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-s4615" xml:space="preserve">1. </s>
            <s xml:id="echoid-s4616" xml:space="preserve">Si fuerit I &</s>
            <s xml:id="echoid-s4617" xml:space="preserve">gt;</s>
            <s xml:id="echoid-s4618" xml:space="preserve">R; </s>
            <s xml:id="echoid-s4619" xml:space="preserve">fiat I-R. </s>
            <s xml:id="echoid-s4620" xml:space="preserve">R:</s>
            <s xml:id="echoid-s4621" xml:space="preserve">: BC. </s>
            <s xml:id="echoid-s4622" xml:space="preserve">CZ; </s>
            <s xml:id="echoid-s4623" xml:space="preserve">quare compo-
              <lb/>
              <note position="right" xlink:label="note-0091-01" xlink:href="note-0091-01a" xml:space="preserve">Fig. 105.</note>
            nendo erit I. </s>
            <s xml:id="echoid-s4624" xml:space="preserve">R:</s>
            <s xml:id="echoid-s4625" xml:space="preserve">: BZ. </s>
            <s xml:id="echoid-s4626" xml:space="preserve">CZ. </s>
            <s xml:id="echoid-s4627" xml:space="preserve">ergò factum.</s>
            <s xml:id="echoid-s4628" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4629" xml:space="preserve">2. </s>
            <s xml:id="echoid-s4630" xml:space="preserve">Sin I &</s>
            <s xml:id="echoid-s4631" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s4632" xml:space="preserve">R; </s>
            <s xml:id="echoid-s4633" xml:space="preserve">fiat R - I. </s>
            <s xml:id="echoid-s4634" xml:space="preserve">I :</s>
            <s xml:id="echoid-s4635" xml:space="preserve">: BC. </s>
            <s xml:id="echoid-s4636" xml:space="preserve">BZ. </s>
            <s xml:id="echoid-s4637" xml:space="preserve">ergò rurſus compo-
              <lb/>
            nendo R. </s>
            <s xml:id="echoid-s4638" xml:space="preserve">I:</s>
            <s xml:id="echoid-s4639" xml:space="preserve">: CZ. </s>
            <s xml:id="echoid-s4640" xml:space="preserve">BZ. </s>
            <s xml:id="echoid-s4641" xml:space="preserve">vel inversè, I. </s>
            <s xml:id="echoid-s4642" xml:space="preserve">R :</s>
            <s xml:id="echoid-s4643" xml:space="preserve">: BZ. </s>
            <s xml:id="echoid-s4644" xml:space="preserve">CZ.</s>
            <s xml:id="echoid-s4645" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4646" xml:space="preserve">XXV. </s>
            <s xml:id="echoid-s4647" xml:space="preserve">Fiat jam CA. </s>
            <s xml:id="echoid-s4648" xml:space="preserve">AB:</s>
            <s xml:id="echoid-s4649" xml:space="preserve">: CZ. </s>
            <s xml:id="echoid-s4650" xml:space="preserve">BZ; </s>
            <s xml:id="echoid-s4651" xml:space="preserve">Dico punctum Z eſſe
              <lb/>
            metam, citra quam (reſpectu centri C) nullus reflexus axem de-
              <lb/>
            cuſſabit; </s>
            <s xml:id="echoid-s4652" xml:space="preserve">hoc eſt præmiſſis inſiſtendo, fore CK &</s>
            <s xml:id="echoid-s4653" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s4654" xml:space="preserve">CZ.</s>
            <s xml:id="echoid-s4655" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4656" xml:space="preserve">Nam ducatur NT circulum contingens ad N. </s>
            <s xml:id="echoid-s4657" xml:space="preserve">erit ergo NK. </s>
            <s xml:id="echoid-s4658" xml:space="preserve">NA
              <lb/>
            :</s>
            <s xml:id="echoid-s4659" xml:space="preserve">: KT. </s>
            <s xml:id="echoid-s4660" xml:space="preserve">AT &</s>
            <s xml:id="echoid-s4661" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s4662" xml:space="preserve">BK. </s>
            <s xml:id="echoid-s4663" xml:space="preserve">AB. </s>
            <s xml:id="echoid-s4664" xml:space="preserve">quare NK. </s>
            <s xml:id="echoid-s4665" xml:space="preserve">NA + AB. </s>
            <s xml:id="echoid-s4666" xml:space="preserve">BZ &</s>
            <s xml:id="echoid-s4667" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s4668" xml:space="preserve">BK.
