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

Page concordance

< >
Scan Original
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
111 93
112 94
113 95
114 96
115 97
116 98
117 99
118 100
119 101
120 102
< >
page |< < (82) of 393 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div113" type="section" level="1" n="19">
          <p>
            <s xml:id="echoid-s5237" xml:space="preserve">
              <pb o="82" file="0100" n="100" rhead=""/>
            habeatur determinatus; </s>
            <s xml:id="echoid-s5238" xml:space="preserve">ſuccedit ut breviter etiam ipſiſſimum in ſin-
              <lb/>
            gulo tali refracto punctum oſtendamus, ad quod illa conſiſtit. </s>
            <s xml:id="echoid-s5239" xml:space="preserve">in cu-
              <lb/>
            jus rei gratiam hoc quaſi _Lemma_ præſternemus.</s>
            <s xml:id="echoid-s5240" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5241" xml:space="preserve">VI. </s>
            <s xml:id="echoid-s5242" xml:space="preserve">In circulo AN B, cujus centrum C, ſint Semidiametro CA
              <lb/>
            perpendiculares NE, RF; </s>
            <s xml:id="echoid-s5243" xml:space="preserve">item Semidiametro CB ſint perpendicu-
              <lb/>
            lares NG, XH; </s>
            <s xml:id="echoid-s5244" xml:space="preserve">ſint autem CE, EF ipſis CG, GH proportiona-
              <lb/>
              <note position="left" xlink:label="note-0100-01" xlink:href="note-0100-01a" xml:space="preserve">Fig. 122.</note>
            les; </s>
            <s xml:id="echoid-s5245" xml:space="preserve">& </s>
            <s xml:id="echoid-s5246" xml:space="preserve">arcus NR, NX indefinitè parvi; </s>
            <s xml:id="echoid-s5247" xml:space="preserve">ſeu quaſi minimi dictâ
              <lb/>
            conditione præditi; </s>
            <s xml:id="echoid-s5248" xml:space="preserve">dicimus arcum NR ad arcum NX rationem ha-
              <lb/>
            bere conflatam è rationibus ipſarum CE ad CG, & </s>
            <s xml:id="echoid-s5249" xml:space="preserve">NG ad NE; </s>
            <s xml:id="echoid-s5250" xml:space="preserve">vel eſſe
              <lb/>
            arc. </s>
            <s xml:id="echoid-s5251" xml:space="preserve">NR, NX:</s>
            <s xml:id="echoid-s5252" xml:space="preserve">: CE x NG. </s>
            <s xml:id="echoid-s5253" xml:space="preserve">CG x NE. </s>
            <s xml:id="echoid-s5254" xml:space="preserve">Nam per N ducatur VT
              <lb/>
            tangens circulum, ipſiſque FR, HX occurrens punctis T, V. </s>
            <s xml:id="echoid-s5255" xml:space="preserve">eſt
              <lb/>
            itaque (propter Summam ex Hypotheſi parvitatem dictorum arcuum)
              <lb/>
            arc NR. </s>
            <s xml:id="echoid-s5256" xml:space="preserve">CN:</s>
            <s xml:id="echoid-s5257" xml:space="preserve">: NT. </s>
            <s xml:id="echoid-s5258" xml:space="preserve">CN:</s>
            <s xml:id="echoid-s5259" xml:space="preserve">: EF. </s>
            <s xml:id="echoid-s5260" xml:space="preserve">EN. </s>
            <s xml:id="echoid-s5261" xml:space="preserve">item CN. </s>
            <s xml:id="echoid-s5262" xml:space="preserve">arc NX:</s>
            <s xml:id="echoid-s5263" xml:space="preserve">:
              <lb/>
            CN. </s>
            <s xml:id="echoid-s5264" xml:space="preserve">NV:</s>
            <s xml:id="echoid-s5265" xml:space="preserve">: NG. </s>
            <s xml:id="echoid-s5266" xml:space="preserve">GH. </s>
            <s xml:id="echoid-s5267" xml:space="preserve">quapropter erit arc NR. </s>
            <s xml:id="echoid-s5268" xml:space="preserve">CN+ CN.
