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

Page concordance

< >
Scan Original
31 13
32 14
33 15
34 16
35 17
36 18
37 19
38 20
39 21
40 22
41 23
42 24
43 25
44 26
45 27
46 28
47 29
48 30
49 31
50 32
51 33
52 34
53 35
54 36
55 37
56 38
57 39
58 40
59 41
60 42
< >
page |< < (16) of 393 > >|
    <echo version="1.0RC">
      <text xml:lang="la" type="free">
        <div xml:id="echoid-div13" type="section" level="1" n="10">
          <p>
            <s xml:id="echoid-s614" xml:space="preserve">
              <pb o="16" file="0034" n="34" rhead=""/>
            Quod (licèt breviùs) conficenetur negotium adſumendo ſicut eadem
              <lb/>
            _Tbebis Atbenas, ac Atbenis Tbebas_ eſt via, ità radium de raro tranſe-
              <lb/>
            untem in denſius, pérque denſius veſtigia ſua replicantem in rarum
              <lb/>
            nil aliud quàm eandem ſemitam repetere; </s>
            <s xml:id="echoid-s615" xml:space="preserve">ut nempe ſi radius ABDC
              <lb/>
            de raro tranſiens in denſius refringatur in α β κ δ; </s>
            <s xml:id="echoid-s616" xml:space="preserve">quòd etiam hic ra-
              <lb/>
            dius α β κ δ è denſiori recidens in rarum viciſſimin ABDC refringe-
              <lb/>
            tur; </s>
            <s xml:id="echoid-s617" xml:space="preserve">quia tamen aſſumptum illud non nemini demonſtrationis & </s>
            <s xml:id="echoid-s618" xml:space="preserve">ip-
              <lb/>
            ſum indigere videatur; </s>
            <s xml:id="echoid-s619" xml:space="preserve">Et univerſim, extremóque rigore ſumptum for-
              <lb/>
            ſan haud adeò verum ſit; </s>
            <s xml:id="echoid-s620" xml:space="preserve">majoris etiam evidentiæ cauſa; </s>
            <s xml:id="echoid-s621" xml:space="preserve">preſertîmq;
              <lb/>
            </s>
            <s xml:id="echoid-s622" xml:space="preserve">demùm quoniam huic caſui nonnulla quodammodò peculiaria ſunt no-
              <lb/>
            tatu non indigna; </s>
            <s xml:id="echoid-s623" xml:space="preserve">quin addo quia præſtare videtur effectum unum-
              <lb/>
            quemque propriis è cauſis deduci) ſeparatim oſtendemus. </s>
            <s xml:id="echoid-s624" xml:space="preserve">Rurſum
              <lb/>
            igitur radius ABDC, quâ priùs figurâ donatus rarioris medii ſuper-
              <lb/>
            ficiem EF incurrat. </s>
            <s xml:id="echoid-s625" xml:space="preserve">Cùm igitur punctum B velociùs procedere jam va-
              <lb/>
            leat quàm anteà (medio ſcilicet illapſum promptiùs cedenti) hoc eſt
              <lb/>
            quàm punctum D, neceſſariò commutabitur rectus utriuſque, quem
              <lb/>
            affectant, motus in ei proximum circularem, circa punctum aliquod
              <lb/>
            in recta BD, puta circa Z; </s>
            <s xml:id="echoid-s626" xml:space="preserve">itâ ut ZD, ZB talem inter ſe proportio-
              <lb/>
              <note position="left" xlink:label="note-0034-01" xlink:href="note-0034-01a" xml:space="preserve">Fig. 9.</note>
            nem obſervent, qualem ſingularis exigit horum in reſiſtentia mediorum
              <lb/>
            diverſitas; </s>
            <s xml:id="echoid-s627" xml:space="preserve">utique ſicut in quæ præceſſerunt; </s>
            <s xml:id="echoid-s628" xml:space="preserve">cùm verò punctum B
              <lb/>
            ità circumductum deſcripſerit arcum B β, & </s>
            <s xml:id="echoid-s629" xml:space="preserve">punctum D arcum D δ;
              <lb/>
            </s>
            <s xml:id="echoid-s630" xml:space="preserve">puncto D ad δ tunc medium rarius ingredienti, ceſſabit iſta motuum
              <lb/>
            inæqualitas; </s>
            <s xml:id="echoid-s631" xml:space="preserve">adeóque ſimul neceſſariò deſinet rotatus circa punctum
              <lb/>
            Z; </s>
            <s xml:id="echoid-s632" xml:space="preserve">ambóque puncta B, D per dictorum arcuum tangentes β α, δ κ (re-
              <lb/>
            ctæ Z β perpendiculares) quod proximum eſt iter arripient. </s>
            <s xml:id="echoid-s633" xml:space="preserve">Rurſus
              <lb/>
            autem, pariter ac in caſu præ cedente, rectæ ZD, ZB (vel Z δ, ZB)
              <lb/>
            proportionem exhibent, quæ refractiones hujuſmodi dimetitur; </s>
            <s xml:id="echoid-s634" xml:space="preserve">ha-
              <lb/>
            bent autem Z δ, ZB ſeipſas, ut recti ſinus angulorum ZB δ, Z δ E; </s>
            <s xml:id="echoid-s635" xml:space="preserve">
              <lb/>
            hoc eſt ut ſinus inclinationis rectæ AB ad ſinum inclinationis rectæ δ κ; </s>
            <s xml:id="echoid-s636" xml:space="preserve">
              <lb/>
            quod propoſitum fuit oſtendere. </s>
            <s xml:id="echoid-s637" xml:space="preserve">Liquet autem quòd hîc ang. </s>
            <s xml:id="echoid-s638" xml:space="preserve">Z δ F
              <lb/>
            major eſt angulo ZB δ, adeóque quod refractus divergit à per-
              <lb/>
            pendiculari.</s>
            <s xml:id="echoid-s639" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s640" xml:space="preserve">V. </s>
            <s xml:id="echoid-s641" xml:space="preserve">Advertendum eſt porrò quoad priorem hypotheſin, ſeu caſum
              <lb/>
            radii de medio rariori contendentis in denſius, eum femper, qualiſcunq;
              <lb/>
            </s>
            <s xml:id="echoid-s642" xml:space="preserve">fit ejus obliquitas, medium denſius ſubire; </s>
            <s xml:id="echoid-s643" xml:space="preserve">& </s>
            <s xml:id="echoid-s644" xml:space="preserve">per ipſum incedere; </s>
            <s xml:id="echoid-s645" xml:space="preserve">
              <lb/>
            modo commonſtratotrato. </s>
            <s xml:id="echoid-s646" xml:space="preserve">[Simpliciter autem hoc, & </s>
            <s xml:id="echoid-s647" xml:space="preserve">abſtractè debet in-
              <lb/>
            telligi, necut accidentarium quicquam interveniat, qualia ſunt, opaci-
              <lb/>
            tas perſpicuitati immiſta, figura diaphanum terminans, ejus craſſities
              <lb/>
            inæqualis, aliud quid poſt poſitum diaphani reſiſtentiam promovens;</s>
            <s xml:id="echoid-s648" xml:space="preserve"/>
          </p>
        </div>
      </text>
    </echo>
Impressum