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

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            <s xml:id="echoid-s7426" xml:space="preserve">
              <pb o="113" file="0131" n="131" rhead=""/>
            R. </s>
            <s xml:id="echoid-s7427" xml:space="preserve">I; </s>
            <s xml:id="echoid-s7428" xml:space="preserve">erit quidem XP imago rectæ FP abſoluta; </s>
            <s xml:id="echoid-s7429" xml:space="preserve">at ejuſdem imago
              <lb/>
            relata (puta P ρ φ ρ) ultra PFR jacet, ab illa ſenſim reclinans; </s>
            <s xml:id="echoid-s7430" xml:space="preserve">e-
              <lb/>
            júſque puncta quælibet ità ſignantur. </s>
            <s xml:id="echoid-s7431" xml:space="preserve">Ab O ducatur recta OK ut-
              <lb/>
            cunque rectam PQ ſecans in M, & </s>
            <s xml:id="echoid-s7432" xml:space="preserve">ſit KM ipſius FM refractus,
              <lb/>
            tum (poſito rurſus S = √ Iq - Rq) fiat PH = {Sq x PMq/lq x PFq} PM,
              <lb/>
            & </s>
            <s xml:id="echoid-s7433" xml:space="preserve">per H ad PF parallela ducatur H φ, ipſam OMK interſecans
              <lb/>
            ad φ; </s>
            <s xml:id="echoid-s7434" xml:space="preserve">erit punctum φ in dicta linea, punctum ſcilicet F repræſentans.
              <lb/>
            </s>
            <s xml:id="echoid-s7435" xml:space="preserve">eodémque modo puncta quotlibet alia deprehendes.</s>
            <s xml:id="echoid-s7436" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7437" xml:space="preserve">VIII. </s>
            <s xml:id="echoid-s7438" xml:space="preserve">Similiter rectæ FG ad ipſam PQ parallelæ, vel inclinatæ
              <lb/>
            imago relata φ α γ (in partes arcuata contrarias illis, ad quas prioris.
              <lb/>
            </s>
            <s xml:id="echoid-s7439" xml:space="preserve">casûs imago videbatur incurvata) determinabitur. </s>
            <s xml:id="echoid-s7440" xml:space="preserve">rem appoſita figura
              <lb/>
            ſatìs exprimit.</s>
            <s xml:id="echoid-s7441" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7442" xml:space="preserve">Hæc autem omnia de ſuprà comprobatis dilucidè conſectantur.</s>
            <s xml:id="echoid-s7443" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7444" xml:space="preserve">IX. </s>
            <s xml:id="echoid-s7445" xml:space="preserve">Ac ità quidem circa ſimplices planas ſuperficies refringentes
              <lb/>
              <note position="right" xlink:label="note-0131-01" xlink:href="note-0131-01a" xml:space="preserve">Fig. 185.</note>
            ſeſe res habet. </s>
            <s xml:id="echoid-s7446" xml:space="preserve">Quòd ſi corpori parallelis planis MN, μν terminato
              <lb/>
            exponatur recta FG; </s>
            <s xml:id="echoid-s7447" xml:space="preserve">Sint rectæ FP, GQ, ADBO ipſi PQ
              <lb/>
            perpendiculares, & </s>
            <s xml:id="echoid-s7448" xml:space="preserve">fiat BD. </s>
            <s xml:id="echoid-s7449" xml:space="preserve">BS :</s>
            <s xml:id="echoid-s7450" xml:space="preserve">: I.</s>
            <s xml:id="echoid-s7451" xml:space="preserve">R; </s>
            <s xml:id="echoid-s7452" xml:space="preserve">adſumatúrque Aα = DS;
              <lb/>
            </s>
            <s xml:id="echoid-s7453" xml:space="preserve">& </s>
            <s xml:id="echoid-s7454" xml:space="preserve">fiat AB. </s>
            <s xml:id="echoid-s7455" xml:space="preserve">αβ :</s>
            <s xml:id="echoid-s7456" xml:space="preserve">: FP. </s>
            <s xml:id="echoid-s7457" xml:space="preserve">XP; </s>
            <s xml:id="echoid-s7458" xml:space="preserve">& </s>
            <s xml:id="echoid-s7459" xml:space="preserve">per X, α ducatur recta X α Y, erit
              <lb/>
            X α Y lineæ FAG imago abſoluta. </s>
            <s xml:id="echoid-s7460" xml:space="preserve">Ergò ejus imago ad oculum O
              <lb/>
            relata (in hoc caſu) citra ipſam X α Y verſus ſuperficiem μν nonnihil
              <lb/>
            incurvata diſponetur, qualem exhibet linea φαγ. </s>
            <s xml:id="echoid-s7461" xml:space="preserve">id quod ex eo ſatìs
              <lb/>
            videtur liquere, quòd recta X α Y ſit imago reſpectu oculiin ipſa
              <lb/>
            OB à B infinitè ſemoti. </s>
            <s xml:id="echoid-s7462" xml:space="preserve">deſignari verò poterit hæc imago ad hunc
              <lb/>
            modum. </s>
            <s xml:id="echoid-s7463" xml:space="preserve">ſit fag (minuſculis elementis indigitata) imago rectæ FAG
              <lb/>
            ad ſuperſiciem refringentem μν relata (hoc eſt ad oculos in refractis
              <lb/>
            f μ M, q ν N, a DB, reliquíſque, nec non in medio μν MN verſus
              <lb/>
            O protenſo, ſitos) juxta proximè commonſtrata delineabilis. </s>
            <s xml:id="echoid-s7464" xml:space="preserve">tum
              <lb/>
            hujus ipſius _fag_ velut in medio MN μν verſus A protenſo poſitæ, ex
              <lb/>
            refractione ad ſuperficiem MN emergens, & </s>
            <s xml:id="echoid-s7465" xml:space="preserve">ad oculum O relata
              <lb/>
            conſtruatur imago φαγ (itidem ad modum nuperrimè præſcriptum)
              <lb/>
            hæc rectam FAG per corpus MN μν ſpectatam repræſentabit. </s>
            <s xml:id="echoid-s7466" xml:space="preserve">ex-
              <lb/>
            perientia teſtis advocetur, ego pluribus in re perplexiore, quàm uti-
              <lb/>
            liore ſuperſedeo.</s>
            <s xml:id="echoid-s7467" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7468" xml:space="preserve">X. </s>
            <s xml:id="echoid-s7469" xml:space="preserve">Porrò quod _plana ſpecula_ (ſimplicia, vel compoſita) attinet,
              <lb/>
            in iis palàm eſt imagines abſolutas ac relatas omnino ſibi coincidere;
              <lb/>
            </s>
            <s xml:id="echoid-s7470" xml:space="preserve">quo fit, ut eæ objectorum magnitudines, figuras, diſtantias </s>
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