              <lb/>
            </s>
            <s xml:id="echoid-s5269" xml:space="preserve">arc NX = (EF. </s>
            <s xml:id="echoid-s5270" xml:space="preserve">EN + NG. </s>
            <s xml:id="echoid-s5271" xml:space="preserve">GH = EF. </s>
            <s xml:id="echoid-s5272" xml:space="preserve">GH+ NG. </s>
            <s xml:id="echoid-s5273" xml:space="preserve">EN
              <lb/>
            = ) CE. </s>
            <s xml:id="echoid-s5274" xml:space="preserve">CG + NG. </s>
            <s xml:id="echoid-s5275" xml:space="preserve">EN. </s>
            <s xml:id="echoid-s5276" xml:space="preserve">hoc eſt arc NR. </s>
            <s xml:id="echoid-s5277" xml:space="preserve">arc NX = CE. </s>
            <s xml:id="echoid-s5278" xml:space="preserve">
              <lb/>
            CG + NG. </s>
            <s xml:id="echoid-s5279" xml:space="preserve">EN: </s>
            <s xml:id="echoid-s5280" xml:space="preserve">Q. </s>
            <s xml:id="echoid-s5281" xml:space="preserve">E. </s>
            <s xml:id="echoid-s5282" xml:space="preserve">D. </s>
            <s xml:id="echoid-s5283" xml:space="preserve">(vel arc NR. </s>
            <s xml:id="echoid-s5284" xml:space="preserve">NX = CE x NG. </s>
            <s xml:id="echoid-s5285" xml:space="preserve">
              <lb/>
            CG x EN.)</s>
            <s xml:id="echoid-s5286" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s5287" xml:space="preserve">VII. </s>
            <s xml:id="echoid-s5288" xml:space="preserve">Sit jam radii cujuſvis talis MNP, refringentem interſecantis
              <lb/>
            punctis N, P, refractus N π (refringentem nempe denuò ſecans
              <lb/>
            in π) huic autem indeſinitè vicinus (& </s>
            <s xml:id="echoid-s5289" xml:space="preserve">quaſi proximus) adjaceat
              <lb/>
            radius QR S, cujus itidem refractus R σ (refringenti nempe rurſus
              <lb/>
            occurrens in σ), priorem N π decuſſans in Z; </s>
            <s xml:id="echoid-s5290" xml:space="preserve">biſecentur autem
              <lb/>
            ſubtenſæ NP, N π punctis G, E: </s>
            <s xml:id="echoid-s5291" xml:space="preserve">Dico rationem NZ ad GZ com-
              <lb/>
            poni è rationibus NG ad NE, & </s>
            <s xml:id="echoid-s5292" xml:space="preserve">CE ad CG.</s>
            <s xml:id="echoid-s5293" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">Fig. 123,
            <lb/>
          124.</note>
          <p>
            <s xml:id="echoid-s5294" xml:space="preserve">Nam ducantur rectæ CE (hæc ipſam RS quoque ſecans in F) & </s>
            <s xml:id="echoid-s5295" xml:space="preserve">
              <lb/>
            C G; </s>
            <s xml:id="echoid-s5296" xml:space="preserve">nec non CI ad R σ perpendicularis, & </s>
            <s xml:id="echoid-s5297" xml:space="preserve">in protracta CG ſu-
              <lb/>
            @@@@@r CH = CI; </s>
            <s xml:id="echoid-s5298" xml:space="preserve">& </s>
            <s xml:id="echoid-s5299" xml:space="preserve">per H ducatur XY ad N π parallela, ſeu per-
              <lb/>
            pendicularis ad CH; </s>
            <s xml:id="echoid-s5300" xml:space="preserve">unde eſt XY = R π; </s>
            <s xml:id="echoid-s5301" xml:space="preserve">& </s>
            <s xml:id="echoid-s5302" xml:space="preserve">arc NX = Y π & </s>
            <s xml:id="echoid-s5303" xml:space="preserve">
              <lb/>
            arc XY = arc R σ adeóque arc NR ±: </s>
            <s xml:id="echoid-s5304" xml:space="preserve">σ π = 2 arc NX. </s>
            <s xml:id="echoid-s5305" xml:space="preserve">Eſt-
              <lb/>
            que prætereà CG. </s>
            <s xml:id="echoid-s5306" xml:space="preserve">CE:</s>
            <s xml:id="echoid-s5307" xml:space="preserve">: R. </s>
            <s xml:id="echoid-s5308" xml:space="preserve">I:</s>
            <s xml:id="echoid-s5309" xml:space="preserve">: CI. </s>
            <s xml:id="echoid-s5310" xml:space="preserve">CF:</s>
            <s xml:id="echoid-s5311" xml:space="preserve">: CH. </s>
            <s xml:id="echoid-s5312" xml:space="preserve">CF; </s>
            <s xml:id="echoid-s5313" xml:space="preserve">adeóque
              <lb/>
            permutatim CG. </s>
            <s xml:id="echoid-s5314" xml:space="preserve">CH:</s>
            <s xml:id="echoid-s5315" xml:space="preserve">: CE. </s>
            <s xml:id="echoid-s5316" xml:space="preserve">CF. </s>
            <s xml:id="echoid-s5317" xml:space="preserve">ergò (juxta præcedentem) eſt
              <lb/>
            arc. </s>
            <s xml:id="echoid-s5318" xml:space="preserve">NR. </s>
            <s xml:id="echoid-s5319" xml:space="preserve">NX = NG. </s>
            <s xml:id="echoid-s5320" xml:space="preserve">NE + CE. </s>
            <s xml:id="echoid-s5321" xml:space="preserve">CG. </s>
            <s xml:id="echoid-s5322" xml:space="preserve">ad hæc ob illam (quæ
              <lb/>
            ponitur) arcuum NR, SP, π σ exiquitatem, erit arc NR. </s>
            <s xml:id="echoid-s5323" xml:space="preserve">π σ :</s>
            <s xml:id="echoid-s5324" xml:space="preserve">:
              <lb/>
            ſubtenſa NR. </s>
            <s xml:id="echoid-s5325" xml:space="preserve">π σ :</s>
            <s xml:id="echoid-s5326" xml:space="preserve">: NZ. </s>
            <s xml:id="echoid-s5327" xml:space="preserve">Zσ :</s>
            <s xml:id="echoid-s5328" xml:space="preserve">: NZ. </s>
            <s xml:id="echoid-s5329" xml:space="preserve">Zπ. </s>
            <s xml:id="echoid-s5330" xml:space="preserve">ergò (inverſè compo-
              <lb/>
            nendo, vel dividendo, tum & </s>
            <s xml:id="echoid-s5331" xml:space="preserve">conſequentes ſubduplando) arc NR.
              <lb/>
            </s>
            <s xml:id="echoid-s5332" xml:space="preserve">{arc NR±:</s>
            <s xml:id="echoid-s5333" xml:space="preserve">π σ/2}:</s>
            <s xml:id="echoid-s5334" xml:space="preserve">: NZ.</s>
            <s xml:id="echoid-s5335" xml:space="preserve">{NZ±Zπ/2}. </s>
            <s xml:id="echoid-s5336" xml:space="preserve">atqui velut modò </s>
          </p>
        </div>
      </text>
    </echo>
Impressum