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">
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          <p>
            <s xml:id="echoid-s14031" xml:space="preserve">Nam ob MN. </s>
            <s xml:id="echoid-s14032" xml:space="preserve">NR:</s>
            <s xml:id="echoid-s14033" xml:space="preserve">: PM. </s>
            <s xml:id="echoid-s14034" xml:space="preserve">MF:</s>
            <s xml:id="echoid-s14035" xml:space="preserve">: PQ. </s>
            <s xml:id="echoid-s14036" xml:space="preserve">QA; </s>
            <s xml:id="echoid-s14037" xml:space="preserve">erit MN x
              <lb/>
            QA = NR x QA; </s>
            <s xml:id="echoid-s14038" xml:space="preserve">hoc eſt rectang. </s>
            <s xml:id="echoid-s14039" xml:space="preserve">μ θ = rectang. </s>
            <s xml:id="echoid-s14040" xml:space="preserve">FH.</s>
            <s xml:id="echoid-s14041" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14042" xml:space="preserve">X. </s>
            <s xml:id="echoid-s14043" xml:space="preserve">Porrò, curvam AB tangat recta MT, ſintque curvæ DXO,
              <lb/>
            α φ δ tales, ut EX æquetur ipſi MT, & </s>
            <s xml:id="echoid-s14044" xml:space="preserve">μ φ ipſi MF; </s>
            <s xml:id="echoid-s14045" xml:space="preserve">erit ſpatium
              <lb/>
            α β δ æquale _ſpatio_ DXOB.</s>
            <s xml:id="echoid-s14046" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">Fig. 158.
            <lb/>
          159.</note>
          <p>
            <s xml:id="echoid-s14047" xml:space="preserve">Nam MN. </s>
            <s xml:id="echoid-s14048" xml:space="preserve">MR:</s>
            <s xml:id="echoid-s14049" xml:space="preserve">: MT. </s>
            <s xml:id="echoid-s14050" xml:space="preserve">MF. </s>
            <s xml:id="echoid-s14051" xml:space="preserve">quare MN x MF = MR x MT;
              <lb/>
            </s>
            <s xml:id="echoid-s14052" xml:space="preserve">hoc eſt μ ν x μφ = ES x EX; </s>
            <s xml:id="echoid-s14053" xml:space="preserve">unde patet.</s>
            <s xml:id="echoid-s14054" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14055" xml:space="preserve">XI. </s>
            <s xml:id="echoid-s14056" xml:space="preserve">Hinc rurſus, _ſuperficies ſolidi ex ſpatii_ ABD circa axem AD
              <lb/>
            converſione progeniti ad _ſpatium_ DX OB ſe habet, ut _Circuli Cir-_
              <lb/>
              <note position="right" xlink:label="note-0285-02" xlink:href="note-0285-02a" xml:space="preserve">Fig. 158.</note>
            _cumf._ </s>
            <s xml:id="echoid-s14057" xml:space="preserve">ad _radium_; </s>
            <s xml:id="echoid-s14058" xml:space="preserve">hoc igitur noto ſimul illa innoteſcet. </s>
            <s xml:id="echoid-s14059" xml:space="preserve">unde rurſus
              <lb/>
            _Spbaroidum, Conoidumque ſuperficies_ dimetiri licebit.</s>
            <s xml:id="echoid-s14060" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14061" xml:space="preserve">XII. </s>
            <s xml:id="echoid-s14062" xml:space="preserve">Si linea DYI talis fuerit, ut ſit EY = √ EX x MF; </s>
            <s xml:id="echoid-s14063" xml:space="preserve">erit
              <lb/>
            _ſolidum_ ex _ſpatio_ αβδ circa axem αβ rotato factum æ quale _ſolido, quod_
              <lb/>
            _ex ſpatio_ DBI circa axem DB rotato progignitur.</s>
            <s xml:id="echoid-s14064" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14065" xml:space="preserve">Etenim eſt MN. </s>
            <s xml:id="echoid-s14066" xml:space="preserve">MR:</s>
            <s xml:id="echoid-s14067" xml:space="preserve">: MT x MF. </s>
            <s xml:id="echoid-s14068" xml:space="preserve">MF q:</s>
            <s xml:id="echoid-s14069" xml:space="preserve">: EX x MF. </s>
            <s xml:id="echoid-s14070" xml:space="preserve">MFq
              <lb/>
              <note position="right" xlink:label="note-0285-03" xlink:href="note-0285-03a" xml:space="preserve">Fig. 158.
