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-s2252" xml:space="preserve">
              <pb o="42" file="0060" n="60" rhead=""/>
            tioribus minores ſunt. </s>
            <s xml:id="echoid-s2253" xml:space="preserve">& </s>
            <s xml:id="echoid-s2254" xml:space="preserve">quod cuivis eâ majori binæ pares interſeri
              <lb/>
            poſſunt, ad ejus utramque partem ſingula. </s>
            <s xml:id="echoid-s2255" xml:space="preserve">nimirum hæc è ſuperiori
              <lb/>
            conſtructione luculentè patent; </s>
            <s xml:id="echoid-s2256" xml:space="preserve">pauxillùm expende Sodes; </s>
            <s xml:id="echoid-s2257" xml:space="preserve">& </s>
            <s xml:id="echoid-s2258" xml:space="preserve">per-
              <lb/>
            ſpicies; </s>
            <s xml:id="echoid-s2259" xml:space="preserve">operámque meam non deſiderabis.</s>
            <s xml:id="echoid-s2260" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2261" xml:space="preserve">XII. </s>
            <s xml:id="echoid-s2262" xml:space="preserve">His præſtratis ad _Principale conſtruendum Problema_ reverti-
              <lb/>
            mur; </s>
            <s xml:id="echoid-s2263" xml:space="preserve">& </s>
            <s xml:id="echoid-s2264" xml:space="preserve">reliqua detexenda. </s>
            <s xml:id="echoid-s2265" xml:space="preserve">ſcilicet imprimis à dato puncto A pro-
              <lb/>
              <note position="left" xlink:label="note-0060-01" xlink:href="note-0060-01a" xml:space="preserve">Fig. 55, 56.</note>
            diens radius eſt deſignandus, cujus refractus per datum punctum X
              <lb/>
            tranſibit. </s>
            <s xml:id="echoid-s2266" xml:space="preserve">‖ hoc ità conficitur. </s>
            <s xml:id="echoid-s2267" xml:space="preserve">per A, X ducantur refringenti perpen-
              <lb/>
            diculares AB, XP. </s>
            <s xml:id="echoid-s2268" xml:space="preserve">tum in primo caſu fiat AB. </s>
            <s xml:id="echoid-s2269" xml:space="preserve">YB :</s>
            <s xml:id="echoid-s2270" xml:space="preserve">: √ Iq - Rq.
              <lb/>
            </s>
            <s xml:id="echoid-s2271" xml:space="preserve">I. </s>
            <s xml:id="echoid-s2272" xml:space="preserve">neque non fiat XP. </s>
            <s xml:id="echoid-s2273" xml:space="preserve">T :</s>
            <s xml:id="echoid-s2274" xml:space="preserve">: √ Iq - Rq. </s>
            <s xml:id="echoid-s2275" xml:space="preserve">R . </s>
            <s xml:id="echoid-s2276" xml:space="preserve">& </s>
            <s xml:id="echoid-s2277" xml:space="preserve">per punctum Y
              <lb/>
            tranſadigatur recta NG ſubtendens angulum APF, & </s>
            <s xml:id="echoid-s2278" xml:space="preserve">ipſam T ex-
              <lb/>
            æquans; </s>
            <s xml:id="echoid-s2279" xml:space="preserve">& </s>
            <s xml:id="echoid-s2280" xml:space="preserve">connectantur AN, XN. </s>
            <s xml:id="echoid-s2281" xml:space="preserve">dico factum; </s>
            <s xml:id="echoid-s2282" xml:space="preserve">ſeu rectam XV
              <lb/>
            incidentis AN refractum eſſe. </s>
            <s xml:id="echoid-s2283" xml:space="preserve">‖ Etenim eſt X P. </s>
            <s xml:id="echoid-s2284" xml:space="preserve">KB :</s>
            <s xml:id="echoid-s2285" xml:space="preserve">: NP. </s>
            <s xml:id="echoid-s2286" xml:space="preserve">NB :</s>
            <s xml:id="echoid-s2287" xml:space="preserve">:
              <lb/>
            NG. </s>
            <s xml:id="echoid-s2288" xml:space="preserve">NY. </s>
            <s xml:id="echoid-s2289" xml:space="preserve">permutandóque XP. </s>
            <s xml:id="echoid-s2290" xml:space="preserve">NG :</s>
            <s xml:id="echoid-s2291" xml:space="preserve">: KB. </s>
            <s xml:id="echoid-s2292" xml:space="preserve">NY. </s>
            <s xml:id="echoid-s2293" xml:space="preserve">hoc eſt X P. </s>
            <s xml:id="echoid-s2294" xml:space="preserve">
              <lb/>
            NG (vel √ Iq - Rq. </s>
            <s xml:id="echoid-s2295" xml:space="preserve">R) :</s>
            <s xml:id="echoid-s2296" xml:space="preserve">: KB. </s>
            <s xml:id="echoid-s2297" xml:space="preserve">YN. </s>
            <s xml:id="echoid-s2298" xml:space="preserve">itaque per theorema præ-
              <lb/>
            miſſum liquet KN ipſius AN refractum eſſe: </s>
