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

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          <p>
            <s xml:id="echoid-s11928" xml:space="preserve">
              <pb o="77" file="0255" n="270" rhead=""/>
            LFK ſeſe contingunt. </s>
            <s xml:id="echoid-s11929" xml:space="preserve"> quare curvæ DIF, KFK ſe quoque
              <note symbol="(_e_)" position="right" xlink:label="note-0255-01" xlink:href="note-0255-01a" xml:space="preserve">2. Lect.
                <lb/>
              VIII.</note>
            tingent. </s>
            <s xml:id="echoid-s11930" xml:space="preserve"> ergò denique recta FS curvam DIF continget.</s>
            <s xml:id="echoid-s11931" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11932" xml:space="preserve">VIII. </s>
            <s xml:id="echoid-s11933" xml:space="preserve">Quòd ſi rectæ DF quamvis aliam conſtanter eandem ad ar-
              <lb/>
            cus AE rationem obtinuerint, itidem deſignari poteſt recta curvam
              <lb/>
            DIF tangens, ex hac, & </s>
            <s xml:id="echoid-s11934" xml:space="preserve">ſeptima octavæ Lectionis; </s>
            <s xml:id="echoid-s11935" xml:space="preserve">erit utique tan-
              <lb/>
            gens iſta huic FS parallela.</s>
            <s xml:id="echoid-s11936" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11937" xml:space="preserve">IX. </s>
            <s xml:id="echoid-s11938" xml:space="preserve">Hinc nedum _ſpiralis circularis_, aſt innumerabilium ſimili ratione
              <lb/>
            progenitarum aliarum curvarum _Tangentes_ determinantur.</s>
            <s xml:id="echoid-s11939" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11940" xml:space="preserve">X. </s>
            <s xml:id="echoid-s11941" xml:space="preserve">Sint curva quæpiam AEH, recta AD (in qua determinatum
              <lb/>
              <note position="right" xlink:label="note-0255-02" xlink:href="note-0255-02a" xml:space="preserve">Fig. 108</note>
            punctum D) recta DH poſitione data; </s>
            <s xml:id="echoid-s11942" xml:space="preserve">ſit item curva AGB talis,
              <lb/>
            ut in hac aſſumpto quocunque puncto G, & </s>
            <s xml:id="echoid-s11943" xml:space="preserve">per hoc ac D projectâ
              <lb/>
            rectâ DGE (quæ curvam AEH ſecet in E) ductâque GF ad DH
              <lb/>
            parallelâ habeant AE, AF aſſignatam rationem X ad Y; </s>
            <s xml:id="echoid-s11944" xml:space="preserve">tangat au-
              <lb/>
            tem recta ET curvam AEH; </s>
            <s xml:id="echoid-s11945" xml:space="preserve">recta deſignetur oportet, quæ curvam
              <lb/>
            AGB ad G tangat.</s>
            <s xml:id="echoid-s11946" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11947" xml:space="preserve">Fiat recta EV æqualis arcui EA; </s>
            <s xml:id="echoid-s11948" xml:space="preserve">& </s>
            <s xml:id="echoid-s11949" xml:space="preserve">concipiatur curva OGO ta-
              <lb/>
            lis, ut projectâ quâcunque rectâ DOL (quæ curvam OGO ſecet
              <lb/>
            puncto O, rectam ET in L) ductâque OQ ad GF parallelâ, ſit
              <lb/>
            VL. </s>
            <s xml:id="echoid-s11950" xml:space="preserve">AQ:</s>
            <s xml:id="echoid-s11951" xml:space="preserve">: X. </s>
            <s xml:id="echoid-s11952" xml:space="preserve">Y; </s>
            <s xml:id="echoid-s11953" xml:space="preserve">eſtque curva OGO (è ſuprà monſtratis) _Hy-_
              <lb/>
            _perboln;_ </s>
            <s xml:id="echoid-s11954" xml:space="preserve">hanc tangat recta GS; </s>
            <s xml:id="echoid-s11955" xml:space="preserve">etiam recta GS curvam AGB
              <lb/>
            continget.</s>
