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-div22" type="section" level="1" n="11">
          <p>
            <s xml:id="echoid-s829" xml:space="preserve">
              <pb o="23" file="0041" n="41" rhead=""/>
            ctum. </s>
            <s xml:id="echoid-s830" xml:space="preserve">His utcunque majoris evidentiæ cauſâ, prælibatis, ad corolla-
              <lb/>
            ria quæ diximus expromenda nos conferemus è veſtigio.</s>
            <s xml:id="echoid-s831" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s832" xml:space="preserve">II. </s>
            <s xml:id="echoid-s833" xml:space="preserve">Imprimis autem (poſthac quidem in decurſu, quoad plures ſibi
              <lb/>
            parallelos, aut ab eodem puncto divergentes (velin idem convergen-
              <lb/>
            tes) & </s>
            <s xml:id="echoid-s834" xml:space="preserve">huic vel illi ſingulari, quæ tractanda veniet, ſuperficiei inciden-
              <lb/>
            tes (radios, ſingularia quotvis inflexos deſignandi compendia, radia-
              <lb/>
            tionibus organicè examinandis profutura, tradituri) generales nunc
              <lb/>
            aliquos incidenti cuivis propoſito competentem inflexum aſſignandi
              <lb/>
            modos proponemus; </s>
            <s xml:id="echoid-s835" xml:space="preserve">quorum adhiberi poſſit, qui rei natæ videbitur
              <lb/>
            accommodatior. </s>
            <s xml:id="echoid-s836" xml:space="preserve">Pro reflectione. </s>
            <s xml:id="echoid-s837" xml:space="preserve">Incidat radius AB ad B; </s>
            <s xml:id="echoid-s838" xml:space="preserve">Et per
              <lb/>
            B ducatur QB reflectenti perpendicularis; </s>
            <s xml:id="echoid-s839" xml:space="preserve">& </s>
            <s xml:id="echoid-s840" xml:space="preserve">fiat ang. </s>
            <s xml:id="echoid-s841" xml:space="preserve">_a_ BQ = ang.
              <lb/>
            </s>
            <s xml:id="echoid-s842" xml:space="preserve">ABQ, vel per B ducta ſit EF reflectentem tangens; </s>
            <s xml:id="echoid-s843" xml:space="preserve">& </s>
            <s xml:id="echoid-s844" xml:space="preserve">fiat ang. </s>
            <s xml:id="echoid-s845" xml:space="preserve">
              <lb/>
            a BF = ang. </s>
            <s xml:id="echoid-s846" xml:space="preserve">ABE; </s>
            <s xml:id="echoid-s847" xml:space="preserve">liquetque factum eſſe, modo utrovis, quod
              <lb/>
              <note position="right" xlink:label="note-0041-01" xlink:href="note-0041-01a" xml:space="preserve">Fig. 16.
                <lb/>
              Fig. 17, 18,
                <lb/>
              19.</note>
            requirebatur, Pro refractione vero; </s>
            <s xml:id="echoid-s848" xml:space="preserve">ducatur QB refringenti per-
              <lb/>
            pendicularis, & </s>
            <s xml:id="echoid-s849" xml:space="preserve">ſuper diametrum (in hac liberè ſumptam) QB de-
              <lb/>
            ſcribatur ſemicirculus, incidentem AB ſecans in R; </s>
            <s xml:id="echoid-s850" xml:space="preserve">tum adjunctâ
              <lb/>
            QR, factóque I. </s>
            <s xml:id="echoid-s851" xml:space="preserve">R :</s>
            <s xml:id="echoid-s852" xml:space="preserve">: QR. </s>
            <s xml:id="echoid-s853" xml:space="preserve">T (terminis autem I, R hìc & </s>
            <s xml:id="echoid-s854" xml:space="preserve">dehinc
              <lb/>
            perpetuò proportio refractiones metiens indignitatur) circulo QRB
              <lb/>
            adaptetur QS ipſam T exæquans; </s>
            <s xml:id="echoid-s855" xml:space="preserve">erit connexa SB protracta nempe)
              <lb/>
            incidentis AB refracta. </s>
            <s xml:id="echoid-s856" xml:space="preserve">? </s>
            <s xml:id="echoid-s857" xml:space="preserve">Vel: </s>
            <s xml:id="echoid-s858" xml:space="preserve">perincidentiæ punctum B ducatur EF
              <lb/>
            refringentem contingens; </s>
            <s xml:id="echoid-s859" xml:space="preserve">& </s>
            <s xml:id="echoid-s860" xml:space="preserve">in hac utcunque ſumpta BK ſit circuli
