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-s9456" xml:space="preserve">
              <pb o="41" file="0219" n="234" rhead=""/>
            punctum Zinfra punctum M; </s>
            <s xml:id="echoid-s9457" xml:space="preserve">erit tum recta PE major arcu PX;
              <lb/>
            </s>
            <s xml:id="echoid-s9458" xml:space="preserve">
              <note position="right" xlink:label="note-0219-01" xlink:href="note-0219-01a" xml:space="preserve">Fig. 27.</note>
            unde arc PA. </s>
            <s xml:id="echoid-s9459" xml:space="preserve">PE &</s>
            <s xml:id="echoid-s9460" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s9461" xml:space="preserve">arc PA. </s>
            <s xml:id="echoid-s9462" xml:space="preserve">PX:</s>
            <s xml:id="echoid-s9463" xml:space="preserve">: PM. </s>
            <s xml:id="echoid-s9464" xml:space="preserve">XZ - PM:</s>
            <s xml:id="echoid-s9465" xml:space="preserve">:
              <lb/>
            PM. </s>
            <s xml:id="echoid-s9466" xml:space="preserve">XZ - EH:</s>
            <s xml:id="echoid-s9467" xml:space="preserve">: PM. </s>
            <s xml:id="echoid-s9468" xml:space="preserve">XE + XZ &</s>
            <s xml:id="echoid-s9469" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s9470" xml:space="preserve">PM. </s>
            <s xml:id="echoid-s9471" xml:space="preserve">HZ. </s>
            <s xml:id="echoid-s9472" xml:space="preserve">& </s>
            <s xml:id="echoid-s9473" xml:space="preserve">viciſſim
              <lb/>
            PA. </s>
            <s xml:id="echoid-s9474" xml:space="preserve">PM &</s>
            <s xml:id="echoid-s9475" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s9476" xml:space="preserve">PE. </s>
            <s xml:id="echoid-s9477" xml:space="preserve">HZ. </s>
            <s xml:id="echoid-s9478" xml:space="preserve">Verum ut priùs) eſt PA. </s>
            <s xml:id="echoid-s9479" xml:space="preserve">PM:</s>
            <s xml:id="echoid-s9480" xml:space="preserve">: PE. </s>
            <s xml:id="echoid-s9481" xml:space="preserve">HK.
              <lb/>
            </s>
            <s xml:id="echoid-s9482" xml:space="preserve">ergò PE. </s>
            <s xml:id="echoid-s9483" xml:space="preserve">HK &</s>
            <s xml:id="echoid-s9484" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s9485" xml:space="preserve">PE. </s>
            <s xml:id="echoid-s9486" xml:space="preserve">HZ; </s>
            <s xml:id="echoid-s9487" xml:space="preserve">proptereáque HK &</s>
            <s xml:id="echoid-s9488" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s9489" xml:space="preserve">HZ; </s>
            <s xml:id="echoid-s9490" xml:space="preserve">ro
              <unsure/>
            rſus
              <lb/>
            itaque liquet Punctum K extra curvam exiſtere. </s>
            <s xml:id="echoid-s9491" xml:space="preserve">Tota proinde recta
              <lb/>
            MKZ extra curvam verſatur; </s>
            <s xml:id="echoid-s9492" xml:space="preserve">& </s>
            <s xml:id="echoid-s9493" xml:space="preserve">eam tangit ad M: </s>
            <s xml:id="echoid-s9494" xml:space="preserve">Q. </s>
            <s xml:id="echoid-s9495" xml:space="preserve">E. </s>
            <s xml:id="echoid-s9496" xml:space="preserve">D. </s>
            <s xml:id="echoid-s9497" xml:space="preserve">
              <lb/>
            In tranſcurſu hoc. </s>
            <s xml:id="echoid-s9498" xml:space="preserve">ad alias curvæ noſtræ paſſiones revertamur.</s>
            <s xml:id="echoid-s9499" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9500" xml:space="preserve">VII. </s>
            <s xml:id="echoid-s9501" xml:space="preserve">Si tangenti cuipiam (ut ipſi MT) parallela ducatur quæ-
              <lb/>
            piam EF (à puncto nempe quopiam E in recta infra punctum T ſum-
              <lb/>
            pto) hæc curvæ occurret.</s>
            <s xml:id="echoid-s9502" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9503" xml:space="preserve">Si enim infra punctum M in curva ſumatur punctum quodlibet, & </s>
            <s xml:id="echoid-s9504" xml:space="preserve">
              <lb/>
              <note position="right" xlink:label="note-0219-02" xlink:href="note-0219-02a" xml:space="preserve">Fig. 28.</note>
            ab eo duci concipiatur curvam tangens recta; </s>
            <s xml:id="echoid-s9505" xml:space="preserve">huic occurret tangens
              <lb/>
            TM infra ordinatam PM. </s>
            <s xml:id="echoid-s9506" xml:space="preserve">ergò recta EF eidem occurret; </s>
            <s xml:id="echoid-s9507" xml:space="preserve">at curvam
              <lb/>
