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-s14473" xml:space="preserve">
              <pb o="114" file="0292" n="307" rhead=""/>
            _utin circumf._ </s>
            <s xml:id="echoid-s14474" xml:space="preserve">AMB ſumpto utcunque puncto M, & </s>
            <s xml:id="echoid-s14475" xml:space="preserve">per hoc trajectâ
              <lb/>
              <note position="left" xlink:label="note-0292-01" xlink:href="note-0292-01a" xml:space="preserve">Fig. 171.</note>
            rectâ BMZ, ductâque rectâ MFZ, quæ curvam AZZ ſecet in Z,
              <lb/>
            ſit MZ = AS) in recta verò α β ſumatur αμ æqualis arcui AM, & </s>
            <s xml:id="echoid-s14476" xml:space="preserve">
              <lb/>
            ad αμ applicentur rectæ perpendiculares μ ξ æquales _arcunm_ AMſinu-
              <lb/>
            _bus verſis_ AF; </s>
            <s xml:id="echoid-s14477" xml:space="preserve">erit _ſpatium trilineum_ MAZ _ſpatii αμξ duplum._</s>
            <s xml:id="echoid-s14478" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14479" xml:space="preserve">Nam ſumatur _arcus_ MNindeſinitè parvus, & </s>
            <s xml:id="echoid-s14480" xml:space="preserve">ei æqualis μν; </s>
            <s xml:id="echoid-s14481" xml:space="preserve">du-
              <lb/>
            catúrque recta NRad ABparallela, connectatúrque recta CM. </s>
            <s xml:id="echoid-s14482" xml:space="preserve">Eſt-
              <lb/>
            que jam AS. </s>
            <s xml:id="echoid-s14483" xml:space="preserve">AB (2 CM):</s>
            <s xml:id="echoid-s14484" xml:space="preserve">: (FM. </s>
            <s xml:id="echoid-s14485" xml:space="preserve">FB:</s>
            <s xml:id="echoid-s14486" xml:space="preserve">:) AF. </s>
            <s xml:id="echoid-s14487" xml:space="preserve">FM. </s>
            <s xml:id="echoid-s14488" xml:space="preserve">& </s>
            <s xml:id="echoid-s14489" xml:space="preserve">2 CM.
              <lb/>
            </s>
            <s xml:id="echoid-s14490" xml:space="preserve">2 MN:</s>
            <s xml:id="echoid-s14491" xml:space="preserve">: CM. </s>
            <s xml:id="echoid-s14492" xml:space="preserve">MN:</s>
            <s xml:id="echoid-s14493" xml:space="preserve">:) FM. </s>
            <s xml:id="echoid-s14494" xml:space="preserve">NR. </s>
            <s xml:id="echoid-s14495" xml:space="preserve">quapropter erit ex æquo AS. </s>
            <s xml:id="echoid-s14496" xml:space="preserve">
              <lb/>
            2 MN:</s>
            <s xml:id="echoid-s14497" xml:space="preserve">: AF. </s>
            <s xml:id="echoid-s14498" xml:space="preserve">NR; </s>
            <s xml:id="echoid-s14499" xml:space="preserve">& </s>
            <s xml:id="echoid-s14500" xml:space="preserve">ideò NR x AS = 2 MN x AF. </s>
            <s xml:id="echoid-s14501" xml:space="preserve">hoc eſt
              <lb/>
            NR x MZ = 2 μν x μξ. </s>
            <s xml:id="echoid-s14502" xml:space="preserve">unde _ſpatium_ MAZ _duplo ſpatio_ α μξ æ-
              <lb/>
            quatur.</s>
            <s xml:id="echoid-s14503" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14504" xml:space="preserve">Hinc cum _ſpatii_ αμξ dimenſio vulgò nota ſit, & </s>
            <s xml:id="echoid-s14505" xml:space="preserve">è ſuprà poſitis
              <lb/>
            etiam facilè deducatur; </s>
            <s xml:id="echoid-s14506" xml:space="preserve">habetur _ſpatii ciſſoidalis_ MAZ _dimenſio._ </s>
            <s xml:id="echoid-s14507" xml:space="preserve">cal-
