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

Page concordance

< >
Scan Original
81 63
82 64
83 65
84 66
85 67
86 68
87 69
88 70
89 71
90 72
91 73
92 74
93 75
94 76
95 77
96 78
97 79
98 80
99 81
100 82
101 83
102 84
103 85
104 86
105 87
106 88
107 89
108 90
109 91
110 92
< >
page |< < (42) of 393 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div58" type="section" level="1" n="14">
          <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"/>
          </p>
          <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"/>
          </p>
          <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>
          </p>
        </div>
      </text>
    </echo>
Impressum