              <lb/>
            diameter, incidentem AB ſecantis ad R; </s>
            <s xml:id="echoid-s861" xml:space="preserve">& </s>
            <s xml:id="echoid-s862" xml:space="preserve">fiat I. </s>
            <s xml:id="echoid-s863" xml:space="preserve">R:</s>
            <s xml:id="echoid-s864" xml:space="preserve">: BR. </s>
            <s xml:id="echoid-s865" xml:space="preserve">T;
              <lb/>
            </s>
            <s xml:id="echoid-s866" xml:space="preserve">& </s>
            <s xml:id="echoid-s867" xml:space="preserve">adaptetur BS = T; </s>
            <s xml:id="echoid-s868" xml:space="preserve">erit SB _a_ ipſius AB refractus: </s>
            <s xml:id="echoid-s869" xml:space="preserve">Vel demum: </s>
            <s xml:id="echoid-s870" xml:space="preserve">
              <lb/>
            In ipſa AB ſumptâ utcunque diametro RB, ſuper hac deſcriptus cir-
              <lb/>
            culus ſecet perpendicularem QB ad Q; </s>
            <s xml:id="echoid-s871" xml:space="preserve">vel tangentem EF in K; </s>
            <s xml:id="echoid-s872" xml:space="preserve">
              <lb/>
            fiátque I. </s>
            <s xml:id="echoid-s873" xml:space="preserve">R :</s>
            <s xml:id="echoid-s874" xml:space="preserve">: BK. </s>
            <s xml:id="echoid-s875" xml:space="preserve">T. </s>
            <s xml:id="echoid-s876" xml:space="preserve">& </s>
            <s xml:id="echoid-s877" xml:space="preserve">adaptetur QS = T; </s>
            <s xml:id="echoid-s878" xml:space="preserve">erit rurſus SB _a_ inci-
              <lb/>
            dentis AB refractus. </s>
            <s xml:id="echoid-s879" xml:space="preserve">quorum ratio è poſitis inflectionum legibus ad-
              <lb/>
            modum eſt manifeſta. </s>
            <s xml:id="echoid-s880" xml:space="preserve">verba piget impendere.</s>
            <s xml:id="echoid-s881" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s882" xml:space="preserve">III. </s>
            <s xml:id="echoid-s883" xml:space="preserve">Radii cujuſvis incidentis inflexus inflexi viciſſim incidens
              <lb/>
            evadet.</s>
            <s xml:id="echoid-s884" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s885" xml:space="preserve">Hoc plerique, diverſè paullò prolatum, accipiunt, aut poſtulant.
              <lb/>
            </s>
            <s xml:id="echoid-s886" xml:space="preserve">
              <note position="right" xlink:label="note-0041-02" xlink:href="note-0041-02a" xml:space="preserve">_Albaz_. VII. 4.
                <lb/>
              _Herig. Catop_.
                <lb/>
              _Axiom._ 2.</note>
            è præmiſtis autem facillimè colligitur. </s>
            <s xml:id="echoid-s887" xml:space="preserve">Idque potius methodi gratiâ
              <lb/>
            (ſicut & </s>
            <s xml:id="echoid-s888" xml:space="preserve">nonnulla quæ ſequentur) quàm quia res meretur, oſtende-
              <lb/>
            mus. </s>
            <s xml:id="echoid-s889" xml:space="preserve">Proreflectione; </s>
            <s xml:id="echoid-s890" xml:space="preserve">Radius AB ſpeculo EF impingens reflectatur
              <lb/>
              <note position="right" xlink:label="note-0041-03" xlink:href="note-0041-03a" xml:space="preserve">Fig. 1, 16.</note>
            in B _a_; </s>
            <s xml:id="echoid-s891" xml:space="preserve">dico radium B _a_ permutatim in BA reflecti. </s>
            <s xml:id="echoid-s892" xml:space="preserve">Nam quoniam
              <lb/>
            AB incidens reflectitur in B _a_, erit ang. </s>
            <s xml:id="echoid-s893" xml:space="preserve">_a_ BF æ qualis angulo ABE.
              <lb/>
            </s>
            <s xml:id="echoid-s894" xml:space="preserve">Poſito jam _a_ B incidere, etiam angulus quem facit ejus reflexus cum
              <lb/>
            BE æquabitur angulo _a_ BF; </s>
            <s xml:id="echoid-s895" xml:space="preserve">proinde non alius erit ab ipſo ABE
              <lb/>
            quare BA ipſius _a_ B reflexus erit.</s>
            <s xml:id="echoid-s896" xml:space="preserve"/>
          </p>
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