              <lb/>
            </s>
            <s xml:id="echoid-s4669" xml:space="preserve">AB + AB. </s>
            <s xml:id="echoid-s4670" xml:space="preserve">BZ = BK. </s>
            <s xml:id="echoid-s4671" xml:space="preserve">BZ. </s>
            <s xml:id="echoid-s4672" xml:space="preserve">eſt verò NK. </s>
            <s xml:id="echoid-s4673" xml:space="preserve">NA :</s>
            <s xml:id="echoid-s4674" xml:space="preserve">: CK. </s>
            <s xml:id="echoid-s4675" xml:space="preserve">CA. </s>
            <s xml:id="echoid-s4676" xml:space="preserve">
              <lb/>
            & </s>
            <s xml:id="echoid-s4677" xml:space="preserve">AB. </s>
            <s xml:id="echoid-s4678" xml:space="preserve">BZ:</s>
            <s xml:id="echoid-s4679" xml:space="preserve">: CA. </s>
            <s xml:id="echoid-s4680" xml:space="preserve">CZ. </s>
            <s xml:id="echoid-s4681" xml:space="preserve">ergò CK. </s>
            <s xml:id="echoid-s4682" xml:space="preserve">CA + CA. </s>
            <s xml:id="echoid-s4683" xml:space="preserve">CZ &</s>
            <s xml:id="echoid-s4684" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s4685" xml:space="preserve">BK. </s>
            <s xml:id="echoid-s4686" xml:space="preserve">
              <lb/>
            BZ. </s>
            <s xml:id="echoid-s4687" xml:space="preserve">hoc eſt CK. </s>
            <s xml:id="echoid-s4688" xml:space="preserve">CZ&</s>
            <s xml:id="echoid-s4689" xml:space="preserve">lt;</s>
            <s xml:id="echoid-s4690" xml:space="preserve">BK. </s>
            <s xml:id="echoid-s4691" xml:space="preserve">BZ. </s>
            <s xml:id="echoid-s4692" xml:space="preserve">vel permutando CK. </s>
            <s xml:id="echoid-s4693" xml:space="preserve">BK &</s>
            <s xml:id="echoid-s4694" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s4695" xml:space="preserve">
              <lb/>
            CZ. </s>
            <s xml:id="echoid-s4696" xml:space="preserve">BZ. </s>
            <s xml:id="echoid-s4697" xml:space="preserve">unde dividendo CB. </s>
            <s xml:id="echoid-s4698" xml:space="preserve">BK &</s>
            <s xml:id="echoid-s4699" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s4700" xml:space="preserve">CB. </s>
            <s xml:id="echoid-s4701" xml:space="preserve">BZ. </s>
            <s xml:id="echoid-s4702" xml:space="preserve">adeóque BK&</s>
            <s xml:id="echoid-s4703" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s4704" xml:space="preserve">
              <lb/>
            BZ. </s>
            <s xml:id="echoid-s4705" xml:space="preserve">unde liquet propoſitum.</s>
            <s xml:id="echoid-s4706" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4707" xml:space="preserve">XXVI. </s>
            <s xml:id="echoid-s4708" xml:space="preserve">Exhinc (ut in caſibus antè pertractatis) conſectatur ejuſ-
              <lb/>
            modi punctum Z eſſe locum ipſiſſimum imaginis punctum A exhiben-
              <lb/>
            tis oculo, puta O, in axe CA conſtituto; </s>
            <s xml:id="echoid-s4709" xml:space="preserve">patétque quàm longè paſſim
              <lb/>
            ab Opticis; </s>
            <s xml:id="echoid-s4710" xml:space="preserve">nominatim à noviſſimis _Stevino, Hobbio, Fabriog_ in eo
