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-s1911" xml:space="preserve">
              <pb o="36" file="0054" n="54" rhead=""/>
            verſam rationem KSq. </s>
            <s xml:id="echoid-s1912" xml:space="preserve">KSq - ZBq + SNq :</s>
            <s xml:id="echoid-s1913" xml:space="preserve">: BAq. </s>
            <s xml:id="echoid-s1914" xml:space="preserve">BZq. </s>
            <s xml:id="echoid-s1915" xml:space="preserve">hoc
              <lb/>
            eſt KSq. </s>
            <s xml:id="echoid-s1916" xml:space="preserve">KNq - ZBq :</s>
            <s xml:id="echoid-s1917" xml:space="preserve">: BAq. </s>
            <s xml:id="echoid-s1918" xml:space="preserve">ZBq. </s>
            <s xml:id="echoid-s1919" xml:space="preserve">quare permutando erit KSq.
              <lb/>
            </s>
            <s xml:id="echoid-s1920" xml:space="preserve">BAq :</s>
            <s xml:id="echoid-s1921" xml:space="preserve">: KNq - ZBq. </s>
            <s xml:id="echoid-s1922" xml:space="preserve">ZBq. </s>
            <s xml:id="echoid-s1923" xml:space="preserve">& </s>
            <s xml:id="echoid-s1924" xml:space="preserve">compoſitè KSq + BAq. </s>
            <s xml:id="echoid-s1925" xml:space="preserve">
              <lb/>
            BAq :</s>
            <s xml:id="echoid-s1926" xml:space="preserve">: KNq ZBq. </s>
            <s xml:id="echoid-s1927" xml:space="preserve">hoc eſt ANq. </s>
            <s xml:id="echoid-s1928" xml:space="preserve">BAq :</s>
            <s xml:id="echoid-s1929" xml:space="preserve">: KNq. </s>
            <s xml:id="echoid-s1930" xml:space="preserve">ZBq. </s>
            <s xml:id="echoid-s1931" xml:space="preserve">qua-
              <lb/>
            re rurſus permutando eſt ANq. </s>
            <s xml:id="echoid-s1932" xml:space="preserve">KNq :</s>
            <s xml:id="echoid-s1933" xml:space="preserve">: BAq. </s>
            <s xml:id="echoid-s1934" xml:space="preserve">ZBq :</s>
            <s xml:id="echoid-s1935" xml:space="preserve">: Rq. </s>
            <s xml:id="echoid-s1936" xml:space="preserve">Jq. </s>
            <s xml:id="echoid-s1937" xml:space="preserve">
              <lb/>
            itaque AN. </s>
            <s xml:id="echoid-s1938" xml:space="preserve">KN :</s>
            <s xml:id="echoid-s1939" xml:space="preserve">: R. </s>
            <s xml:id="echoid-s1940" xml:space="preserve">I. </s>
            <s xml:id="echoid-s1941" xml:space="preserve">unde patet KN ipſius AN refractum fore: </s>
            <s xml:id="echoid-s1942" xml:space="preserve">
              <lb/>
            Q. </s>
            <s xml:id="echoid-s1943" xml:space="preserve">E. </s>
            <s xml:id="echoid-s1944" xml:space="preserve">D.</s>
            <s xml:id="echoid-s1945" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1946" xml:space="preserve">XIX. </s>
            <s xml:id="echoid-s1947" xml:space="preserve">Exhinc, ut in priore caſu, patet quòd diſtantiæ (ZI, IK,
              <lb/>
            KL) concurſuum æquantur differentiis ipſarum ZB, RM, SN, TO
              <lb/>
            ordinatarum ad ellipſim. </s>
            <s xml:id="echoid-s1948" xml:space="preserve">Et quod ZI, ZK &</s>
            <s xml:id="echoid-s1949" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s1950" xml:space="preserve">IR. </s>
            <s xml:id="echoid-s1951" xml:space="preserve">KS. </s>
            <s xml:id="echoid-s1952" xml:space="preserve">&</s>
            <s xml:id="echoid-s1953" xml:space="preserve">c dif-
              <lb/>
            ferentiæ porrò dictæ circa verticem ellipſis Z admodum exiguæ ſunt,
              <lb/>
            adeóque propinquiorum axi radiorum refracti circa Z denſè congre-
              <lb/>
            gantur, & </s>
