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-div434" type="section" level="1" n="43">
          <head xml:id="echoid-head46" xml:space="preserve">
            <emph style="sc">Lect</emph>
          . XII.</head>
          <p>
            <s xml:id="echoid-s13930" xml:space="preserve">IN ſuſcepto negotio progredimur; </s>
            <s xml:id="echoid-s13931" xml:space="preserve">quod ut (quatenus licet) decurte-
              <lb/>
              <note position="right" xlink:label="note-0283-01" xlink:href="note-0283-01a" xml:space="preserve">_Praparati@_
                <lb/>
              _Communis_.</note>
            mus, verbíſque parcamus; </s>
            <s xml:id="echoid-s13932" xml:space="preserve">obſervetur, in ſequentibus ubique _line-_
              <lb/>
            _am_ AB _curvam_ eſſe (quales tractamus) quampiam; </s>
            <s xml:id="echoid-s13933" xml:space="preserve">cujus _Axis_ AD;
              <lb/>
            </s>
            <s xml:id="echoid-s13934" xml:space="preserve">huic applicatas omnes rectas BD, CA, MF, NG perpendiculares; </s>
            <s xml:id="echoid-s13935" xml:space="preserve">
              <lb/>
            & </s>
            <s xml:id="echoid-s13936" xml:space="preserve">ME, NS, CB parallelas eſſe; </s>
            <s xml:id="echoid-s13937" xml:space="preserve">_punctum_ M liberè ſumi; </s>
            <s xml:id="echoid-s13938" xml:space="preserve">_arcum_
              <lb/>
            MN indefinitè parvum eſſe; </s>
            <s xml:id="echoid-s13939" xml:space="preserve">rectam α β curvæ VB, α μ curvæ AM,
              <lb/>
            μ ν _arcui_ MN æquales eſſe; </s>
            <s xml:id="echoid-s13940" xml:space="preserve">ad rectam α β applicatas ei perpendicu-
              <lb/>
            lares eſſe. </s>
            <s xml:id="echoid-s13941" xml:space="preserve">His præſtratis,</s>
          </p>
          <p>
            <s xml:id="echoid-s13942" xml:space="preserve">I. </s>
            <s xml:id="echoid-s13943" xml:space="preserve">Sit MP curvæ AB perpendicularis; </s>
            <s xml:id="echoid-s13944" xml:space="preserve">& </s>
            <s xml:id="echoid-s13945" xml:space="preserve">lineæ KZ L, α φ δta-
              <lb/>
              <note position="right" xlink:label="note-0283-02" xlink:href="note-0283-02a" xml:space="preserve">Fig. 156,
                <lb/>
              157.</note>
            les, ut FZ ipſi MP, & </s>
            <s xml:id="echoid-s13946" xml:space="preserve">μ φ ipſi M Fæquentur; </s>
            <s xml:id="echoid-s13947" xml:space="preserve">erît _ſpatium_ α β δ ipſi
              <lb/>
            AD LK æquale.</s>
            <s xml:id="echoid-s13948" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13949" xml:space="preserve">Nam _Triangula_ MRN, PFM ſimilia ſunt, adeoque MN. </s>
            <s xml:id="echoid-s13950" xml:space="preserve">NR
              <lb/>
            :</s>
            <s xml:id="echoid-s13951" xml:space="preserve">: PM. </s>
            <s xml:id="echoid-s13952" xml:space="preserve">MF. </s>
            <s xml:id="echoid-s13953" xml:space="preserve">unde MN x MF = NR x PM, hoc eſt (ſubſtitutis
              <lb/>
            æqualibus) μ ν x μ φ = FG x FZ; </s>
            <s xml:id="echoid-s13954" xml:space="preserve">ſeu rectang. </s>
            <s xml:id="echoid-s13955" xml:space="preserve">μ θ = rectang. </s>
            <s xml:id="echoid-s13956" xml:space="preserve">FH;
              <lb/>
            </s>
            <s xml:id="echoid-s13957" xml:space="preserve">ſpatium verò α β δ minimè differt ab indeſinitè multis rectangulis,
              <lb/>
            qualia μθ & </s>
            <s xml:id="echoid-s13958" xml:space="preserve">ſpatium AD LK totidem rectangulis, qualia FH, æ-
              <lb/>
            quivalet. </s>
            <s xml:id="echoid-s13959" xml:space="preserve">unde liquet Propoſitum.</s>
            <s xml:id="echoid-s13960" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13961" xml:space="preserve">II. </s>
            <s xml:id="echoid-s13962" xml:space="preserve">Hinc, ſi curva AMB circa axem AD rotetur, habebit ſe _pro._
              <lb/>
            </s>
            <s xml:id="echoid-s13963" xml:space="preserve">_ducta ſuperficies_ ad _ſpatium_ AD LK, ut _Circumferentia circuli Ad ra-_
              <lb/>
              <note position="right" xlink:label="note-0283-03" xlink:href="note-0283-03a" xml:space="preserve">Fig. 156.</note>
            _dium_; </s>
            <s xml:id="echoid-s13964" xml:space="preserve">unde noto ſpatio AD LK cognoſcetur dicta _ſuperficies._ </s>
            <s xml:id="echoid-s13965" xml:space="preserve">Con-
              <lb/>
            ſequentiæ rationem jam anteà pridem aſſignavimus.</s>
            <s xml:id="echoid-s13966" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s13967" xml:space="preserve">III. </s>
            <s xml:id="echoid-s13968" xml:space="preserve">Exhinc _Spbæræ, Spbæroidis_ utriuſque, _Conidúmque ſuperficies_
              <lb/>
            _dimenſionem_ accipiunt; </s>
            <s xml:id="echoid-s13969" xml:space="preserve">nam ſi AD ſit conicæ ſectionis, à qua iſtæ
              <lb/>
            figuræ oriuntur, axis; </s>
            <s xml:id="echoid-s13970" xml:space="preserve">linea KZL ſemper aliqua conicarum exiſtet,
              <lb/>
            haud difficili negotio determinabilis. </s>
            <s xml:id="echoid-s13971" xml:space="preserve">Hoc ſuggero tantùm, quoniam
              <lb/>
            nunc evulgatum habet ur.</s>
            <s xml:id="echoid-s13972" xml:space="preserve"/>
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