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

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          <p>
            <s xml:id="echoid-s2979" xml:space="preserve">
              <pb o="54" file="0072" n="72" rhead=""/>
            ducatur CHL ad RS parallela; </s>
            <s xml:id="echoid-s2980" xml:space="preserve">erit intercepta HL (quod requiri-
              <lb/>
            tur) æqualis ipſi Z. </s>
            <s xml:id="echoid-s2981" xml:space="preserve">Nam connectatur CG; </s>
            <s xml:id="echoid-s2982" xml:space="preserve">& </s>
            <s xml:id="echoid-s2983" xml:space="preserve">huic perpendicu-
              <lb/>
            laris ducatur GT; </s>
            <s xml:id="echoid-s2984" xml:space="preserve">ad CF proinde parallela. </s>
            <s xml:id="echoid-s2985" xml:space="preserve">quia jam ang. </s>
            <s xml:id="echoid-s2986" xml:space="preserve">GCT
              <lb/>
            = CGR = FSR, liquet rectangula trigona CGT, RFS aſſi-
              <lb/>
            milari. </s>
            <s xml:id="echoid-s2987" xml:space="preserve">adeóque fore CT. </s>
            <s xml:id="echoid-s2988" xml:space="preserve">CG :</s>
            <s xml:id="echoid-s2989" xml:space="preserve">: SR . </s>
            <s xml:id="echoid-s2990" xml:space="preserve">SF. </s>
            <s xml:id="echoid-s2991" xml:space="preserve">item (ob ſimilitudinem
              <lb/>
            triangulorum CGH, SFG) eſt CG. </s>
            <s xml:id="echoid-s2992" xml:space="preserve">GH :</s>
            <s xml:id="echoid-s2993" xml:space="preserve">: SF. </s>
            <s xml:id="echoid-s2994" xml:space="preserve">FG. </s>
            <s xml:id="echoid-s2995" xml:space="preserve">erit igi-
              <lb/>
            tur ex æquo CT. </s>
            <s xml:id="echoid-s2996" xml:space="preserve">GH :</s>
            <s xml:id="echoid-s2997" xml:space="preserve">: SR. </s>
            <s xml:id="echoid-s2998" xml:space="preserve">FG. </s>
            <s xml:id="echoid-s2999" xml:space="preserve">(hoc eſt) :</s>
            <s xml:id="echoid-s3000" xml:space="preserve">: FG. </s>
            <s xml:id="echoid-s3001" xml:space="preserve">Z. </s>
            <s xml:id="echoid-s3002" xml:space="preserve">verùm
              <lb/>
            eſt CT. </s>
            <s xml:id="echoid-s3003" xml:space="preserve">FG :</s>
            <s xml:id="echoid-s3004" xml:space="preserve">: CH. </s>
            <s xml:id="echoid-s3005" xml:space="preserve">FH :</s>
            <s xml:id="echoid-s3006" xml:space="preserve">: HG. </s>
            <s xml:id="echoid-s3007" xml:space="preserve">HL. </s>
            <s xml:id="echoid-s3008" xml:space="preserve">permutandóque CT. </s>
            <s xml:id="echoid-s3009" xml:space="preserve">HG
              <lb/>
            :</s>
            <s xml:id="echoid-s3010" xml:space="preserve">: FG. </s>
            <s xml:id="echoid-s3011" xml:space="preserve">HL. </s>
            <s xml:id="echoid-s3012" xml:space="preserve">quare FG. </s>
            <s xml:id="echoid-s3013" xml:space="preserve">Z :</s>
            <s xml:id="echoid-s3014" xml:space="preserve">: FG. </s>
            <s xml:id="echoid-s3015" xml:space="preserve">HL. </s>
            <s xml:id="echoid-s3016" xml:space="preserve">liquet igitur HL ipſi Z
              <lb/>
            datæ æquari: </s>
            <s xml:id="echoid-s3017" xml:space="preserve">Q. </s>
            <s xml:id="echoid-s3018" xml:space="preserve">E. </s>
            <s xml:id="echoid-s3019" xml:space="preserve">F.</s>
            <s xml:id="echoid-s3020" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3021" xml:space="preserve">Plures eſſe caſus poſſunt; </s>
            <s xml:id="echoid-s3022" xml:space="preserve">ut nempe punctum L ſit intra Semicircu-
              <lb/>
            lum GCF (ídque poſitum inter puncta C, G, vel inter ipſa C, F) vel
              <lb/>
              <note position="left" xlink:label="note-0072-01" xlink:href="note-0072-01a" xml:space="preserve">Fig. 73, 74.</note>
            in altero Semicirculo GE F, ultra GF ſito reſpectu puncti C; </s>
            <s xml:id="echoid-s3023" xml:space="preserve">ſed
              <lb/>
