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

Table of Notes

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            <s xml:id="echoid-s7935" xml:space="preserve">
              <pb o="121" file="0139" n="139" rhead=""/>
            ellipſin jacent. </s>
            <s xml:id="echoid-s7936" xml:space="preserve">Nam punctum K inter F & </s>
            <s xml:id="echoid-s7937" xml:space="preserve">Z; </s>
            <s xml:id="echoid-s7938" xml:space="preserve">ac punctum φ inter
              <lb/>
            O, & </s>
            <s xml:id="echoid-s7939" xml:space="preserve">K; </s>
            <s xml:id="echoid-s7940" xml:space="preserve">nec non punctum L inter G, & </s>
            <s xml:id="echoid-s7941" xml:space="preserve">Y; </s>
            <s xml:id="echoid-s7942" xml:space="preserve">atque punctum γ in-
              <lb/>
            ter O, & </s>
            <s xml:id="echoid-s7943" xml:space="preserve">L cadunt. </s>
            <s xml:id="echoid-s7944" xml:space="preserve">imaginis itaque φαγ figura ad ellipticam accedit;
              <lb/>
            </s>
            <s xml:id="echoid-s7945" xml:space="preserve">eâ tamen aliquanto planior & </s>
            <s xml:id="echoid-s7946" xml:space="preserve">compreſſior. </s>
            <s xml:id="echoid-s7947" xml:space="preserve">non diſſimili ratione quo-
              <lb/>
            ad imagines ad concava factas, & </s>
            <s xml:id="echoid-s7948" xml:space="preserve">quoad cæteros caſus inſtituetur
              <lb/>
            judicium. </s>
            <s xml:id="echoid-s7949" xml:space="preserve">tædii plenum eſſet omnia ſingillatim percenſere. </s>
            <s xml:id="echoid-s7950" xml:space="preserve">quinetiam
              <lb/>
            ê præmiſſis luculentè conſtat quo pacto linea φαγ præcisè deſcribatur,
              <lb/>
            punctatim utique. </s>
            <s xml:id="echoid-s7951" xml:space="preserve">circa refractiones paria veniunt præſtanda; </s>
            <s xml:id="echoid-s7952" xml:space="preserve">poſt-
              <lb/>
            quam tamen paullùm reſpiravero; </s>
            <s xml:id="echoid-s7953" xml:space="preserve">nunc enim verbo quidem pauca,
              <lb/>
            rei qualitatem, ſtudiúmque demonſtrandis iſtis impenſum reſpectan-
              <lb/>
            do, ſatìs fortaſſe multa videor tradidiſſe.</s>
            <s xml:id="echoid-s7954" xml:space="preserve">‖</s>
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        <div xml:id="echoid-div206" type="section" level="1" n="25">
          <head xml:id="echoid-head28" xml:space="preserve">
            <emph style="sc">Lect.</emph>
          XVIII.</head>
          <p>
            <s xml:id="echoid-s7955" xml:space="preserve">I.</s>
            <s xml:id="echoid-s7956" xml:space="preserve">P_Ropoſitum eſt jam nobis rectæ lineæ ex refractione prognatas. </s>
            <s xml:id="echoid-s7957" xml:space="preserve">ad_
              <lb/>
            _circulum imagines aeſignare_; </s>
            <s xml:id="echoid-s7958" xml:space="preserve">nempe primùm abſolutas;
              <lb/>
            </s>
            <s xml:id="echoid-s7959" xml:space="preserve">quorſum hoc ſpectat I
              <unsure/>
            heorema:</s>
            <s xml:id="echoid-s7960" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7961" xml:space="preserve">In circulum (e. </s>
            <s xml:id="echoid-s7962" xml:space="preserve">g. </s>
            <s xml:id="echoid-s7963" xml:space="preserve">medii denſioris) refractivum MBND radiet
              <lb/>
            recta FAG; </s>
            <s xml:id="echoid-s7964" xml:space="preserve">huic verò perpendicularis ſit recta CA (circuli cen-
              <lb/>
              <note position="right" xlink:label="note-0139-01" xlink:href="note-0139-01a" xml:space="preserve">Fig. 197.</note>
            trum C permeans) tum in recta FG ſumpto liberè puncto F ducatur
              <lb/>
            recta FC; </s>
            <s xml:id="echoid-s7965" xml:space="preserve">& </s>
            <s xml:id="echoid-s7966" xml:space="preserve">in hac ſit punctum Z limes (qualem anteà fiximus)
              <lb/>
            radiationis à puncto F; </s>
            <s xml:id="echoid-s7967" xml:space="preserve">ſit autem ZX ad AC normalis. </s>
            <s xml:id="echoid-s7968" xml:space="preserve">porrò fiat
              <lb/>
            CA. </s>
            <s xml:id="echoid-s7969" xml:space="preserve">CR :</s>
            <s xml:id="echoid-s7970" xml:space="preserve">: I. </s>
            <s xml:id="echoid-s7971" xml:space="preserve">R; </s>
            <s xml:id="echoid-s7972" xml:space="preserve">& </s>
            <s xml:id="echoid-s7973" xml:space="preserve">AR. </s>
            <s xml:id="echoid-s7974" xml:space="preserve">CB :</s>
            <s xml:id="echoid-s7975" xml:space="preserve">: CR. </s>
            <s xml:id="echoid-s7976" xml:space="preserve">CE (ponatur autem
              <lb/>
            CE ad XZ parallela) tum connexa RE cum ipſa XZ conveniat in
              <lb/>
            H. </s>
            <s xml:id="echoid-s7977" xml:space="preserve">dico fore XH = CZ.</s>
            <s xml:id="echoid-s7978" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7979" xml:space="preserve">Nam (è præmonſtratis) eſt FC x MZ. </s>
            <s xml:id="echoid-s7980" xml:space="preserve">FM x CZ :</s>
            <s xml:id="echoid-s7981" xml:space="preserve">: I. </s>
            <s xml:id="echoid-s7982" xml:space="preserve">R:</s>
            <s xml:id="echoid-s7983" xml:space="preserve">:
              <lb/>
            CA. </s>
            <s xml:id="echoid-s7984" xml:space="preserve">CR. </s>
            <s xml:id="echoid-s7985" xml:space="preserve">hoceſt FC x CM + FC x CZ. </s>
            <s xml:id="echoid-s7986" xml:space="preserve">FC x CZ - CM
              <lb/>
            x CZ :</s>
            <s xml:id="echoid-s7987" xml:space="preserve">: CA. </s>
            <s xml:id="echoid-s7988" xml:space="preserve">CR. </s>
            <s xml:id="echoid-s7989" xml:space="preserve">quare (ducendo in ſe extrema, mediáque)
              <lb/>
            eſt FC x CM x CR + FC x CZ x CR = FC x CZ x CA -
              <lb/>
            CM x CZ x CA = FC x CZ x CA - CM x FC x CX (quoniam ſcilicet </s>
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