
              <lb/>
            NA nihil, ex eadem hypotheſi, differentes):</s>
            <s xml:id="echoid-s4175" xml:space="preserve">: PA. </s>
            <s xml:id="echoid-s4176" xml:space="preserve">NA. </s>
            <s xml:id="echoid-s4177" xml:space="preserve">ergò,
              <lb/>
            bis componendo, erit PS + 2 RN. </s>
            <s xml:id="echoid-s4178" xml:space="preserve">RN:</s>
            <s xml:id="echoid-s4179" xml:space="preserve">: PA + 2 NA. </s>
            <s xml:id="echoid-s4180" xml:space="preserve">NA.</s>
            <s xml:id="echoid-s4181" xml:space="preserve"/>
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