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="85" file="0263" n="278"/>
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        <div xml:id="echoid-div381" type="section" level="1" n="41">
          <head xml:id="echoid-head44" xml:space="preserve">
            <emph style="sc">Lect</emph>
          . XI.</head>
          <p>
            <s xml:id="echoid-s12449" xml:space="preserve">R Eliquis utcunque patratis, apponemus iam _quæ ad magnitudinum_
              <lb/>
            è _tangentibus_ (ſeu è perpendicularibus ad curvas) _Dimenſiones_
              <lb/>
            _eliciendas pertinentia ſe objecerunt Tbeoremata_; </s>
            <s xml:id="echoid-s12450" xml:space="preserve">de compluribus utiq;
              <lb/>
            </s>
            <s xml:id="echoid-s12451" xml:space="preserve">ſelectiora quædam.</s>
            <s xml:id="echoid-s12452" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12453" xml:space="preserve">I Sit curva quæpiam VH (cujus axis VD, applicata HD ad VD
              <lb/>
            normalis) item linea φZψ talis, ut ſi à curvæ puncto liberè ſumpto
              <lb/>
              <note position="right" xlink:label="note-0263-01" xlink:href="note-0263-01a" xml:space="preserve">Fig. 122.</note>
            (putaE) ducatur recta EP ad curvam perpendicularis, & </s>
            <s xml:id="echoid-s12454" xml:space="preserve">recta EAZ ad
              <lb/>
            axem perpenicularis, ſit recta AZ interceptæ AP æqualis; </s>
            <s xml:id="echoid-s12455" xml:space="preserve">erit _ſpatium_
              <lb/>
            ADψφ_æq@ lis ſemiſſi quadr ati_ ex recta DH.</s>
            <s xml:id="echoid-s12456" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12457" xml:space="preserve">Nam ſit angulus HDO ſemirectus; </s>
            <s xml:id="echoid-s12458" xml:space="preserve">& </s>
            <s xml:id="echoid-s12459" xml:space="preserve">æquiſecetur recta V Din-
              <lb/>
            definitè punctis A, B, C; </s>
            <s xml:id="echoid-s12460" xml:space="preserve">per quæ ducantur rectæ EAZ, FBZ,
              <lb/>
            GCZ, ad HD parallelæ; </s>
            <s xml:id="echoid-s12461" xml:space="preserve">curvæ occurrentes in E, F, G; </s>
            <s xml:id="echoid-s12462" xml:space="preserve">à quibus
              <lb/>
            rectæ EIY, FKY, GLY ad VD (vel HO) parallelæ ducantur;
              <lb/>
            </s>
            <s xml:id="echoid-s12463" xml:space="preserve">quin & </s>
            <s xml:id="echoid-s12464" xml:space="preserve">rectæ EP, FP, GP, HP curvæ VH perpendiculares ſint; </s>
            <s xml:id="echoid-s12465" xml:space="preserve">li-
              <lb/>
            neæ verò ſe interſecent; </s>
            <s xml:id="echoid-s12466" xml:space="preserve">ut vides. </s>
            <s xml:id="echoid-s12467" xml:space="preserve">Eſtque triangulum HLG ſimile
              <lb/>
            triangulo PDH (nam ob indefinitam ſectionem curvula GH pro re-
              <lb/>
            ctà haberiporeſt) quare HL. </s>
            <s xml:id="echoid-s12468" xml:space="preserve">LG:</s>
            <s xml:id="echoid-s12469" xml:space="preserve">: PD. </s>
            <s xml:id="echoid-s12470" xml:space="preserve">DH. </s>
            <s xml:id="echoid-s12471" xml:space="preserve">adeóque HL x DH
              <lb/>
            = LG x PD; </s>
            <s xml:id="echoid-s12472" xml:space="preserve">hoc eſt HL x HO = DC x Dψ. </s>
            <s xml:id="echoid-s12473" xml:space="preserve">Simili monſtra
              <lb/>
            bitur diſcurſu, quoniam triangulum GMF triangulo PCG aſſimila-
              <lb/>
            tur, fore LK x LY = CB x CZ; </s>
            <s xml:id="echoid-s12474" xml:space="preserve">& </s>
            <s xml:id="echoid-s12475" xml:space="preserve">ſimiliter KI x KY = BA x
              <lb/>
            BZ; </s>
            <s xml:id="echoid-s12476" xml:space="preserve">itidem denuò ID x IY = AV x AZ; </s>
            <s xml:id="echoid-s12477" xml:space="preserve">unde conſtat triangu-
              <lb/>
            lum HDO (quod a rectangulis HL x HO + LK x LY + KI x
              <lb/>
            KY + ID x IY mi@mè differt) æqu@i ſoatio VDψφ (quod iti-
              <lb/>
            dem à rectangulis DC x Dψ + CB x CZ + BA x BZ + AV
              <lb/>
            x AZ minimè differt); </s>
            <s xml:id="echoid-s12478" xml:space="preserve">hoc eſt {DHq/2} æquari ſpatio VDψφ.</s>
            <s xml:id="echoid-s12479" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s12480" xml:space="preserve">Longiordiſcurſus apagogicus adhiberi poſſit, at quorſum?</s>
            <s xml:id="echoid-s12481" xml:space="preserve"/>
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