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

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            <s xml:id="echoid-s2927" xml:space="preserve">V. </s>
            <s xml:id="echoid-s2928" xml:space="preserve">Verùm extra caſus hos, & </s>
            <s xml:id="echoid-s2929" xml:space="preserve">particulares alios (mihi non incog-
              <lb/>
            nitos, at nunc άΠροσ{δι}ονύ?</s>
            <s xml:id="echoid-s2930" xml:space="preserve">?{ου}ς) _Problema_ magìs ſolidum eſt; </s>
            <s xml:id="echoid-s2931" xml:space="preserve">in ſummo
              <lb/>
            quippe gradu tale; </s>
            <s xml:id="echoid-s2932" xml:space="preserve">quatuórque ſubinde Solutiones admittens; </s>
            <s xml:id="echoid-s2933" xml:space="preserve">perque
              <lb/>
            lineam evolvi poteſt (ut alia pleraque, ſicutì pridem admonitum
              <lb/>
            nobis) ſibi peculiarem; </s>
            <s xml:id="echoid-s2934" xml:space="preserve">illam hoc modo quàm expeditiſſimè per
              <lb/>
            puncta deſcribendam: </s>
            <s xml:id="echoid-s2935" xml:space="preserve">Per datum punctum X protendatur indefinitè
              <lb/>
            recta GF. </s>
            <s xml:id="echoid-s2936" xml:space="preserve">ad datam CB parallela; </s>
            <s xml:id="echoid-s2937" xml:space="preserve">connectatúrque recta XC;
              <lb/>
            </s>
            <s xml:id="echoid-s2938" xml:space="preserve">& </s>
            <s xml:id="echoid-s2939" xml:space="preserve">ſuper hanc ceu diametrum deſcribatur circulus XICI. </s>
            <s xml:id="echoid-s2940" xml:space="preserve">tum è
              <lb/>
            puncto C prodeant quotcunque rectæ circulum XIC ſecantes punctis
              <lb/>
            I, rectamque GF punctis H; </s>
            <s xml:id="echoid-s2941" xml:space="preserve">& </s>
            <s xml:id="echoid-s2942" xml:space="preserve">adſumantur in rectis CHI rectæ
              <lb/>
            IN æquales interceptis IH (ità ſcilicet ut puncta I rectas NH per-
              <lb/>
              <note position="right" xlink:label="note-0071-01" xlink:href="note-0071-01a" xml:space="preserve">Fig. 72.</note>
            petuo biſecent) perque puncta quotvis ejuſmodi N traducta concipia-
              <lb/>
            tur linea; </s>
            <s xml:id="echoid-s2943" xml:space="preserve">nimirum hæc (quà certè nulla Sectio conica faciliùs de-
              <lb/>
            lineatur) problematis noſtri conſtructioni deſervit, ejúſque liquidò
              <lb/>
            naturam patefacit; </s>
            <s xml:id="echoid-s2944" xml:space="preserve">ſiquidem ejuſce cum dati circuli interſectiones
              <lb/>
            N (illæ verò ſubinde quatuor erunt, interdum tres (contactum e-
              <lb/>
            nim interſectionibus adnumero) nonnunquam Solummodò duæ; </s>
            <s xml:id="echoid-s2945" xml:space="preserve">pro-
              <lb/>
            ut datus circulus magnitudine præditus eſt aliâ ac aliâ; </s>
            <s xml:id="echoid-s2946" xml:space="preserve">quæ ſtrictim
              <lb/>
            adnoto tantùm, animum advertenti manifeſtè conſtitura) poſſibiles
              <lb/>
            quaſque Solutiones exhibebunt. </s>
            <s xml:id="echoid-s2947" xml:space="preserve">ducatur enim ab ipſo X ad ejuſmodi
              <lb/>
            quamvis interſectionem N recta XN; </s>
            <s xml:id="echoid-s2948" xml:space="preserve">& </s>
            <s xml:id="echoid-s2949" xml:space="preserve">per N tranſeat MP ad BC
              <lb/>
            parailela (vel ad GX) connexaque CN circulum XIC ſecet in I,
              <lb/>
            rectámque GX in H; </s>
            <s xml:id="echoid-s2950" xml:space="preserve">item jungatur XI. </s>
            <s xml:id="echoid-s2951" xml:space="preserve">& </s>
            <s xml:id="echoid-s2952" xml:space="preserve">quoniam è deſcriptæ
              <lb/>
            lineæ naturâ ſeu conſtructione eſt IH = IN; </s>
            <s xml:id="echoid-s2953" xml:space="preserve">angulúſque CIX, in
              <lb/>
            Semicirculo, rectus eſt; </s>
            <s xml:id="echoid-s2954" xml:space="preserve">erit XN = XH; </s>
            <s xml:id="echoid-s2955" xml:space="preserve">vel ang. </s>
            <s xml:id="echoid-s2956" xml:space="preserve">XNI = ang.