              <lb/>
              <note position="left" xlink:label="note-0292-02" xlink:href="note-0292-02a" xml:space="preserve">Fig 172.</note>
            culum ineat qui volet.</s>
            <s xml:id="echoid-s14508" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14509" xml:space="preserve">Iſta claudet hoc _Conſectariolum:_</s>
            <s xml:id="echoid-s14510" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14511" xml:space="preserve">XV. </s>
            <s xml:id="echoid-s14512" xml:space="preserve">Sit _circuli quadrans_ ACB, _circulúmque_ tangant AH, BG;
              <lb/>
            </s>
            <s xml:id="echoid-s14513" xml:space="preserve">ſintque curvæ KZZ, LEO _byperbolœ_, eædem quæ ſuperiùs. </s>
            <s xml:id="echoid-s14514" xml:space="preserve">
              <note position="left" xlink:label="note-0292-03" xlink:href="note-0292-03a" xml:space="preserve">Fig. 173.</note>
              <note symbol="(_a_)" position="left" xlink:label="note-0292-04" xlink:href="note-0292-04a" xml:space="preserve">7, & 12.</note>
            cus verò ſumptus AMin partes diviſus concipiatur indefinitè multas
              <lb/>
            punctis N; </s>
            <s xml:id="echoid-s14515" xml:space="preserve">per quæ trajiciantur radii CN; </s>
            <s xml:id="echoid-s14516" xml:space="preserve">& </s>
            <s xml:id="echoid-s14517" xml:space="preserve">his occurrant rectæ
              <lb/>
            NXad puncta X; </s>
            <s xml:id="echoid-s14518" xml:space="preserve">_ſumma rectarum_ NX(in radiis) æquatur ſpatio
              <lb/>
            {AFZK/Rad}; </s>
            <s xml:id="echoid-s14519" xml:space="preserve">& </s>
            <s xml:id="echoid-s14520" xml:space="preserve">_ſummarectarum_ NX (in parallelis ad AS) æquatur _ſpatio_
              <lb/>
            {PLQO/3 Rad.</s>
            <s xml:id="echoid-s14521" xml:space="preserve">}.</s>
            <s xml:id="echoid-s14522" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14523" xml:space="preserve">Nam triangulum XMN triangulo SAC ſimile eſt; </s>
            <s xml:id="echoid-s14524" xml:space="preserve">& </s>
            <s xml:id="echoid-s14525" xml:space="preserve">inde XM.
              <lb/>
            </s>
            <s xml:id="echoid-s14526" xml:space="preserve">MN:</s>
            <s xml:id="echoid-s14527" xml:space="preserve">: AS. </s>
            <s xml:id="echoid-s14528" xml:space="preserve">CA. </s>
            <s xml:id="echoid-s14529" xml:space="preserve">& </s>
            <s xml:id="echoid-s14530" xml:space="preserve">XN. </s>
            <s xml:id="echoid-s14531" xml:space="preserve">MN:</s>
            <s xml:id="echoid-s14532" xml:space="preserve">: CS. </s>
            <s xml:id="echoid-s14533" xml:space="preserve">CA. </s>
            <s xml:id="echoid-s14534" xml:space="preserve">unde XM =
              <lb/>
            {MN x AS/CA}; </s>
            <s xml:id="echoid-s14535" xml:space="preserve">& </s>
            <s xml:id="echoid-s14536" xml:space="preserve">XN = {MN x CS/CA}. </s>
            <s xml:id="echoid-s14537" xml:space="preserve">& </s>
            <s xml:id="echoid-s14538" xml:space="preserve">ità in reliquis; </s>
            <s xml:id="echoid-s14539" xml:space="preserve">unde liquet
              <lb/>
            Proſitum, ex 2, & </s>
            <s xml:id="echoid-s14540" xml:space="preserve">7 harum.</s>
            <s xml:id="echoid-s14541" xml:space="preserve"/>
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