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

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          <pb o="116" file="0134" n="134" rhead=""/>
          <p>
            <s xml:id="echoid-s7585" xml:space="preserve">XVI. </s>
            <s xml:id="echoid-s7586" xml:space="preserve">Addiametrum CO deſcribatur circulus CFH; </s>
            <s xml:id="echoid-s7587" xml:space="preserve">& </s>
            <s xml:id="echoid-s7588" xml:space="preserve">ab O
              <lb/>
              <note position="left" xlink:label="note-0134-01" xlink:href="note-0134-01a" xml:space="preserve">Fig. 187.</note>
            radiusincidat talis, ut cum ejus reflexus ſit DS, contingat fore DS
              <lb/>
            = {1/2} DH, vel {1/2} DI; </s>
            <s xml:id="echoid-s7589" xml:space="preserve">poſitâ CI ad DS perpendiculari (talis autem
              <lb/>
            radius facilè duci poſſe concipiatur; </s>
            <s xml:id="echoid-s7590" xml:space="preserve">& </s>
            <s xml:id="echoid-s7591" xml:space="preserve">per curvam appropriatam re-
              <lb/>
            verà ſtatim determinetur; </s>
            <s xml:id="echoid-s7592" xml:space="preserve">id proinde nos non diſtinebit). </s>
            <s xml:id="echoid-s7593" xml:space="preserve">Erit tum
              <lb/>
            puncti Simago, puta σ, à puncto D infinitè disjuncta; </s>
            <s xml:id="echoid-s7594" xml:space="preserve">quoniam (id
              <lb/>
            quod fieri nequit, niſi H σ, σ D ſint infinitæ) eſt H σ. </s>
            <s xml:id="echoid-s7595" xml:space="preserve">σ D :</s>
            <s xml:id="echoid-s7596" xml:space="preserve">: IS.
              <lb/>
            </s>
            <s xml:id="echoid-s7597" xml:space="preserve">SD. </s>
            <s xml:id="echoid-s7598" xml:space="preserve">Jam in arcum DB cadat utcunque radius OM, cujus reflexus
              <lb/>
            ſit MA E; </s>
            <s xml:id="echoid-s7599" xml:space="preserve">& </s>
            <s xml:id="echoid-s7600" xml:space="preserve">in hac ſumatur ME = MF; </s>
            <s xml:id="echoid-s7601" xml:space="preserve">tum in OM producta
              <lb/>
            capiatur punctum α, ut ſit F α. </s>
            <s xml:id="echoid-s7602" xml:space="preserve">α M :</s>
            <s xml:id="echoid-s7603" xml:space="preserve">: EA. </s>
            <s xml:id="echoid-s7604" xml:space="preserve">AM; </s>
            <s xml:id="echoid-s7605" xml:space="preserve">erit α puncti A
              <lb/>
            imago. </s>
            <s xml:id="echoid-s7606" xml:space="preserve">ſimili methodo reperiatur ρ puncti R imago; </s>
            <s xml:id="echoid-s7607" xml:space="preserve">neque non reliqua
              <lb/>
            totius R ρασ, ipſam BS referentis, puncta.</s>
            <s xml:id="echoid-s7608" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7609" xml:space="preserve">XVII. </s>
            <s xml:id="echoid-s7610" xml:space="preserve">In harc verò conſtructionem quædam veniunt adnotanda.</s>
            <s xml:id="echoid-s7611" xml:space="preserve"/>
          </p>
          <note position="left" xml:space="preserve">Fig. 187,
            <lb/>
          188.</note>
          <p>
            <s xml:id="echoid-s7612" xml:space="preserve">1. </s>
            <s xml:id="echoid-s7613" xml:space="preserve">Quòd CS &</s>
            <s xml:id="echoid-s7614" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s7615" xml:space="preserve">CZ. </s>
            <s xml:id="echoid-s7616" xml:space="preserve">Nam 4 CZq = CBq = 3 SDq +
              <lb/>
            CSq. </s>
            <s xml:id="echoid-s7617" xml:space="preserve">ergò quum ſit CZ &</s>
            <s xml:id="echoid-s7618" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s7619" xml:space="preserve">SD; </s>
            <s xml:id="echoid-s7620" xml:space="preserve">erit CS &</s>
            <s xml:id="echoid-s7621" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s7622" xml:space="preserve">CZ.</s>
            <s xml:id="echoid-s7623" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7624" xml:space="preserve">2. </s>
            <s xml:id="echoid-s7625" xml:space="preserve">Quod CA &</s>
            <s xml:id="echoid-s7626" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s7627" xml:space="preserve">CS. </s>
            <s xml:id="echoid-s7628" xml:space="preserve">Nam (è ſuprà monſtratis) ſi ducatur
              <lb/>
            recta M ψ ad DO parallela, ejuſce reflexa (puta M ξ) ſecabit ipſam
              <lb/>
            DS, verſus I, puta ad ξ. </s>
            <s xml:id="echoid-s7629" xml:space="preserve">ergò M ξ ipſam CB ſecabit ſupra punctum S,
              <lb/>
            velut ad φ. </s>
            <s xml:id="echoid-s7630" xml:space="preserve">atqui quoniam ang. </s>
            <s xml:id="echoid-s7631" xml:space="preserve">CMO &</s>
            <s xml:id="echoid-s7632" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s7633" xml:space="preserve">CMψ, ſeu ang. </s>
            <s xml:id="echoid-s7634" xml:space="preserve">CMA
              <lb/>
            &</s>
            <s xml:id="echoid-s7635" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s7636" xml:space="preserve">CMφ, eſt CA &</s>
            <s xml:id="echoid-s7637" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s7638" xml:space="preserve">C φ; </s>
            <s xml:id="echoid-s7639" xml:space="preserve">adeóque magìs eſt CA &</s>