              <lb/>
            aſſignando loco aberratur; </s>
            <s xml:id="echoid-s4711" xml:space="preserve">quorum ex ſententia verſatur is ad pun-
              <lb/>
            ctum (puta Q) tanto ſemotum à vertice B intervallo, quanto radi-
              <lb/>
            ans A ab ipſo B diſtat. </s>
            <s xml:id="echoid-s4712" xml:space="preserve">id quod præterquam quòd nullâ veriſimili rati-
              <lb/>
            one nititur (imò rationi prorſus adverſatur; </s>
            <s xml:id="echoid-s4713" xml:space="preserve">cùm nullus omnino
              <lb/>
            radius oculum ingrediatur tanquam à puncto Q proveniens) experi-
              <lb/>
            entiâ facilimè refutatur. </s>
            <s xml:id="echoid-s4714" xml:space="preserve">Nam ſi tanquam circa punctum A accenſa
              <lb/>
            candela ſpeculo cavo GB γ exponatur, oculo velut ad O ſito longè
              <lb/>
            majori diſtans intervallo conſpicietur, quàm ipſo BQ, quod ipſam
              <lb/>
            AB exæquat. </s>
            <s xml:id="echoid-s4715" xml:space="preserve">quinimò tantillo verſus centrum illum adducendo non
              <lb/>
            æquali diſtantiâ, ſed admodum majori videbitur elongari; </s>
            <s xml:id="echoid-s4716" xml:space="preserve">tantâ
              <lb/>
            circiter ad ſenſum, probabilémque conjecturam; </s>
            <s xml:id="echoid-s4717" xml:space="preserve">quantam proportio
              <lb/>
            requirit à nobis præſtituta. </s>
            <s xml:id="echoid-s4718" xml:space="preserve">quo circà diſcurſus noſter experientiæ
              <lb/>
            ſuffragio conſtabilitur.</s>
            <s xml:id="echoid-s4719" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s4720" xml:space="preserve">XXVII. </s>
            <s xml:id="echoid-s4721" xml:space="preserve">Quod demum attinet ad locum imaginis reſpectu visûs
              <lb/>
              <note position="right" xlink:label="note-0091-02" xlink:href="note-0091-02a" xml:space="preserve">Fig. 106.</note>
            extra radiationis axem poſiti; </s>
            <s xml:id="echoid-s4722" xml:space="preserve">determinatur is eodem ac in caſibus
              <lb/>
            antecedaneis modo; </s>
            <s xml:id="echoid-s4723" xml:space="preserve">biſecando ſcilicet ipſas NP, N @ punctis E, F;
              <lb/>
            </s>
            <s xml:id="echoid-s4724" xml:space="preserve">faciendóque EA. </s>
            <s xml:id="echoid-s4725" xml:space="preserve">AN:</s>
            <s xml:id="echoid-s4726" xml:space="preserve">: FZ. </s>
            <s xml:id="echoid-s4727" xml:space="preserve">ZN. </s>
            <s xml:id="echoid-s4728" xml:space="preserve">Adnotandum ſaltem in recti-
              <lb/>
            oribus reflexis imaginem extra circulum conſiſtere; </s>
            <s xml:id="echoid-s4729" xml:space="preserve">ſed in obliquio@i-
              <lb/>
            bus intra illum, nempe ſi fuerit AE &</s>
            <s xml:id="echoid-s4730" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s4731" xml:space="preserve">AN punctum Z ultra </s>
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