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

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        <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"/>
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