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-div173" type="section" level="1" n="21">
          <pb o="107" file="0125" n="125" rhead=""/>
          <p>
            <s xml:id="echoid-s7130" xml:space="preserve">Quinimò methodum hanc leviculam adhibendo pleraſque ſuperfi-
              <lb/>
            cierum quarumvis inſlectentium hujus generis affectiones (illas nempe
              <lb/>
            quæ magnitudinum apparentes quantitates, poſitiones, diſtantias,
              <lb/>
            figuras reſpiciunt) compluriúmque _Phænomenωv_ cauſas ipſe ſtatim o-
              <lb/>
            perâ levi deprehendes; </s>
            <s xml:id="echoid-s7131" xml:space="preserve">quibus in expreſſiùs deducendis libri plures ad
              <lb/>
            tantam molem extumeſcere vel poſſunt, vel ſolent; </s>
            <s xml:id="echoid-s7132" xml:space="preserve">ut mihi ſaltem
              <lb/>
            opus non ſit hujuſmodi plura congerere. </s>
            <s xml:id="echoid-s7133" xml:space="preserve">veruntamen nè pars hæc
              <lb/>
            nimium deficiat, & </s>
            <s xml:id="echoid-s7134" xml:space="preserve">quoniam nonnulla ſuccurrunt animadverſione non
              <lb/>
            indigna, de magnitudinum etiam apparentiis, tam _Dioptricis_ quàm
              <lb/>
            _Catoptricis,_ ſpecialia quædam proponam; </s>
            <s xml:id="echoid-s7135" xml:space="preserve">ea verò commodius ſe-
              <lb/>
            quentem præſtolabuntur Lectionem.</s>
            <s xml:id="echoid-s7136" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7137" xml:space="preserve">Huic interim, nè abnormiter curta ſit, aliquatenus explendæ _Pro-_
              <lb/>
            _blemation_ hoc adnectam:</s>
            <s xml:id="echoid-s7138" xml:space="preserve"/>
          </p>
          <p style="it">
            <s xml:id="echoid-s7139" xml:space="preserve">Exponatur oculo, cujus centrum O, longinquum objectum FG,
              <lb/>
            ab oculi, circulique refringentis axe ABO biſectum; </s>
            <s xml:id="echoid-s7140" xml:space="preserve">datúſque ſit
              <lb/>
            angulus ſimpliciter (oculo nempe nudo) apparens FOG. </s>
            <s xml:id="echoid-s7141" xml:space="preserve">item aſſig-
              <lb/>
            netur punctum Z, quod imago ſit puncti A à circulo refringeute facta;
              <lb/>
            </s>
            <s xml:id="echoid-s7142" xml:space="preserve">datus ſit denuò ex refractione apparens angulus POQ; </s>
            <s xml:id="echoid-s7143" xml:space="preserve">propoſitum eſt
              <lb/>
              <note position="right" xlink:label="note-0125-01" xlink:href="note-0125-01a" xml:space="preserve">Fig. 175.</note>
            circulum iſtum refringentem deſcribere (vel determinare).</s>
            <s xml:id="echoid-s7144" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7145" xml:space="preserve">_Analyſis._ </s>
            <s xml:id="echoid-s7146" xml:space="preserve">Factum eſto; </s>
            <s xml:id="echoid-s7147" xml:space="preserve">ſit nempe circulus BN, qualis requiritur,
              <lb/>
            cujus ſit centrum C, vertex B; </s>
            <s xml:id="echoid-s7148" xml:space="preserve">& </s>
            <s xml:id="echoid-s7149" xml:space="preserve">qui rectam OP in N ſecet. </s>
            <s xml:id="echoid-s7150" xml:space="preserve">duca-
              <lb/>
            tur CY ad OF parallela, rectæque OP occurrens in Y, & </s>
            <s xml:id="echoid-s7151" xml:space="preserve">con-
              <lb/>
            nectatur CN. </s>
            <s xml:id="echoid-s7152" xml:space="preserve">cum itaque ſit NY refractus radii ad FO, vel CY
              <lb/>
            paralleli; </s>
            <s xml:id="echoid-s7153" xml:space="preserve">erit CY. </s>
            <s xml:id="echoid-s7154" xml:space="preserve">YN :</s>
            <s xml:id="echoid-s7155" xml:space="preserve">: R. </s>
            <s xml:id="echoid-s7156" xml:space="preserve">I. </s>
            <s xml:id="echoid-s7157" xml:space="preserve">ergò ratio CY ad YN datur; </s>
            <s xml:id="echoid-s7158" xml:space="preserve">& </s>
            <s xml:id="echoid-s7159" xml:space="preserve">
              <lb/>
            cùm prætereà angulus Y (dato FOP æqualis) detur, etiam (in tri-
              <lb/>
            angulo CYN) angulus CNY innoteſcet. </s>
            <s xml:id="echoid-s7160" xml:space="preserve">itaque triangulum CON
