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

Page concordance

< >
Scan Original
301 108
302 109
303 110
304 111
305 112
306 113
307 114
308 115
309 116
310 117
311 118
312 119
313 120
314 121
315 122
316 123
317 124
318 125
319 126
320 127
321 128
322 129
323 130
324 131
325 132
326 133
327 134
328 135
329 136
330 137
< >
page |< < (132) of 393 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div540" type="section" level="1" n="76">
          <pb o="132" file="0310" n="325" rhead=""/>
        </div>
        <div xml:id="echoid-div542" type="section" level="1" n="77">
          <head xml:id="echoid-head80" xml:space="preserve">_Notetur autem_,</head>
          <p>
            <s xml:id="echoid-s15272" xml:space="preserve">1. </s>
            <s xml:id="echoid-s15273" xml:space="preserve">Ducta AD ad BH perpendiculari, ſi in hac capiatur AE = _n_;
              <lb/>
            </s>
            <s xml:id="echoid-s15274" xml:space="preserve">ducatúrque EF ad AH parallela; </s>
            <s xml:id="echoid-s15275" xml:space="preserve">hujus cum lineis expoſitis interſe-
              <lb/>
            ctiones æquationum propoſitarum radices exhibebunt reſpectivè; </s>
            <s xml:id="echoid-s15276" xml:space="preserve">erit
              <lb/>
              <note position="left" xlink:label="note-0310-01" xlink:href="note-0310-01a" xml:space="preserve">Fig. 206.</note>
            utique EK, vel EI, vel EM, vel EN æqualis ipſi _a_;
              <lb/>
            </s>
            <s xml:id="echoid-s15277" xml:space="preserve">hoc eſt ipſis AG, concipiendo à ſingula interſectione deduci ad AH
              <lb/>
            perpendiculares, quæ puncta G determinet.</s>
            <s xml:id="echoid-s15278" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15279" xml:space="preserve">2. </s>
            <s xml:id="echoid-s15280" xml:space="preserve">Quò punctum G magîs à termino A removetur (& </s>
            <s xml:id="echoid-s15281" xml:space="preserve">quidem poteſt
              <lb/>
            GA deſumi quavis deſignatâ major) eò ordinatæ GK, GL, GM, GN
              <lb/>
            magìs increſcunt; </s>
            <s xml:id="echoid-s15282" xml:space="preserve">adeo ut quantacunque ponatur AE, parallela EF
              <lb/>
            curvis occurſura ſit; </s>
            <s xml:id="echoid-s15283" xml:space="preserve">& </s>
            <s xml:id="echoid-s15284" xml:space="preserve">proinde ſemper habetur vera radix iſtarum
              <lb/>
            æquationum cuilibet conveniens; </s>
            <s xml:id="echoid-s15285" xml:space="preserve">& </s>
            <s xml:id="echoid-s15286" xml:space="preserve">ea tantùm una, quoniam EF
              <lb/>
            curvas iſtas unico puncto interſecat.</s>
            <s xml:id="echoid-s15287" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15288" xml:space="preserve">3. </s>
            <s xml:id="echoid-s15289" xml:space="preserve">_Curva_ ALL eſt _hyperbola æquilatera_, cujus _axis_ AB, reliquæ
              <lb/>
            AMM, ANN ſunt _hiperboliformes_.</s>
            <s xml:id="echoid-s15290" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15291" xml:space="preserve">4. </s>
            <s xml:id="echoid-s15292" xml:space="preserve">Si AO ſit {1/2} AB; </s>
            <s xml:id="echoid-s15293" xml:space="preserve">& </s>
            <s xml:id="echoid-s15294" xml:space="preserve">AP = {1/3} AB, & </s>
            <s xml:id="echoid-s15295" xml:space="preserve">AQ = {1/4} AB, du-
              <lb/>
            cantúrque OT, PV, QX ad BS parallelæ, erunt hæ curvarum ALL,
              <lb/>
            AMM, ANN _aſymptoti_.</s>
            <s xml:id="echoid-s15296" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15297" xml:space="preserve">5. </s>
            <s xml:id="echoid-s15298" xml:space="preserve">Hinc conſtat in ſecundo gradu fore _a_ &</s>
            <s xml:id="echoid-s15299" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s15300" xml:space="preserve">_n_ - {_b_/2}; </s>
            <s xml:id="echoid-s15301" xml:space="preserve">in tertio _a_&</s>
            <s xml:id="echoid-s15302" xml:space="preserve">gt;
              <lb/>
            </s>
            <s xml:id="echoid-s15303" xml:space="preserve">_n_ - {_b_/3}; </s>
            <s xml:id="echoid-s15304" xml:space="preserve">in quarto _a_&</s>
            <s xml:id="echoid-s15305" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s15306" xml:space="preserve">_n_ - {_b_/4}; </s>
            <s xml:id="echoid-s15307" xml:space="preserve">quæ tamen inæqualitates, ſi AE
              <lb/>
            benemagna ſit, exiguæ erunt.</s>
            <s xml:id="echoid-s15308" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15309" xml:space="preserve">6. </s>
            <s xml:id="echoid-s15310" xml:space="preserve">Æquationibus iſtis nulla competit _maxima, vel minima_.</s>
            <s xml:id="echoid-s15311" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div544" type="section" level="1" n="78">
          <head xml:id="echoid-head81" style="it" xml:space="preserve">Series ſecunda.</head>
          <p>
            <s xml:id="echoid-s15312" xml:space="preserve">_a_ - _b_ = _n_.</s>
            <s xml:id="echoid-s15313" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15314" xml:space="preserve">_aa_ - _ba_ = _nn_.</s>
            <s xml:id="echoid-s15315" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15316" xml:space="preserve">_a_
              <emph style="sub">3</emph>
            - _baa_ = _n_
              <emph style="sub">3</emph>
            .</s>
            <s xml:id="echoid-s15317" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15318" xml:space="preserve">_a_
              <emph style="sub">4</emph>
            - _ba_
              <emph style="sub">3</emph>
            = _n_
              <emph style="sub">4</emph>
            , &</s>
            <s xml:id="echoid-s15319" xml:space="preserve">c.</s>
            <s xml:id="echoid-s15320" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15321" xml:space="preserve">Sit rurſus AB = _b_; </s>
            <s xml:id="echoid-s15322" xml:space="preserve">& </s>
            <s xml:id="echoid-s15323" xml:space="preserve">indefinitè protrahatur AB verſus I, & </s>
            <s xml:id="echoid-s15324" xml:space="preserve">
              <lb/>
              <note position="left" xlink:label="note-0310-02" xlink:href="note-0310-02a" xml:space="preserve">Fig. 207.</note>
            ſint anguli RAI, SBI ſemirecti; </s>
            <s xml:id="echoid-s15325" xml:space="preserve">tum concipiantur curvæ BLL,
              <lb/>
            BMM, BNN tales, ut ſi utcunque ducatur GZ ad AI perpendicu-
              <lb/>
            laris (dictas lineas ſecans, utì cernis, punctis K, L, M, N, Z) ſit </s>
          </p>
        </div>
      </text>
    </echo>
Impressum