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

Page concordance

< >
Scan Original
231 38
232 39
233 40
234 41
235 42
236 43
237 44
238 45
239 46
240 47
241 48
242 49
243 50
244 51
245 52
246 53
247 54
248 55
249 56
250 57
251 58
252 59
253 60
254 61
255 62
256 63
257 64
258 65
259 66
260 67
< >
page |< < (45) of 393 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div222" type="section" level="1" n="31">
          <pb o="45" file="0223" n="238" rhead=""/>
          <p>
            <s xml:id="echoid-s9729" xml:space="preserve">AD eaſdem partes vergentium curvarum, è communi quadam
              <lb/>
            generatione deductas, generales aliquot affectiones jam antea
              <lb/>
            dudum expoſui; </s>
            <s xml:id="echoid-s9730" xml:space="preserve">illas præſertim, quas à veteribus _Geometris_ obſer-
              <lb/>
            varam ſpecialibus, quas ipſi tractant, curvis applicari. </s>
            <s xml:id="echoid-s9731" xml:space="preserve">Jam non
              <lb/>
            ingratum facturus videor, ſi complures alias (abſtruſiores quidem
              <lb/>
            illas, at non injucundas prorſus, aut inutiles) appoſuero; </s>
            <s xml:id="echoid-s9732" xml:space="preserve">pro mèo
              <lb/>
            more quàm conciciſſimè demonſtratas, eâ tamen ratione quoad po-
              <lb/>
            tero, quæ cumprimis ſcientifica videtur, hoc eſt quæ nedum con-
              <lb/>
            cluſionum veritatem aſſerit, at fontes etiam aperit, unde illa pro-
              <lb/>
            manat. </s>
            <s xml:id="echoid-s9733" xml:space="preserve">Verſantur autem præcipuè quæ proferemus, partim _circa_
              <lb/>
            _tangentium abſque calculi moleſtia vel faſtidio inveſtigationem ſi-_
              <lb/>
            _mul ac demonſtrationem expeditam_ (è ſimplicioribus nempe vulga-
              <lb/>
            tioribúſque perplexiora minúsque perſpecta deducendo) _partim cir-_
              <lb/>
            _ca mnltarum magnitudinum dimenſiones, tangentium deſignatarum o-_
              <lb/>
            _pe, quam promptiſſimè determinandas_; </s>
            <s xml:id="echoid-s9734" xml:space="preserve">quæ materiæ cùm præ Ge-
              <lb/>
            ometricis aliis quodammodò difficiles videntur, tum non penitus
              <lb/>
            adhuc (ſicut aliæ quædam) occupatæ vel exhauſtæ ſunt, ad hunc
              <lb/>
            ſaltem modum quod ſciam nondum tractatæ Quin è veſtigiorem aggre-
              <lb/>
            dimur, _Lemmatica_ quædam utcunque, quorum in reliquis clariùs & </s>
            <s xml:id="echoid-s9735" xml:space="preserve">
              <lb/>
            breviùs oſtendendis aliquem proſpicimus uſum, prælibantes.</s>
            <s xml:id="echoid-s9736" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9737" xml:space="preserve">II Sit _angulus rectilineus_ ABC, & </s>
            <s xml:id="echoid-s9738" xml:space="preserve">datum punctum D, ſit i-
              <lb/>
              <note position="right" xlink:label="note-0223-01" xlink:href="note-0223-01a" xml:space="preserve">Fig. 38.</note>
            tem linea ODO talis, ut per D ductâ quâvis rectâ DN; </s>
            <s xml:id="echoid-s9739" xml:space="preserve">ſit an-
              <lb/>
            guli lateribus intercepta MN æqualis à puncto D, & </s>
            <s xml:id="echoid-s9740" xml:space="preserve">linea ODO
              <lb/>
            interceptæ DO; </s>
            <s xml:id="echoid-s9741" xml:space="preserve">erit linea ODO _Hyperbola._</s>
            <s xml:id="echoid-s9742" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9743" xml:space="preserve">Nam ducatur DL ad CB parallela occurrénſq; </s>
            <s xml:id="echoid-s9744" xml:space="preserve">ipſi AB in L; </s>
            <s xml:id="echoid-s9745" xml:space="preserve">& </s>
            <s xml:id="echoid-s9746" xml:space="preserve">
              <lb/>
            in protracta BL ſumatur LZ = LB; </s>
            <s xml:id="echoid-s9747" xml:space="preserve">ducatúrq; </s>
            <s xml:id="echoid-s9748" xml:space="preserve">ZS ad BC paral-
              <lb/>
            lela; </s>
            <s xml:id="echoid-s9749" xml:space="preserve">item ducatur OK ad BZ parallela. </s>
            <s xml:id="echoid-s9750" xml:space="preserve">Et ob poſitam DO = MN;
              <lb/>
            </s>
            <s xml:id="echoid-s9751" xml:space="preserve">erit HO = BN; </s>
            <s xml:id="echoid-s9752" xml:space="preserve">ergò quum ſit DH. </s>
            <s xml:id="echoid-s9753" xml:space="preserve">HO:</s>
            <s xml:id="echoid-s9754" xml:space="preserve">: (DL. </s>
            <s xml:id="echoid-s9755" xml:space="preserve">LN:</s>
            <s xml:id="echoid-s9756" xml:space="preserve">: </s>
          </p>
        </div>
      </text>
    </echo>
Impressum