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

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            <s xml:id="echoid-s14341" xml:space="preserve">
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            @ibus μνκμψ par) æquatur ſubduplo ſpatii PLOQ.</s>
            <s xml:id="echoid-s14342" xml:space="preserve"/>
          </p>
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            <s xml:id="echoid-s14343" xml:space="preserve">VII. </s>
            <s xml:id="echoid-s14344" xml:space="preserve">Omnia quadrata ex rectis μψ (ad rectam αμ applicais) æquant
              <lb/>
              <note position="left" xlink:label="note-0290-01" xlink:href="note-0290-01a" xml:space="preserve">Fig. 167.</note>
            CA x CP x PX(hoc eſt _parallelipipedum Baſe Rectangulo_ ACPD,
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            _Altitudine_ CS).</s>
            <s xml:id="echoid-s14345" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14346" xml:space="preserve">Hujus _Effati demonſtrationem_ (quanquam π&</s>
            <s xml:id="echoid-s14347" xml:space="preserve">χΗ&</s>
            <s xml:id="echoid-s14348" xml:space="preserve">ν) tranſilio; </s>
            <s xml:id="echoid-s14349" xml:space="preserve">quo-
              <lb/>
            niam aliud _Scbema_ diſcursúmque præ reliquis pleríſque longiuſculum
              <lb/>
            expoſcit; </s>
            <s xml:id="echoid-s14350" xml:space="preserve">neque rem tanti video.</s>
            <s xml:id="echoid-s14351" xml:space="preserve"/>
          </p>
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            <s xml:id="echoid-s14352" xml:space="preserve">VIII. </s>
            <s xml:id="echoid-s14353" xml:space="preserve">Curva AYY talis ſit, ut FY æquetur ipſi AS; </s>
            <s xml:id="echoid-s14354" xml:space="preserve">ductâ tum rectâ YI
              <lb/>
              <note position="left" xlink:label="note-0290-02" xlink:href="note-0290-02a" xml:space="preserve">Fig. 166.</note>
            ad AC parallela, erit etiam _ſpatium_ AC IY YA (hoc eſt _ſumma_
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            _Tangentium_ ad _arcum_ AM pertinentium, & </s>
            <s xml:id="echoid-s14355" xml:space="preserve">ad rectam AC applica-
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            tarum, unà cum _rectangulo_ FCIY) æquale _ſubduplo ſpatio byperbo-_
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            _lico_ PL OQ.</s>
            <s xml:id="echoid-s14356" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14357" xml:space="preserve">Nam _ſpatium_ α γ π μ æquatur _rectangule_ ACPD; </s>
            <s xml:id="echoid-s14358" xml:space="preserve">hoc
              <note symbol="a" position="left" xlink:label="note-0290-03" xlink:href="note-0290-03a" xml:space="preserve">1. Lect.
                <lb/>
              XII.</note>
            _rectangulo_ FC IY (nam eſt CA. </s>
            <s xml:id="echoid-s14359" xml:space="preserve">AS:</s>
            <s xml:id="echoid-s14360" xml:space="preserve">: CF. </s>
            <s xml:id="echoid-s14361" xml:space="preserve">FM; </s>
            <s xml:id="echoid-s14362" xml:space="preserve">vel CAFY:</s>
            <s xml:id="echoid-s14363" xml:space="preserve">:
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            CF. </s>
            <s xml:id="echoid-s14364" xml:space="preserve">CP. </s>
            <s xml:id="echoid-s14365" xml:space="preserve">adeoq; </s>
            <s xml:id="echoid-s14366" xml:space="preserve">CA x CP = FY x CF). </s>
            <s xml:id="echoid-s14367" xml:space="preserve">item ſpatium γπψ (hoc eſt omnes
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              <note symbol="(b)" position="left" xlink:label="note-0290-04" xlink:href="note-0290-04a" xml:space="preserve">14. Lect.