            hæc una conſtructio ſimul ac demonſtratio pariter omnibus convenit;
              <lb/>
            </s>
            <s xml:id="echoid-s3024" xml:space="preserve">ut pluribus huc non ſit opus.</s>
            <s xml:id="echoid-s3025" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3026" xml:space="preserve">VII. </s>
            <s xml:id="echoid-s3027" xml:space="preserve">Adnotetur ſaltem quoad iſtos caſus, quod ſicuti per punctum
              <lb/>
            G (ut antea commoſtratum) aliquando quatnor rectæ duci poſſunt
              <lb/>
            datam adæquantes, rectíſque FC, FV terminatæ; </s>
            <s xml:id="echoid-s3028" xml:space="preserve">binæ ſcilicet inter
              <lb/>
            angulum quo punctum G continetur, alteræque totidem extra ipſum;
              <lb/>
            </s>
            <s xml:id="echoid-s3029" xml:space="preserve">nonnunquam verò tres ſolæ; </s>
            <s xml:id="echoid-s3030" xml:space="preserve">quum data recta minima continget eſſe
              <lb/>
            cunctarum, quæ dicto punctum G continenti angulo poſſunt interſeri; </s>
            <s xml:id="echoid-s3031" xml:space="preserve">
              <lb/>
            ſubinde tantùm duæ, quando data tali minimæ cedit; </s>
            <s xml:id="echoid-s3032" xml:space="preserve">ita reſpectivè
              <lb/>
            Problema jam expoſitum plures totidem ſolutiones accipit. </s>
            <s xml:id="echoid-s3033" xml:space="preserve">Sanè
              <lb/>
            quò major eſt hîc data Z, cò minor evadet intercepta RS; </s>
            <s xml:id="echoid-s3034" xml:space="preserve">& </s>
            <s xml:id="echoid-s3035" xml:space="preserve">viciſſim
              <lb/>
            quò minor RS, eò major ipſa IZ; </s>
            <s xml:id="echoid-s3036" xml:space="preserve">unde ſi fuerit RS omnium mini-
              <lb/>
            ma, quæ angulo CFV punctum G capienti inſeri poſſunt, etiam HL
              <lb/>
            maxima erit è C prodeuntium rectarum, quæ inter diametrum GF,
              <lb/>
            & </s>
            <s xml:id="echoid-s3037" xml:space="preserve">Semicirculum GEF comprchendi poſſunt. </s>
            <s xml:id="echoid-s3038" xml:space="preserve">unde Poriſmatis loco patet,
              <lb/>
            è ſupradictis, quo pacto talis maxima ducí poſſit; </s>
            <s xml:id="echoid-s3039" xml:space="preserve">& </s>
            <s xml:id="echoid-s3040" xml:space="preserve">hoc ipſum Pro-
              <lb/>
            blema penitus determinari. </s>
            <s xml:id="echoid-s3041" xml:space="preserve">quod attendenti non obſcurum innuiſſe
              <lb/>
            ſatìs videtur. </s>
            <s xml:id="echoid-s3042" xml:space="preserve">jam ad principalis quæſiti rcſolutionem accedimus; </s>
            <s xml:id="echoid-s3043" xml:space="preserve">ità
              <lb/>
            jam brevitur propoſiti.</s>
            <s xml:id="echoid-s3044" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3045" xml:space="preserve">VIII. </s>
            <s xml:id="echoid-s3046" xml:space="preserve">Per datum punctum X rectam ducere, cujus reflexus datæ
              <lb/>
              <note position="left" xlink:label="note-0072-02" xlink:href="note-0072-02a" xml:space="preserve">Fig. 73, 74.</note>
            poſitione rectæ BC ſit parallelus.</s>
            <s xml:id="echoid-s3047" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3048" xml:space="preserve">Id ſic efficitur. </s>
            <s xml:id="echoid-s3049" xml:space="preserve">Centro X per C deſcribæur circulus GLFC;
              <lb/>
            </s>
            <s xml:id="echoid-s3050" xml:space="preserve">item per X ducatur GF ad BC parallela; </s>
            <s xml:id="echoid-s3051" xml:space="preserve">tum ex C prjoiciatur
              <lb/>
            recta, cujus ſecundum Lemma mox præcedens, intercepta pars H L
              <lb/>
            æquetur Semidiametro reflectentis circuli; </s>
            <s xml:id="echoid-s3052" xml:space="preserve">quæ & </s>
            <s xml:id="echoid-s3053" xml:space="preserve">illum ſecet in N;</s>
            <s xml:id="echoid-s3054" xml:space="preserve"/>
          </p>
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