            <s xml:id="echoid-s7640" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s7641" xml:space="preserve">CS.</s>
            <s xml:id="echoid-s7642" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7643" xml:space="preserve">3. </s>
            <s xml:id="echoid-s7644" xml:space="preserve">Quòd EA &</s>
            <s xml:id="echoid-s7645" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s7646" xml:space="preserve">AM. </s>
            <s xml:id="echoid-s7647" xml:space="preserve">cùm enim ſit EM (vel FM) &</s>
            <s xml:id="echoid-s7648" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s7649" xml:space="preserve">HD,
              <lb/>
            atque DS &</s>
            <s xml:id="echoid-s7650" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s7651" xml:space="preserve">MA; </s>
            <s xml:id="echoid-s7652" xml:space="preserve">erit EM. </s>
            <s xml:id="echoid-s7653" xml:space="preserve">MA &</s>
            <s xml:id="echoid-s7654" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s7655" xml:space="preserve">FD. </s>
            <s xml:id="echoid-s7656" xml:space="preserve">DS :</s>
            <s xml:id="echoid-s7657" xml:space="preserve">: 2. </s>
            <s xml:id="echoid-s7658" xml:space="preserve">1.</s>
            <s xml:id="echoid-s7659" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7660" xml:space="preserve">4. </s>
            <s xml:id="echoid-s7661" xml:space="preserve">Hinc denuò liquebit totam lineam B ρασ ultra rectam CBL
              <lb/>
            jacere. </s>
            <s xml:id="echoid-s7662" xml:space="preserve">nam ducatur FQ ad AM parallela eſt hîc ang FCA &</s>
            <s xml:id="echoid-s7663" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s7664" xml:space="preserve">ang
              <lb/>
            ACE. </s>
            <s xml:id="echoid-s7665" xml:space="preserve">& </s>
            <s xml:id="echoid-s7666" xml:space="preserve">ang FQA = ang CAE. </s>
            <s xml:id="echoid-s7667" xml:space="preserve">quapropter erit CF. </s>
            <s xml:id="echoid-s7668" xml:space="preserve">FQ
              <lb/>
            &</s>
            <s xml:id="echoid-s7669" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s7670" xml:space="preserve">CE. </s>
            <s xml:id="echoid-s7671" xml:space="preserve">AE. </s>
            <s xml:id="echoid-s7672" xml:space="preserve">adeóque FQ &</s>
            <s xml:id="echoid-s7673" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s7674" xml:space="preserve">AE. </s>
            <s xml:id="echoid-s7675" xml:space="preserve">acindè FQ. </s>
            <s xml:id="echoid-s7676" xml:space="preserve">AM &</s>
            <s xml:id="echoid-s7677" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s7678" xml:space="preserve">AE.
              <lb/>
            </s>
            <s xml:id="echoid-s7679" xml:space="preserve">AM; </s>
            <s xml:id="echoid-s7680" xml:space="preserve">hoc eſt FK, KM &</s>
            <s xml:id="echoid-s7681" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s7682" xml:space="preserve">Fα. </s>
            <s xml:id="echoid-s7683" xml:space="preserve">αM. </s>
            <s xml:id="echoid-s7684" xml:space="preserve">dividendóque FM. </s>
            <s xml:id="echoid-s7685" xml:space="preserve">KM &</s>
            <s xml:id="echoid-s7686" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s7687" xml:space="preserve">
              <lb/>
            FM. </s>
            <s xml:id="echoid-s7688" xml:space="preserve">αM. </s>
            <s xml:id="echoid-s7689" xml:space="preserve">quare α M &</s>
            <s xml:id="echoid-s7690" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s7691" xml:space="preserve">KM. </s>
            <s xml:id="echoid-s7692" xml:space="preserve">adeóque punctum α ultra K in
              <lb/>
            recta OK protenſa jacet.</s>
            <s xml:id="echoid-s7693" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7694" xml:space="preserve">XVIII. </s>
            <s xml:id="echoid-s7695" xml:space="preserve">Quòd ſiad partes alteras rectæ OD ducatur radius ON’
              <lb/>
            cujus reflexus NGT = NV; </s>
            <s xml:id="echoid-s7696" xml:space="preserve">ſitque TG. </s>
            <s xml:id="echoid-s7697" xml:space="preserve">GN &</s>
            <s xml:id="echoid-s7698" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s7699" xml:space="preserve">2. </s>
            <s xml:id="echoid-s7700" xml:space="preserve">1; </s>
            <s xml:id="echoid-s7701" xml:space="preserve">ſtatuen-
              <lb/>
            da eſt puncti Gimago (puta γ) ad partes O. </s>
            <s xml:id="echoid-s7702" xml:space="preserve">quinimò cùm in hanc
              <lb/>
            rem plura ſubjici poſſent, ego jam _Specimina_ tantùm inſtituens
              <lb/>
            (quippe cùm operâ dignum haud arbitrer adeò tenuem materiam curi-
              <lb/>
            oſiùs proſequi) à minutiis abſtineo. </s>
            <s xml:id="echoid-s7703" xml:space="preserve">quo & </s>
            <s xml:id="echoid-s7704" xml:space="preserve">indè pronior ſum, quo-
              <lb/>
            niam in hac re copioſus videtur A. </s>
            <s xml:id="echoid-s7705" xml:space="preserve">_Tacquetus;_ </s>
            <s xml:id="echoid-s7706" xml:space="preserve">ſubinde quidem is,
              <lb/>
            ob admiſſum iſtud falſum principium, ceſpitans, at bene multa </s>
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