            <s xml:id="echoid-s11956" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11957" xml:space="preserve">Nam concipiatur altera curva NGN talis, ut cùm hanc ſecet recta
              <lb/>
            arbitraria DL in N, curvam AEH in K, rectam TE in L; </s>
            <s xml:id="echoid-s11958" xml:space="preserve">ductáq;
              <lb/>
            </s>
            <s xml:id="echoid-s11959" xml:space="preserve">ſit NR ad GF parallela, ſit VL + LK. </s>
            <s xml:id="echoid-s11960" xml:space="preserve">AR:</s>
            <s xml:id="echoid-s11961" xml:space="preserve">: X. </s>
            <s xml:id="echoid-s11962" xml:space="preserve">Y; </s>
            <s xml:id="echoid-s11963" xml:space="preserve">manife-
              <lb/>
            ſtum eſt curvam NGN utramque curvam AGB, & </s>
            <s xml:id="echoid-s11964" xml:space="preserve">OGO tange-
              <lb/>
            re. </s>
            <s xml:id="echoid-s11965" xml:space="preserve">[ſecet enim recta DL curvam AEB in I, ducatúrque IP ad
              <lb/>
            GF parallela; </s>
            <s xml:id="echoid-s11966" xml:space="preserve">quum ergò ſit VL + LK. </s>
            <s xml:id="echoid-s11967" xml:space="preserve">AR:</s>
            <s xml:id="echoid-s11968" xml:space="preserve">: X. </s>
            <s xml:id="echoid-s11969" xml:space="preserve">Y:</s>
            <s xml:id="echoid-s11970" xml:space="preserve">: AK. </s>
            <s xml:id="echoid-s11971" xml:space="preserve">
              <lb/>
            AP, & </s>
            <s xml:id="echoid-s11972" xml:space="preserve">ſit VL + LK &</s>
            <s xml:id="echoid-s11973" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s11974" xml:space="preserve">AK; </s>
            <s xml:id="echoid-s11975" xml:space="preserve">erit AR &</s>
            <s xml:id="echoid-s11976" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s11977" xml:space="preserve">AP; </s>
            <s xml:id="echoid-s11978" xml:space="preserve">vel DR &</s>
            <s xml:id="echoid-s11979" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s11980" xml:space="preserve">
              <lb/>
            DP; </s>
            <s xml:id="echoid-s11981" xml:space="preserve">adeóque DN &</s>
            <s xml:id="echoid-s11982" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s11983" xml:space="preserve">DI; </s>
            <s xml:id="echoid-s11984" xml:space="preserve">unde punctum N intra curvam AGB
              <lb/>
            ſemper cadet; </s>
            <s xml:id="echoid-s11985" xml:space="preserve">ac proinde curva NGN curvam AGB tan-
              <lb/>
            get; </s>
            <s xml:id="echoid-s11986" xml:space="preserve">ſimilique planè diſcurſu curva NGN curvam OGO contin-
              <lb/>
            get.</s>
            <s xml:id="echoid-s11987" xml:space="preserve">] Itaque curvæ AGB, OGO ſeſe (æquipollentèr) tangunt. </s>
            <s xml:id="echoid-s11988" xml:space="preserve">
              <lb/>
            Quare cùm recta GS curvam OGO tangat; </s>
            <s xml:id="echoid-s11989" xml:space="preserve">eadem curvam AGB
              <lb/>
            quoque continget: </s>
            <s xml:id="echoid-s11990" xml:space="preserve">Q. </s>
            <s xml:id="echoid-s11991" xml:space="preserve">E. </s>
            <s xml:id="echoid-s11992" xml:space="preserve">F.</s>
            <s xml:id="echoid-s11993" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s11994" xml:space="preserve">Si curva AEH ſit circuli quadrans, cujus centrum D; </s>
            <s xml:id="echoid-s11995" xml:space="preserve">erit curva
              <lb/>
            AGB _Quadratrix communis_. </s>
            <s xml:id="echoid-s11996" xml:space="preserve">Ejus igitur _Tangens_ (unà cùm omni-
              <lb/>
            um ſimili ratione genitarum tangentibus) hoc pacto deſignatur,</s>
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