            priùs tranſiliat oportet. </s>
            <s xml:id="echoid-s9508" xml:space="preserve">ergò liquet Propoſitum.</s>
            <s xml:id="echoid-s9509" xml:space="preserve">
              <unsure/>
            </s>
          </p>
          <p>
            <s xml:id="echoid-s9510" xml:space="preserve">VIII. </s>
            <s xml:id="echoid-s9511" xml:space="preserve">Eâdem operâ patet, ſi punctum aſſumptum E puncto T,
              <lb/>
            & </s>
            <s xml:id="echoid-s9512" xml:space="preserve">vertici A interjiciatur, rectum EF curvæ bis occurſuram, tam ſupra
              <lb/>
            quàm infra contactum M.</s>
            <s xml:id="echoid-s9513" xml:space="preserve"/>
          </p>
          <note position="right" xml:space="preserve">con. 1. 27, 28.</note>
          <p>
            <s xml:id="echoid-s9514" xml:space="preserve">Operosè conniſus eſt _Apollonius_ hæc de _Sectionibus Conicis_ oſtendere.</s>
            <s xml:id="echoid-s9515" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9516" xml:space="preserve">Cæterùm ad penitus determinandos occurſuum locos _Specialis mo-_
              <lb/>
            _dus ſeu ratio motuum deſcendentis atq; </s>
            <s xml:id="echoid-s9517" xml:space="preserve">tranſverſi cognoſci debet_; </s>
            <s xml:id="echoid-s9518" xml:space="preserve">tunc
              <lb/>
            eos _Analyſis_ ſtatim prodet.</s>
            <s xml:id="echoid-s9519" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9520" xml:space="preserve">IX. </s>
            <s xml:id="echoid-s9521" xml:space="preserve">Si duæ rectæ quævis (HM, KN) ad curvam propoſi-
              <lb/>
              <note position="right" xlink:label="note-0219-04" xlink:href="note-0219-04a" xml:space="preserve">Fig. 29.</note>
            tam æqualiter inclinentur (hoc eſt æquales cum ejus ad occurſus tan-
              <lb/>
            gentibus (puta cum ipſis MT, NX) angulos efficiant) hæ extrorſum
              <lb/>
            divergent, ſeu ad partes EF productæ concurrent.</s>
            <s xml:id="echoid-s9522" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9523" xml:space="preserve">Nam ducatur ſubtenſa NM; </s>
            <s xml:id="echoid-s9524" xml:space="preserve">hæc utiq; </s>
            <s xml:id="echoid-s9525" xml:space="preserve">ſecundum antedicta cum
              <lb/>
            ipſa AZ conveniet, puta ad O. </s>
            <s xml:id="echoid-s9526" xml:space="preserve">Eſt ergò ang OMH &</s>
            <s xml:id="echoid-s9527" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s9528" xml:space="preserve">(ang.
              <lb/>
            </s>
            <s xml:id="echoid-s9529" xml:space="preserve">TMH = ang. </s>
            <s xml:id="echoid-s9530" xml:space="preserve">XNK &</s>
            <s xml:id="echoid-s9531" xml:space="preserve">lt;) </s>
            <s xml:id="echoid-s9532" xml:space="preserve">ang. </s>
            <s xml:id="echoid-s9533" xml:space="preserve">ONK. </s>
            <s xml:id="echoid-s9534" xml:space="preserve">ergo ang. </s>
            <s xml:id="echoid-s9535" xml:space="preserve">HMN +
              <lb/>
            MNK &</s>
            <s xml:id="echoid-s9536" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s9537" xml:space="preserve">2 rect. </s>
            <s xml:id="echoid-s9538" xml:space="preserve">ergò rectæ HM, KN concurrunt ad partes EF. </s>
            <s xml:id="echoid-s9539" xml:space="preserve">
              <lb/>
            Limitandum eſt hoc, intelligendo pares angulos HMA, KNA ad
              <lb/>
            eaſdem partes veſari; </s>
            <s xml:id="echoid-s9540" xml:space="preserve">ſeu alterum alteri fore externum interno. </s>
            <s xml:id="echoid-s9541" xml:space="preserve">alias
              <lb/>
            cotnrà eveniet.</s>
            <s xml:id="echoid-s9542" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s9543" xml:space="preserve">X. </s>
            <s xml:id="echoid-s9544" xml:space="preserve">Si fuerit recta HM _curvæ_ perpendicularis (hoc ejus tan-
              <lb/>
              <note position="right" xlink:label="note-0219-05" xlink:href="note-0219-05a" xml:space="preserve">Fig. 30.</note>
            genti MT) & </s>
            <s xml:id="echoid-s9545" xml:space="preserve">in hac ſumatnr quæpiam definita HM; </s>
            <s xml:id="echoid-s9546" xml:space="preserve">erit HM mi-
              <lb/>
              <note position="right" xlink:label="note-0219-06" xlink:href="note-0219-06a" xml:space="preserve">_Apoll. V._ 38.&c.</note>
            nima rectarum omnium, quæ à puncto H duci poſſunt ad curvam.</s>
            <s xml:id="echoid-s9547" xml:space="preserve"/>
          </p>
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