                <lb/>
              159.</note>
            :</s>
            <s xml:id="echoid-s14071" xml:space="preserve">: EYq. </s>
            <s xml:id="echoid-s14072" xml:space="preserve">MFq. </s>
            <s xml:id="echoid-s14073" xml:space="preserve">quare MN x MFq = MR x EYq. </s>
            <s xml:id="echoid-s14074" xml:space="preserve">hoc eſt μ ν
              <lb/>
            x μ φ q = ES x EYq.</s>
            <s xml:id="echoid-s14075" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14076" xml:space="preserve">XIII. </s>
            <s xml:id="echoid-s14077" xml:space="preserve">Simili ratione _Cuborum (aliarumque poteſtatum)_ ex ordina-
              <lb/>
            tis μ φ _ſummas_ cum _ſpatiis_ ad rectam DB computatis licebit conferre.</s>
            <s xml:id="echoid-s14078" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14079" xml:space="preserve">XIV. </s>
            <s xml:id="echoid-s14080" xml:space="preserve">Sint prætereà lineæ AZK, αξψ ætales, ut FZ ipſi MT, & </s>
            <s xml:id="echoid-s14081" xml:space="preserve">
              <lb/>
            μξ ipſi TF æquentur; </s>
            <s xml:id="echoid-s14082" xml:space="preserve">_ſpatium_ αβψ æquabitur _ſpatio_ ADK.</s>
            <s xml:id="echoid-s14083" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14084" xml:space="preserve">Etenim MN. </s>
            <s xml:id="echoid-s14085" xml:space="preserve">NR:</s>
            <s xml:id="echoid-s14086" xml:space="preserve">: MT. </s>
            <s xml:id="echoid-s14087" xml:space="preserve">TF; </s>
            <s xml:id="echoid-s14088" xml:space="preserve">hoc eſt μ ν. </s>
            <s xml:id="echoid-s14089" xml:space="preserve">FG:</s>
            <s xml:id="echoid-s14090" xml:space="preserve">: FZ. </s>
            <s xml:id="echoid-s14091" xml:space="preserve">μ ξ.
              <lb/>
            </s>
            <s xml:id="echoid-s14092" xml:space="preserve">
              <note position="right" xlink:label="note-0285-04" xlink:href="note-0285-04a" xml:space="preserve">Fig. 158.
                <lb/>
              159.</note>
            quare μ ν x μ ξ = FG x FZ.</s>
            <s xml:id="echoid-s14093" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14094" xml:space="preserve">XV. </s>
            <s xml:id="echoid-s14095" xml:space="preserve">Etiam _ſumma quadratorum_ ex qpplicatis μ ξ æquatur _ſummæ_
              <lb/>
            _Rectangulorum_ ex TF, FZ; </s>
            <s xml:id="echoid-s14096" xml:space="preserve">& </s>
            <s xml:id="echoid-s14097" xml:space="preserve">_ſumma Cuborum_ ex μ ξ æquantur
              <lb/>
            ipſis TFq x FZ (ad rectam ſcilicet AD computationem exigendo)
              <lb/>
              <note position="right" xlink:label="note-0285-05" xlink:href="note-0285-05a" xml:space="preserve">Fig. 158,
                <lb/>
              159.</note>
            paríque quoad cæteras poteſtates modò.</s>
            <s xml:id="echoid-s14098" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14099" xml:space="preserve">XVI. </s>
            <s xml:id="echoid-s14100" xml:space="preserve">Rurſus ponatur recta QMP curvæ AMB perpendicularis;
              <lb/>
            </s>
            <s xml:id="echoid-s14101" xml:space="preserve">ſitque recta β δ æqualis ipſi BD, & </s>
            <s xml:id="echoid-s14102" xml:space="preserve">compleatur _Rectangulum_ αβδζ; </s>
            <s xml:id="echoid-s14103" xml:space="preserve">
              <lb/>
            tum curva KZL talis ſit, ut FZ ipſi QP æquetur; </s>
            <s xml:id="echoid-s14104" xml:space="preserve">erit _rectang._ </s>
            <s xml:id="echoid-s14105" xml:space="preserve">αβδζ
              <lb/>
              <note position="right" xlink:label="note-0285-06" xlink:href="note-0285-06a" xml:space="preserve">Fig. 160,
                <lb/>
              161.</note>
            æquale _ſpatio_ AD LK.</s>
            <s xml:id="echoid-s14106" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s14107" xml:space="preserve">Nam eſt MN. </s>
            <s xml:id="echoid-s14108" xml:space="preserve">NR:</s>
            <s xml:id="echoid-s14109" xml:space="preserve">: (PM. </s>
            <s xml:id="echoid-s14110" xml:space="preserve">MF:</s>
            <s xml:id="echoid-s14111" xml:space="preserve">:) PQIF. </s>
            <s xml:id="echoid-s14112" xml:space="preserve">quare MN
              <lb/>
            x IF = NR x PQ; </s>
            <s xml:id="echoid-s14113" xml:space="preserve">hoc eſt μν x μξ = FG x FZ. </s>
            <s xml:id="echoid-s14114" xml:space="preserve">unde patet.</s>
            <s xml:id="echoid-s14115" xml:space="preserve"/>
          </p>
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