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              XII.</note>
            rectæ TF ad αε applicatæ, quotquot ad arcum AM pertinent) æ- quatur _ſpatio_ AFY; </s>
            <s xml:id="echoid-s14368" xml:space="preserve">ergo _ſpatium_ ACIYA æquatur _ſpatio_ αγψμ;
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            </s>
            <s xml:id="echoid-s14369" xml:space="preserve">hoc eſt (ut mox oſtenſum) _ſemiſſi ſpatii byperbolici_ PL OQ.</s>
            <s xml:id="echoid-s14370" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14371" xml:space="preserve">Aliter illud, (eíque connexa) dimenſus ſum, _boc præmiſſo Lem-_
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            _mate._</s>
            <s xml:id="echoid-s14372" xml:space="preserve"/>
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            <s xml:id="echoid-s14373" xml:space="preserve">IX. </s>
            <s xml:id="echoid-s14374" xml:space="preserve">Sit _Hyperbola aquilatera_ (axes nempe pares habens) ERK ad
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            cujus axes CE D, CI; </s>
            <s xml:id="echoid-s14375" xml:space="preserve">& </s>
            <s xml:id="echoid-s14376" xml:space="preserve">ad hos ordinatæ KI, KD; </s>
            <s xml:id="echoid-s14377" xml:space="preserve">ſit item curvâ
              <lb/>
              <note position="left" xlink:label="note-0290-05" xlink:href="note-0290-05a" xml:space="preserve">Fig. 168.</note>
            EVY talis, ut in _byperbola_ liberè ſumpto puncto R, ductâque recta
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            RVS ad DC parallelâ, ſint SR, CE, SV continuè proportiona-
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            les; </s>
            <s xml:id="echoid-s14378" xml:space="preserve">connexâ rectâ CK, erit _Spatium_ CE YI _Sectoris byperbolici_
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            KCE duplum.</s>
            <s xml:id="echoid-s14379" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14380" xml:space="preserve">Nam ducatur RT _byperbolam_ tangens, & </s>
            <s xml:id="echoid-s14381" xml:space="preserve">R Had CI parallela.
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            </s>
            <s xml:id="echoid-s14382" xml:space="preserve">Eſtque CH. </s>
            <s xml:id="echoid-s14383" xml:space="preserve">CE:</s>
            <s xml:id="echoid-s14384" xml:space="preserve">: CE. </s>
            <s xml:id="echoid-s14385" xml:space="preserve">CT. </s>
            <s xml:id="echoid-s14386" xml:space="preserve">quare CT = SV; </s>
            <s xml:id="echoid-s14387" xml:space="preserve">vel HT = RV. </s>
            <s xml:id="echoid-s14388" xml:space="preserve">
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            itaque _Spatium_ ED KY duplum eſt _ſegmenti_ EDK. </s>
            <s xml:id="echoid-s14389" xml:space="preserve">item _rectangu-_
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              <note position="left" xlink:label="note-0290-06" xlink:href="note-0290-06a" xml:space="preserve">10 Lect. XI.</note>
            _lum_ IKDC _trianguli_ CDK duplum eſt; </s>
            <s xml:id="echoid-s14390" xml:space="preserve">ergo _reliquum ſpatium_
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            CE YI _reliqui ſectoris_ ECK duplum eſt.</s>
            <s xml:id="echoid-s14391" xml:space="preserve"/>
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            <s xml:id="echoid-s14392" xml:space="preserve">X. </s>
            <s xml:id="echoid-s14393" xml:space="preserve">Reſumptâ jam quadrante circulari AC B, ſit CE = CA;
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            </s>
            <s xml:id="echoid-s14394" xml:space="preserve">& </s>
            <s xml:id="echoid-s14395" xml:space="preserve">axe AE, _parametro etiam_ AE, deſcripta ſit _Hyperbola_ EKK; </s>
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              <note position="left" xlink:label="note-0290-07" xlink:href="note-0290-07a" xml:space="preserve">Fig. 169.</note>
            poſitóque curvam AYY talem eſſe, ut ordinatâ quâcunque rectâ
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            MFY, ſit FY tangenti AS æqualis; </s>
            <s xml:id="echoid-s14397" xml:space="preserve">ducatur recta YIK </s>
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