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-s4181" xml:space="preserve">
              <pb o="68" file="0086" n="86" rhead=""/>
            hoc eſt σ π. </s>
            <s xml:id="echoid-s4182" xml:space="preserve">RN:</s>
            <s xml:id="echoid-s4183" xml:space="preserve">: PA + 2 NA. </s>
            <s xml:id="echoid-s4184" xml:space="preserve">NA. </s>
            <s xml:id="echoid-s4185" xml:space="preserve">eſt autem arc σ π. </s>
            <s xml:id="echoid-s4186" xml:space="preserve">RN
              <lb/>
            :</s>
            <s xml:id="echoid-s4187" xml:space="preserve">: ſubtenſa σ π. </s>
            <s xml:id="echoid-s4188" xml:space="preserve">RN:</s>
            <s xml:id="echoid-s4189" xml:space="preserve">: π ZZ R:</s>
            <s xml:id="echoid-s4190" xml:space="preserve">: π Z. </s>
            <s xml:id="echoid-s4191" xml:space="preserve">ZN. </s>
            <s xml:id="echoid-s4192" xml:space="preserve">ergo π Z. </s>
            <s xml:id="echoid-s4193" xml:space="preserve">ZN:</s>
            <s xml:id="echoid-s4194" xml:space="preserve">:
              <lb/>
            PA + 2 NA. </s>
            <s xml:id="echoid-s4195" xml:space="preserve">NA. </s>
            <s xml:id="echoid-s4196" xml:space="preserve">& </s>
            <s xml:id="echoid-s4197" xml:space="preserve">componendo π N. </s>
            <s xml:id="echoid-s4198" xml:space="preserve">ZN:</s>
            <s xml:id="echoid-s4199" xml:space="preserve">: PA + 3 NA. </s>
            <s xml:id="echoid-s4200" xml:space="preserve">NA
              <lb/>
            & </s>
            <s xml:id="echoid-s4201" xml:space="preserve">antecedentes ſubduplando FN. </s>
            <s xml:id="echoid-s4202" xml:space="preserve">ZN:</s>
            <s xml:id="echoid-s4203" xml:space="preserve">: {PA + 3 NA/2}. </s>
            <s xml:id="echoid-s4204" xml:space="preserve">NA. </s>
            <s xml:id="echoid-s4205" xml:space="preserve">de-
              <lb/>
            nique dividendo FZ. </s>
            <s xml:id="echoid-s4206" xml:space="preserve">ZN:</s>
            <s xml:id="echoid-s4207" xml:space="preserve">: {PA + NA / 2}. </s>
            <s xml:id="echoid-s4208" xml:space="preserve">NA. </s>
            <s xml:id="echoid-s4209" xml:space="preserve">eſt autem EA =
              <lb/>
            {PA + NA/2}. </s>
            <s xml:id="echoid-s4210" xml:space="preserve">ergò tandem eſt FZZN:</s>
            <s xml:id="echoid-s4211" xml:space="preserve">: EA. </s>
            <s xml:id="echoid-s4212" xml:space="preserve">NA: </s>
            <s xml:id="echoid-s4213" xml:space="preserve">Q. </s>
            <s xml:id="echoid-s4214" xml:space="preserve">E. </s>
            <s xml:id="echoid-s4215" xml:space="preserve">D.</s>
            <s xml:id="echoid-s4216" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4217" xml:space="preserve">XIII. </s>
            <s xml:id="echoid-s4218" xml:space="preserve">Hinc colligitur punctum Z eſſe locum ipſiſſimum, circa quem
              <lb/>
            puncti Z imago conſiſtit; </s>
            <s xml:id="echoid-s4219" xml:space="preserve">oculi reſpectu in reflexo GN π conſ@ituti,
              <lb/>
            tanquam ad O. </s>
            <s xml:id="echoid-s4220" xml:space="preserve">etenim ſuperiùs nec ſemel argumentis, ut mihi vide-
              <lb/>
              <note position="left" xlink:label="note-0086-01" xlink:href="note-0086-01a" xml:space="preserve">Fig. 95, 96.</note>
            tur, admodum luculentis adfirmatum eſt (ut jam ad inſtar regulæ
              <lb/>
            legíſve ratum, fixúmque cenſeri queat iſthic imaginem verſari, ubi
              <lb/>
            propiorum incidenti principali (hoc eſt ei cujus reflexus oculi centrum
              <lb/>
            tranſiens axis Optici vicem ſubit) radiorum reflexi principalem illum
              <lb/>
            reflexum interſecant; </s>
            <s xml:id="echoid-s4221" xml:space="preserve">itaque circa Z in hoc caſu verſatur.</s>
            <s xml:id="echoid-s4222" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4223" xml:space="preserve">XIV. </s>
            <s xml:id="echoid-s4224" xml:space="preserve">Et hoc argumentatione collegi, non illâ quidem incertâ
              <lb/>
            vel ambiguâ, ſed nec ad _Geometrici_ rigoris amuſſim præ illa quam in
              <lb/>
            præcedentibus uſurpavi (quanquam & </s>
            <s xml:id="echoid-s4225" xml:space="preserve">hæc è cognatis fontibus pro-
              <lb/>
            Huxerit) adeò exactâ; </s>
            <s xml:id="echoid-s4226" xml:space="preserve">concisâ tamen, & </s>
            <s xml:id="echoid-s4227" xml:space="preserve">facili, talíque quæ conclu-
              <lb/>
            ſionis adſertæ cauſam apprimè detegit. </s>
            <s xml:id="echoid-s4228" xml:space="preserve">Enim verò ſi pleraque cuncta,
              <lb/>
            quæ ſe oggerunt huc attinentia, minutatim ac moroſè perſequi vellem,
              <lb/>
            immane quantum tædii (commodo veſtro fortaſſè non tanto) mihi-
              <lb/>
            met accerſerem, & </s>
            <s xml:id="echoid-s4229" xml:space="preserve">temporis plurimum veſtri pariter ac mei exhauri-
              <lb/>
            rem. </s>
            <s xml:id="echoid-s4230" xml:space="preserve">ſuffecerit itaque jam, & </s>
            <s xml:id="echoid-s4231" xml:space="preserve">poſthac in reliquis Hypotheſibus ſuffi-
              <lb/>
            ciat, viâ quàm breviſſimâ (modò tamen certiſſimâ) metam attingere.
              <lb/>
            </s>
            <s xml:id="echoid-s4232" xml:space="preserve">De convexis hactenus; </s>
            <s xml:id="echoid-s4233" xml:space="preserve">ad concava proximè nos conferemus, aliquan-
              <lb/>
            to breviùs exponenda.</s>
            <s xml:id="echoid-s4234" xml:space="preserve">‖</s>
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