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-div506" type="section" level="1" n="61">
          <head xml:id="echoid-head64" xml:space="preserve">_Probl_. IV.</head>
          <p>
            <s xml:id="echoid-s14929" xml:space="preserve">Sit angulus BDHrectus, & </s>
            <s xml:id="echoid-s14930" xml:space="preserve">BF ad DH parallela; </s>
            <s xml:id="echoid-s14931" xml:space="preserve">& </s>
            <s xml:id="echoid-s14932" xml:space="preserve">_aſymptotis_
              <lb/>
              <note position="left" xlink:label="note-0302-01" xlink:href="note-0302-01a" xml:space="preserve">Fig. 187.</note>
            DB, DH per F deſcripta ſit _hyperbola_ FXG; </s>
            <s xml:id="echoid-s14933" xml:space="preserve">item centro Ddeſcrip-
              <lb/>
            tus ſit circulus KZL; </s>
            <s xml:id="echoid-s14934" xml:space="preserve">ſit denuò
              <unsure/>
            curva AMB talis, ut in hac ſumpto
              <lb/>
            quocunque puncto M, & </s>
            <s xml:id="echoid-s14935" xml:space="preserve">per hoc trajectâ rectâ DMZ, item ſumptâ
              <lb/>
            DI = DM; </s>
            <s xml:id="echoid-s14936" xml:space="preserve">& </s>
            <s xml:id="echoid-s14937" xml:space="preserve">ductâ IX ad BF parallelâ, ſit _ſpatium hyperbolicum_
              <lb/>
            BFXI æquale duplo _circulari ſectori_ ZDK; </s>
            <s xml:id="echoid-s14938" xml:space="preserve">curvæ AMB tangens
              <lb/>
            ad M determinetur.</s>
            <s xml:id="echoid-s14939" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14940" xml:space="preserve">Ducatur DS ad DM perpendicularis; </s>
            <s xml:id="echoid-s14941" xml:space="preserve">ſitque DB x BF = Rq;
              <lb/>
            </s>
            <s xml:id="echoid-s14942" xml:space="preserve">fiátque DK. </s>
            <s xml:id="echoid-s14943" xml:space="preserve">R:</s>
            <s xml:id="echoid-s14944" xml:space="preserve">: R. </s>
            <s xml:id="echoid-s14945" xml:space="preserve">P; </s>
            <s xml:id="echoid-s14946" xml:space="preserve">tum DK. </s>
            <s xml:id="echoid-s14947" xml:space="preserve">P:</s>
            <s xml:id="echoid-s14948" xml:space="preserve">: DM. </s>
            <s xml:id="echoid-s14949" xml:space="preserve">DT; </s>
            <s xml:id="echoid-s14950" xml:space="preserve">& </s>
            <s xml:id="echoid-s14951" xml:space="preserve">connecta-
              <lb/>
            tur TM; </s>
            <s xml:id="echoid-s14952" xml:space="preserve">hæc curvam AMB tanget.</s>
            <s xml:id="echoid-s14953" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14954" xml:space="preserve">Adnotetur curvæ AMB hanc eſſe proprietatatem; </s>
            <s xml:id="echoid-s14955" xml:space="preserve">ut DI ſit inter
              <lb/>
            DB, DO (vel DA) eodem ordine _media proportionalis Geometricè_,
              <lb/>
            quo arcus KZ inter _o_
              <unsure/>
            (ſeu nihilum) & </s>
            <s xml:id="echoid-s14956" xml:space="preserve">arcum KL eſt medius _Arith-_
              <lb/>
            _meticè_. </s>
            <s xml:id="echoid-s14957" xml:space="preserve">hoc eſt, ſi DI ſit numerus in ſerie _Geometricè proprtionalium_
              <lb/>
            incipiente à DB, & </s>
            <s xml:id="echoid-s14958" xml:space="preserve">terminatâ in DA; </s>
            <s xml:id="echoid-s14959" xml:space="preserve">ac _o_
              <unsure/>
            , KL ſint Logarithmi
              <lb/>
            ipſarum DB, DA; </s>
            <s xml:id="echoid-s14960" xml:space="preserve">erit KZLogarithmus ipſius DI. </s>
            <s xml:id="echoid-s14961" xml:space="preserve">Vel
              <lb/>
            retrò (prout vulgares _Logarithmi_ procedunt, ſi DI ſit numerus in
              <lb/>
            ſerie _Geometrica_ exorſa à DO, & </s>
            <s xml:id="echoid-s14962" xml:space="preserve">deſinente in DB ac _o_
              <unsure/>
            ſit _Logarith-_
              <lb/>
            _mus_ ipſius DO, & </s>
            <s xml:id="echoid-s14963" xml:space="preserve">arcus LK ipſius DB, erit arcus LZ _Logarithmus_
              <lb/>
            ipfius DI.</s>
            <s xml:id="echoid-s14964" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14965" xml:space="preserve">Quod ſi abſolutè conſtruatur curva AMB, ejúſque _tangens Me-_
              <lb/>
            _chanicè_ deprehendatur, inde patet _hpperbolici ſpatii Cycliſmum_ dari,
              <lb/>
            vel _Circuli hyperboliſmum_.</s>
            <s xml:id="echoid-s14966" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14967" xml:space="preserve">Hujuſce _Spiralis_ naturam, ac dimenſionem (ut & </s>
            <s xml:id="echoid-s14968" xml:space="preserve">Spatii BDA di-
              <lb/>
            menſionem) luculentè proſecutus eſt præclariſſimus D. </s>
            <s xml:id="echoid-s14969" xml:space="preserve">_Walliſſius
              <unsure/>
            _, in
              <lb/>
            Libro dè
              <unsure/>
            _Cycloide_; </s>
            <s xml:id="echoid-s14970" xml:space="preserve">quapropter de illa plura reticeo.</s>
            <s xml:id="echoid-s14971" xml:space="preserve"/>
          </p>
        </div>
        <div xml:id="echoid-div508" type="section" level="1" n="62">
          <head xml:id="echoid-head65" xml:space="preserve">_Probl_. V.</head>
          <p>
            <s xml:id="echoid-s14972" xml:space="preserve">Sit ſpatium quodpiam EDG (rectis DE, DG, & </s>
            <s xml:id="echoid-s14973" xml:space="preserve">linea ENG
              <lb/>
              <note position="left" xlink:label="note-0302-02" xlink:href="note-0302-02a" xml:space="preserve">Fig. 188.</note>
            comprehenſa) & </s>
            <s xml:id="echoid-s14974" xml:space="preserve">data quædam R; </s>
            <s xml:id="echoid-s14975" xml:space="preserve">curva AMB reperiatur talis, u
              <lb/>
            ſi utcunque à D projiciatur recta DNM, & </s>
            <s xml:id="echoid-s14976" xml:space="preserve">DT ad hanc perpendi
              <emph style="sub">t</emph>
              <unsure/>
              <lb/>
            cularis ſit, & </s>
            <s xml:id="echoid-s14977" xml:space="preserve">MT curvam AMB contingat; </s>
            <s xml:id="echoid-s14978" xml:space="preserve">ſit DT. </s>
            <s xml:id="echoid-s14979" xml:space="preserve">DM:</s>
            <s xml:id="echoid-s14980" xml:space="preserve">: R-
              <lb/>
            DN.</s>
            <s xml:id="echoid-s14981" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14982" xml:space="preserve">Sit curva KZL talis, ut DZ = √ R x DN; </s>
            <s xml:id="echoid-s14983" xml:space="preserve">ſumptâque </s>
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