              <lb/>
            ſpecie datur; </s>
            <s xml:id="echoid-s7161" xml:space="preserve">unde ratio CO ad CN (vel CB) datur. </s>
            <s xml:id="echoid-s7162" xml:space="preserve">eſt autem
              <lb/>
            CB. </s>
            <s xml:id="echoid-s7163" xml:space="preserve">CZ :</s>
            <s xml:id="echoid-s7164" xml:space="preserve">: I - R. </s>
            <s xml:id="echoid-s7165" xml:space="preserve">R ergò ratio CB ad CZ datur. </s>
            <s xml:id="echoid-s7166" xml:space="preserve">itaque ratio
              <lb/>
            CO ad CZ quoque datur; </s>
            <s xml:id="echoid-s7167" xml:space="preserve">unde ratio CO ad OZ datur. </s>
            <s xml:id="echoid-s7168" xml:space="preserve">verùm
              <lb/>
            OZ datur; </s>
            <s xml:id="echoid-s7169" xml:space="preserve">ergò etiam CO datur. </s>
            <s xml:id="echoid-s7170" xml:space="preserve">hinc demùm & </s>
            <s xml:id="echoid-s7171" xml:space="preserve">ipſa CB datur.</s>
            <s xml:id="echoid-s7172" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7173" xml:space="preserve">Componitur autem in hunc modum. </s>
            <s xml:id="echoid-s7174" xml:space="preserve">In OF utcunque capiatur
              <lb/>
            O ρ, & </s>
            <s xml:id="echoid-s7175" xml:space="preserve">fiat O ρ. </s>
            <s xml:id="echoid-s7176" xml:space="preserve">O σ :</s>
            <s xml:id="echoid-s7177" xml:space="preserve">: R. </s>
            <s xml:id="echoid-s7178" xml:space="preserve">I. </s>
            <s xml:id="echoid-s7179" xml:space="preserve">& </s>
            <s xml:id="echoid-s7180" xml:space="preserve">connectatur σ ρ ζ; </s>
            <s xml:id="echoid-s7181" xml:space="preserve">ducatúrque
              <lb/>
            ZRS ad ζ σ parallela. </s>
            <s xml:id="echoid-s7182" xml:space="preserve">tum fiat OZ. </s>
            <s xml:id="echoid-s7183" xml:space="preserve">ZT :</s>
            <s xml:id="echoid-s7184" xml:space="preserve">: I - R. </s>
            <s xml:id="echoid-s7185" xml:space="preserve">R (unde com-
              <lb/>
            ponendo OT. </s>
            <s xml:id="echoid-s7186" xml:space="preserve">ZT :</s>
            <s xml:id="echoid-s7187" xml:space="preserve">: I. </s>
            <s xml:id="echoid-s7188" xml:space="preserve">R) item V = √ ZT x ZS; </s>
            <s xml:id="echoid-s7189" xml:space="preserve">& </s>
            <s xml:id="echoid-s7190" xml:space="preserve">X =
              <lb/>
            √ OZq - Vq; </s>
            <s xml:id="echoid-s7191" xml:space="preserve">tum X. </s>
            <s xml:id="echoid-s7192" xml:space="preserve">OZ :</s>
            <s xml:id="echoid-s7193" xml:space="preserve">: OZ. </s>
            <s xml:id="echoid-s7194" xml:space="preserve">Y. </s>
            <s xml:id="echoid-s7195" xml:space="preserve">denique X. </s>
            <s xml:id="echoid-s7196" xml:space="preserve">Y :</s>
            <s xml:id="echoid-s7197" xml:space="preserve">: OZ.
              <lb/>
            </s>
            <s xml:id="echoid-s7198" xml:space="preserve">OC (unde erit Xq. </s>
            <s xml:id="echoid-s7199" xml:space="preserve">OZq :</s>
            <s xml:id="echoid-s7200" xml:space="preserve">: OZ. </s>
            <s xml:id="echoid-s7201" xml:space="preserve">OC; </s>
            <s xml:id="echoid-s7202" xml:space="preserve">hoc eſt OZq - Vq. </s>
            <s xml:id="echoid-s7203" xml:space="preserve">
              <lb/>
            OZq :</s>
            <s xml:id="echoid-s7204" xml:space="preserve">: OZ. </s>
            <s xml:id="echoid-s7205" xml:space="preserve">OC; </s>
            <s xml:id="echoid-s7206" xml:space="preserve">hoc eſt OZq - ZT x ZS. </s>
            <s xml:id="echoid-s7207" xml:space="preserve">OZq :</s>
            <s xml:id="echoid-s7208" xml:space="preserve">: OZ. </s>
            <s xml:id="echoid-s7209" xml:space="preserve">
              <lb/>
            OC). </s>
            <s xml:id="echoid-s7210" xml:space="preserve">per C verò ducatur CN ad ZS parallela, ſecans OP in N. </s>
            <s xml:id="echoid-s7211" xml:space="preserve">
              <lb/>
            denique centro C per N ducatur circulus BN; </s>
            <s xml:id="echoid-s7212" xml:space="preserve">is propoſito ſatis-
              <lb/>
            facit.</s>
            <s xml:id="echoid-s7213" xml:space="preserve"/>
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