              <lb/>
            </s>
            <s xml:id="echoid-s2957" xml:space="preserve">XHI. </s>
            <s xml:id="echoid-s2958" xml:space="preserve">atqui ang. </s>
            <s xml:id="echoid-s2959" xml:space="preserve">XHI alterno HN P par eſt. </s>
            <s xml:id="echoid-s2960" xml:space="preserve">quapropter anguli
              <lb/>
            XNI, HNP pares ſunt. </s>
            <s xml:id="echoid-s2961" xml:space="preserve">adeóque recta NX ipſius NP reflexus
              <lb/>
            erit. </s>
            <s xml:id="echoid-s2962" xml:space="preserve">quod oportebat fieri. </s>
            <s xml:id="echoid-s2963" xml:space="preserve">ſic, inquam, enodari poterat id Pro-
              <lb/>
            blematis. </s>
            <s xml:id="echoid-s2964" xml:space="preserve">at quoniam (ut innuebam ſuprà) _Geometrarum palato mi-_
              <lb/>
            _nùs ſapiunt hujuſmodi Problematum inuſitatæ ſolutiones;_ </s>
            <s xml:id="echoid-s2965" xml:space="preserve">aliter id
              <lb/>
            (ſatis breviter atque perſpicuè) dabimus effectum hoc ſaltem eò
              <lb/>
            faciens Lemmaticum Problema præmittentes.</s>
            <s xml:id="echoid-s2966" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2967" xml:space="preserve">VI. </s>
            <s xml:id="echoid-s2968" xml:space="preserve">Dato circulo (cujus poſitione data diameter GF) & </s>
            <s xml:id="echoid-s2969" xml:space="preserve">puncto
              <lb/>
            C in ejuſce circumſerentia quoque dato; </s>
            <s xml:id="echoid-s2970" xml:space="preserve">per hoc recta ducatur, cujus
              <lb/>
            pars diametro circumferentiæ que interjecta æquetur datæ rectæ Z.</s>
            <s xml:id="echoid-s2971" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s2972" xml:space="preserve">Id ſic exequimur. </s>
            <s xml:id="echoid-s2973" xml:space="preserve">Connectatur recta CF; </s>
            <s xml:id="echoid-s2974" xml:space="preserve">& </s>
            <s xml:id="echoid-s2975" xml:space="preserve">huic perpen-
              <lb/>
            dicularis ducatur recta FV; </s>
            <s xml:id="echoid-s2976" xml:space="preserve">& </s>
            <s xml:id="echoid-s2977" xml:space="preserve">accipiatur ad ipſas Z, GF tertia
              <lb/>
            proportionalis P; </s>
            <s xml:id="echoid-s2978" xml:space="preserve">& </s>
            <s xml:id="echoid-s2979" xml:space="preserve">per G angulo CFV inſeratur recta RS par
              <lb/>
            ipſi P (id autem quomodò præſtandum, edocuimus ſupra) tum per </s>
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