            <s xml:id="echoid-s1954" xml:space="preserve">velut ab eo procedere videntur.</s>
            <s xml:id="echoid-s1955" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s1956" xml:space="preserve">XX Ex his tandem univerſis colligitur quòd puncti radiantis A
              <lb/>
            imago (reſpectu ſcilicet oculi centrum O habentis uſpiam in axe AB
              <lb/>
            conſtitutum) circa punctum Z conſiſtet. </s>
            <s xml:id="echoid-s1957" xml:space="preserve">Sit enim D δ diameter pu-
              <lb/>
            pillæ (illa nempe quæ in plano EAFO ) & </s>
            <s xml:id="echoid-s1958" xml:space="preserve">per hujus extrema tranſe-
              <lb/>
            ant radiorum AM, A μ reſracti IMD, I μ δ ; </s>
            <s xml:id="echoid-s1959" xml:space="preserve">ſanè patet quòd nullius
              <lb/>
            obliquioris (ceu ipſius AN, vel A @) refractus oculum ingredi poterit ;
              <lb/>
            </s>
            <s xml:id="echoid-s1960" xml:space="preserve">quin univerſi tales aliorſum digredientur, adeóque nec illi quicquam
              <lb/>
            adviſum attinebunt; </s>
            <s xml:id="echoid-s1961" xml:space="preserve">eique nil omnino conferent efficiendo quaquam,
              <lb/>
            nedum determinando. </s>
            <s xml:id="echoid-s1962" xml:space="preserve">Quinimò cùm viſus a ſolis afficiatur radiis in-
              <lb/>
              <note position="left" xlink:label="note-0054-01" xlink:href="note-0054-01a" xml:space="preserve">Fig 46.</note>
            tra ſpatium ZI axem interſecantibus, adeóque velut ab eo procedenti-
              <lb/>
            bus, intra ſpatium ZI neceſſariò verſabitur imago ; </s>
            <s xml:id="echoid-s1963" xml:space="preserve">quia verò ex his
              <lb/>
            qui circa Z concurrunt oculo rectiùs incidunt, ideóque præcipuâ vi
              <lb/>
            pollent; </s>
            <s xml:id="echoid-s1964" xml:space="preserve">cùm & </s>
            <s xml:id="echoid-s1965" xml:space="preserve">ii (uti mox oſtendimus) ſpiſſiores ſint, & </s>
            <s xml:id="echoid-s1966" xml:space="preserve">præ cæte-
              <lb/>
            ris confertim incedant ( id quod etiam nonnihil illorum vim adauget)
              <lb/>
            cùm etiam iidem faciliùs ab oculo rurſus in idem punctum recolligantur
              <lb/>
            (id quod poſthac aliquatenus oſtendemus; </s>
            <s xml:id="echoid-s1967" xml:space="preserve">& </s>
            <s xml:id="echoid-s1968" xml:space="preserve">interim ex eo fit veriſimile,
              <lb/>
            quòd res per exiguum foramen ſpectatæ, radiis ſcilicet obliquioribus
              <lb/>
            excluſis, longè diſtinctiùs, apprehenduntur) quoniam, inquam, hæc
              <lb/>
            ita ſe habent, iis perpenſis omninò rationi conſentaneum eſt objectum
              <lb/>
            videri ceu radios projiciens à puncto Z, hoc eſt ejus imaginem inibi con-
              <lb/>
            ſiſtere Addo, quòd ob exilem pupillæ latitudinem, & </s>
            <s xml:id="echoid-s1969" xml:space="preserve">propter ali-
              <lb/>
            quantam oculi diſtantiam à refringente; </s>
            <s xml:id="echoid-s1970" xml:space="preserve">totum ſpacium ZI perquam
              <lb/>
            anguſtum erit, & </s>
            <s xml:id="echoid-s1971" xml:space="preserve">inſtar puncti merebitur exiſtimari: </s>
            <s xml:id="echoid-s1972" xml:space="preserve">quæ cuncta
              <lb/>
            propoſitum abunde videntur confirmare.</s>
            <s xml:id="echoid-s1973" xml:space="preserve"/>
          </p>
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      </text>
    </echo>
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