            <s xml:id="echoid-s2299" xml:space="preserve">Q. </s>
            <s xml:id="echoid-s2300" xml:space="preserve">EF.</s>
            <s xml:id="echoid-s2301" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2302" xml:space="preserve">Haud abſimiliter in ſecundo caſu; </s>
            <s xml:id="echoid-s2303" xml:space="preserve">fiat X P. </s>
            <s xml:id="echoid-s2304" xml:space="preserve">YP :</s>
            <s xml:id="echoid-s2305" xml:space="preserve">: √ Rq - Iq. </s>
            <s xml:id="echoid-s2306" xml:space="preserve">R;
              <lb/>
            </s>
            <s xml:id="echoid-s2307" xml:space="preserve">itémque AB. </s>
            <s xml:id="echoid-s2308" xml:space="preserve">T :</s>
            <s xml:id="echoid-s2309" xml:space="preserve">: √ Rq - Iq. </s>
            <s xml:id="echoid-s2310" xml:space="preserve">I; </s>
            <s xml:id="echoid-s2311" xml:space="preserve">angulóque ABF per Y tranſi-
              <lb/>
            ens, ipſámque T adæquans inſeratur recta N G; </s>
            <s xml:id="echoid-s2312" xml:space="preserve">connectantúrque
              <lb/>
            AN, XN; </s>
            <s xml:id="echoid-s2313" xml:space="preserve">factum erit. </s>
            <s xml:id="echoid-s2314" xml:space="preserve">‖ Nam ipſam XP protractam ſecet AN in
              <lb/>
            S. </s>
            <s xml:id="echoid-s2315" xml:space="preserve">èſtque SP. </s>
            <s xml:id="echoid-s2316" xml:space="preserve">YN :</s>
            <s xml:id="echoid-s2317" xml:space="preserve">: AB. </s>
            <s xml:id="echoid-s2318" xml:space="preserve">GN :</s>
            <s xml:id="echoid-s2319" xml:space="preserve">: AB. </s>
            <s xml:id="echoid-s2320" xml:space="preserve">T :</s>
            <s xml:id="echoid-s2321" xml:space="preserve">: √ Rq - Iq. </s>
            <s xml:id="echoid-s2322" xml:space="preserve">I . </s>
            <s xml:id="echoid-s2323" xml:space="preserve">unde
              <lb/>
            conſequitur è præmonſtratis fore XN ipſius SN refractum Q. </s>
            <s xml:id="echoid-s2324" xml:space="preserve">E . </s>
            <s xml:id="echoid-s2325" xml:space="preserve">F .</s>
            <s xml:id="echoid-s2326" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s2327" xml:space="preserve">XIII. </s>
            <s xml:id="echoid-s2328" xml:space="preserve">Exhinc, & </s>
            <s xml:id="echoid-s2329" xml:space="preserve">præmiſſa reſpiciendo ſatìs diluceſcit non ultra
              <lb/>
            duos ad unas perpendicularis AB partes incidentium refractos in uno
              <lb/>
            puncto convenire. </s>
            <s xml:id="echoid-s2330" xml:space="preserve">nam (ut ſupra declaratum) per puntum Y (quod
              <lb/>
            univerſis hujuſmodi conſtructionibus commune, vel invariatum per-
              <lb/>
            perſiſtit; </s>
            <s xml:id="echoid-s2331" xml:space="preserve">in primo caſu quoad omnes ab A incidentes; </s>
            <s xml:id="echoid-s2332" xml:space="preserve">in ſecundo
              <lb/>
            qnoad omnes per X tranſeuntes refractos) plures duabus ſibi pares
              <lb/>
            duabus ſibi pares rectæ angulo recto XP F, vel ABF interſeri ne-
              <lb/>
            queunt; </s>
            <s xml:id="echoid-s2333" xml:space="preserve">adeóque nec plures refracti per ipſum X tranſibunt.</s>
            <s xml:id="echoid-s2334" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2335" xml:space="preserve">XIV. </s>
            <s xml:id="echoid-s2336" xml:space="preserve">Porrò, cùm è dictis definita habeatur recta, in qua puncti
              <lb/>
            A Imago verſatur; </s>
            <s xml:id="echoid-s2337" xml:space="preserve">iſte nimirum refractus qui per oculi centrum
              <lb/>
            tranſit, modo jam expoſito ducendus; </s>
            <s xml:id="echoid-s2338" xml:space="preserve">ipſum jam punctum determi-
              <lb/>
            nandum venit, ad quod illa præcisè conſiſtit; </s>
            <s xml:id="echoid-s2339" xml:space="preserve">id quod etiam è præce-
              <lb/>
            dentibus haud difficulter eliciemus.</s>
            <s xml:id="echoid-s2340" xml:space="preserve"/>
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          <p>
            <s xml:id="echoid-s2341" xml:space="preserve">XV. </s>
            <s xml:id="echoid-s2342" xml:space="preserve">Sumatur, in caſu primo, punctum Y conditione </s>
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