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

Page concordance

< >
Scan Original
211 18
212 19
213 20
214 21
215 22
216 23
217 24
218 25
219 26
220 27
221 28
222 29
223 30
224 31
225 32
226 33
227 34
228 35
229 36
230 37
231 38
232 39
233 40
234 41
235 42
236 43
237 44
238 45
239 46
240 47
< >
page |< < (125) of 393 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div508" type="section" level="1" n="62">
          <p>
            <s xml:id="echoid-s14983" xml:space="preserve">
              <pb o="125" file="0303" n="318" rhead=""/>
            rectâ DB, ſit DB. </s>
            <s xml:id="echoid-s14984" xml:space="preserve">R:</s>
            <s xml:id="echoid-s14985" xml:space="preserve">: R. </s>
            <s xml:id="echoid-s14986" xml:space="preserve">BF (ſit autem BF, ut & </s>
            <s xml:id="echoid-s14987" xml:space="preserve">DHipſi DB
              <lb/>
            perpendicularis) tum per F, angulo BDHincluſa, tranſeat _hyperbola_
              <lb/>
            FXX; </s>
            <s xml:id="echoid-s14988" xml:space="preserve">ſitque ſpatium BFXI (poſitâ nempe IX ad B
              <unsure/>
            F _parallelâ_)
              <lb/>
            æquale duplo ſpatio ZDL; </s>
            <s xml:id="echoid-s14989" xml:space="preserve">ſit denuò DM = DG; </s>
            <s xml:id="echoid-s14990" xml:space="preserve">erit Min cur-
              <lb/>
            va quæſita; </s>
            <s xml:id="echoid-s14991" xml:space="preserve">quam utique ſi tangat recta TM, erit TD. </s>
            <s xml:id="echoid-s14992" xml:space="preserve">DM:</s>
            <s xml:id="echoid-s14993" xml:space="preserve">: R.
              <lb/>
            </s>
            <s xml:id="echoid-s14994" xml:space="preserve">DN.</s>
            <s xml:id="echoid-s14995" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div510" type="section" level="1" n="63">
          <head xml:id="echoid-head66" xml:space="preserve">_Probl_. VI.</head>
          <p>
            <s xml:id="echoid-s14996" xml:space="preserve">Sit rurſus ſpatium EDG (ut in præcedente) reperienda eſt curva
              <lb/>
            AMB, ad quam ſi projiciatur recta DNM, & </s>
            <s xml:id="echoid-s14997" xml:space="preserve">ſit DT huic perpen-
              <lb/>
              <note position="right" xlink:label="note-0303-01" xlink:href="note-0303-01a" xml:space="preserve">Fig. 188.</note>
            dicularis, & </s>
            <s xml:id="echoid-s14998" xml:space="preserve">MT curvam AMB tangat, fuerit DT = DN.</s>
            <s xml:id="echoid-s14999" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15000" xml:space="preserve">Adſumatur quæpiam R, & </s>
            <s xml:id="echoid-s15001" xml:space="preserve">ſit DZ q = {R
              <emph style="sub">3</emph>
            /DN}; </s>
            <s xml:id="echoid-s15002" xml:space="preserve">item acceptâ DB
              <lb/>
            (cui perpendiculares DH, BF = {R
              <emph style="sub">3</emph>
            /DBq}; </s>
            <s xml:id="echoid-s15003" xml:space="preserve">& </s>
            <s xml:id="echoid-s15004" xml:space="preserve">per F intra _aſymptotos_
              <lb/>
            DB, DH deſcribatur _hyperboliformis_ ſecundi generis (in qua nempe
              <lb/>
            ordinatæ, ceu BF, vel IX, ſint quartæ proportionales in ratione DB
              <lb/>
            ad R, vel DG ad R) tum capiatur ſpatium BIXF æquale duplo
              <lb/>
            ZDL; </s>
            <s xml:id="echoid-s15005" xml:space="preserve">& </s>
            <s xml:id="echoid-s15006" xml:space="preserve">ſit DM = DI; </s>
            <s xml:id="echoid-s15007" xml:space="preserve">erit M in curva quæſita; </s>
            <s xml:id="echoid-s15008" xml:space="preserve">quam ſi tan-
              <lb/>
            gat MT, erit DT = DN.</s>
            <s xml:id="echoid-s15009" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div512" type="section" level="1" n="64">
          <head xml:id="echoid-head67" xml:space="preserve">_Probl_. VII</head>
          <p>
            <s xml:id="echoid-s15010" xml:space="preserve">Sit figura quævis ADB (cujus _axis_ AD, _baſis_ DB) & </s>
            <s xml:id="echoid-s15011" xml:space="preserve">utcunque
              <lb/>
              <note position="right" xlink:label="note-0303-02" xlink:href="note-0303-02a" xml:space="preserve">Fig. 189.</note>
            ductâ PM ad DB parallelâ datum ſit (ſeu expreſſum quomodocunque)
              <lb/>
            ſpatium APM, oportet hinc ordinatam PM exhibere, vel expri-
              <lb/>
            mere.</s>
            <s xml:id="echoid-s15012" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15013" xml:space="preserve">Acceptâ quâqiam R, ſit R x PZ = APM; </s>
            <s xml:id="echoid-s15014" xml:space="preserve">hinc emergat linea
              <lb/>
            AZZK; </s>
            <s xml:id="echoid-s15015" xml:space="preserve">huic perpendicularis reperiatur ZO; </s>
            <s xml:id="echoid-s15016" xml:space="preserve">tum erit PZPO
              <lb/>
            :</s>
            <s xml:id="echoid-s15017" xml:space="preserve">: R. </s>
            <s xml:id="echoid-s15018" xml:space="preserve">PM.</s>
            <s xml:id="echoid-s15019" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s15020" xml:space="preserve">_Exemp_. </s>
            <s xml:id="echoid-s15021" xml:space="preserve">AP vocetur x & </s>
            <s xml:id="echoid-s15022" xml:space="preserve">ſit APM = √ r x
              <emph style="sub">3</emph>
            , ergo PZ = √
              <lb/>
            {x
              <emph style="sub">3</emph>
            /r}; </s>
            <s xml:id="echoid-s15023" xml:space="preserve">unde reperietur PO = {3 x x/2 r}. </s>
            <s xml:id="echoid-s15024" xml:space="preserve">Eſtque √ {x
              <emph style="sub">3</emph>
            /r}. </s>
            <s xml:id="echoid-s15025" xml:space="preserve">{3 x x/2 r}
              <lb/>
            :</s>
            <s xml:id="echoid-s15026" xml:space="preserve">: r. </s>
            <s xml:id="echoid-s15027" xml:space="preserve">{3/2} √ r x = PM. </s>
            <s xml:id="echoid-s15028" xml:space="preserve">unde AMB eſt _Parabola_, cujus _Pa-_
              <lb/>
            rameter eſt {9/4} r.</s>
            <s xml:id="echoid-s15029" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum