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-s3616" xml:space="preserve">
              <pb o="61" file="0079" n="79" rhead=""/>
            CAN = ang. </s>
            <s xml:id="echoid-s3617" xml:space="preserve">NCR + NAR. </s>
            <s xml:id="echoid-s3618" xml:space="preserve">itaque rurſus ang. </s>
            <s xml:id="echoid-s3619" xml:space="preserve">KXL =
              <lb/>
            2 ang. </s>
            <s xml:id="echoid-s3620" xml:space="preserve">NCR + ang. </s>
            <s xml:id="echoid-s3621" xml:space="preserve">NAR. </s>
            <s xml:id="echoid-s3622" xml:space="preserve">liquent igitur quæ propoſita ſunt;
              <lb/>
            </s>
            <s xml:id="echoid-s3623" xml:space="preserve">in uſum (ſi fortè) ſequentium. </s>
            <s xml:id="echoid-s3624" xml:space="preserve">pro quibus itidem hæc proponenda
              <lb/>
            ſunt.</s>
            <s xml:id="echoid-s3625" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3626" xml:space="preserve">XIV. </s>
            <s xml:id="echoid-s3627" xml:space="preserve">Etiam palàm eſt è dictis ipſos reflexos GN, HR directè
              <lb/>
              <note position="right" xlink:label="note-0079-01" xlink:href="note-0079-01a" xml:space="preserve">Fig. 83.</note>
            procurrentes à ſe divergere; </s>
            <s xml:id="echoid-s3628" xml:space="preserve">adeóque duntaxat unum hujuſmodi re-
              <lb/>
            flexum oculi centrum tranſire; </s>
            <s xml:id="echoid-s3629" xml:space="preserve">conſequentèr & </s>
            <s xml:id="echoid-s3630" xml:space="preserve">puncti A tantùm u-
              <lb/>
            nam à convexo ſpeculo imaginem exhiberi.</s>
            <s xml:id="echoid-s3631" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3632" xml:space="preserve">XV. </s>
            <s xml:id="echoid-s3633" xml:space="preserve">_Lemmatia_ 1. </s>
            <s xml:id="echoid-s3634" xml:space="preserve">Sint quæcunque tria quanta A, P, C; </s>
            <s xml:id="echoid-s3635" xml:space="preserve">primó-
              <lb/>
            que ſit A. </s>
            <s xml:id="echoid-s3636" xml:space="preserve">B &</s>
            <s xml:id="echoid-s3637" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s3638" xml:space="preserve">B. </s>
            <s xml:id="echoid-s3639" xml:space="preserve">C; </s>
            <s xml:id="echoid-s3640" xml:space="preserve">dico fore A + C &</s>
            <s xml:id="echoid-s3641" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s3642" xml:space="preserve">2 B. </s>
            <s xml:id="echoid-s3643" xml:space="preserve">ponatur enim
              <lb/>
            fore A. </s>
            <s xml:id="echoid-s3644" xml:space="preserve">B :</s>
            <s xml:id="echoid-s3645" xml:space="preserve">: B. </s>
            <s xml:id="echoid-s3646" xml:space="preserve">E. </s>
            <s xml:id="echoid-s3647" xml:space="preserve">erit ergò A + E &</s>
            <s xml:id="echoid-s3648" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s3649" xml:space="preserve">2 B. </s>
            <s xml:id="echoid-s3650" xml:space="preserve">quinetiam erit ergò
              <lb/>
            B. </s>
            <s xml:id="echoid-s3651" xml:space="preserve">E &</s>
            <s xml:id="echoid-s3652" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s3653" xml:space="preserve">B. </s>
            <s xml:id="echoid-s3654" xml:space="preserve">C adeóque C &</s>
            <s xml:id="echoid-s3655" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s3656" xml:space="preserve">E. </s>
            <s xml:id="echoid-s3657" xml:space="preserve">ergo magis A + C &</s>
            <s xml:id="echoid-s3658" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s3659" xml:space="preserve">2 B.</s>
            <s xml:id="echoid-s3660" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3661" xml:space="preserve">2. </s>
            <s xml:id="echoid-s3662" xml:space="preserve">Sit (iiſdem adhibitis quantis) ſecundò A + C &</s>
            <s xml:id="echoid-s3663" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s3664" xml:space="preserve">2 B. </s>
            <s xml:id="echoid-s3665" xml:space="preserve">dico
              <lb/>
            fore A. </s>
            <s xml:id="echoid-s3666" xml:space="preserve">B &</s>
            <s xml:id="echoid-s3667" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s3668" xml:space="preserve">B. </s>
            <s xml:id="echoid-s3669" xml:space="preserve">C. </s>
            <s xml:id="echoid-s3670" xml:space="preserve">nam ſive dicatur eſſe A. </s>
            <s xml:id="echoid-s3671" xml:space="preserve">B :</s>
            <s xml:id="echoid-s3672" xml:space="preserve">: B. </s>
            <s xml:id="echoid-s3673" xml:space="preserve">C. </s>
            <s xml:id="echoid-s3674" xml:space="preserve">vel A. </s>
            <s xml:id="echoid-s3675" xml:space="preserve">B
              <lb/>
            &</s>
            <s xml:id="echoid-s3676" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s3677" xml:space="preserve">B. </s>
            <s xml:id="echoid-s3678" xml:space="preserve">C. </s>
            <s xml:id="echoid-s3679" xml:space="preserve">ſequetur utrobique fore A + C &</s>
            <s xml:id="echoid-s3680" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s3681" xml:space="preserve">2 B; </s>
            <s xml:id="echoid-s3682" xml:space="preserve">contra hypothe-
              <lb/>
            ſin. </s>
            <s xml:id="echoid-s3683" xml:space="preserve">itaque potiùs eſt A. </s>
            <s xml:id="echoid-s3684" xml:space="preserve">B &</s>
            <s xml:id="echoid-s3685" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s3686" xml:space="preserve">B. </s>
            <s xml:id="echoid-s3687" xml:space="preserve">C.</s>
            <s xml:id="echoid-s3688" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3689" xml:space="preserve">XVI. </s>
            <s xml:id="echoid-s3690" xml:space="preserve">Etiam hoc adjungo. </s>
            <s xml:id="echoid-s3691" xml:space="preserve">Si duo ſumantur ad eaſdem axi partes
              <lb/>
              <note position="right" xlink:label="note-0079-02" xlink:href="note-0079-02a" xml:space="preserve">Fig. 84.</note>
            (circulíque convexâ parte comprehenſi) ſibimet æquales arcus NR,
              <lb/>
            R X; </s>
            <s xml:id="echoid-s3692" xml:space="preserve">& </s>
            <s xml:id="echoid-s3693" xml:space="preserve">ducantur rectæ AN, AR, AX; </s>
            <s xml:id="echoid-s3694" xml:space="preserve">erit ANq + AXq
              <lb/>
            &</s>
            <s xml:id="echoid-s3695" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s3696" xml:space="preserve">2 ARq.</s>
            <s xml:id="echoid-s3697" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3698" xml:space="preserve">Nam ducantur CN, CR, CX; </s>
            <s xml:id="echoid-s3699" xml:space="preserve">& </s>
            <s xml:id="echoid-s3700" xml:space="preserve">demittantur ad AC perpen-
              <lb/>
            diculares NE, RF, X G; </s>
            <s xml:id="echoid-s3701" xml:space="preserve">ſint item NP, RQ ad AC parallelæ
              <lb/>
            ducantúrque ſubtenſæ NR, RX. </s>
            <s xml:id="echoid-s3702" xml:space="preserve">; </s>
            <s xml:id="echoid-s3703" xml:space="preserve">& </s>
            <s xml:id="echoid-s3704" xml:space="preserve">quoniam ang. </s>
            <s xml:id="echoid-s3705" xml:space="preserve">RXQ &</s>
            <s xml:id="echoid-s3706" xml:space="preserve">gt;
              <lb/>
            </s>
            <s xml:id="echoid-s3707" xml:space="preserve">ang. </s>
            <s xml:id="echoid-s3708" xml:space="preserve">NRP; </s>
            <s xml:id="echoid-s3709" xml:space="preserve">patet eſſe R X. </s>
            <s xml:id="echoid-s3710" xml:space="preserve">RQ &</s>
            <s xml:id="echoid-s3711" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s3712" xml:space="preserve">NR. </s>
            <s xml:id="echoid-s3713" xml:space="preserve">NP; </s>
            <s xml:id="echoid-s3714" xml:space="preserve">adeóque cum
              <lb/>
            RX = NR, erit RQ &</s>
            <s xml:id="echoid-s3715" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s3716" xml:space="preserve">NP; </s>
            <s xml:id="echoid-s3717" xml:space="preserve">hoc eſt FG &</s>
            <s xml:id="echoid-s3718" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s3719" xml:space="preserve">EF. </s>
            <s xml:id="echoid-s3720" xml:space="preserve">ergò 2 CF
              <lb/>
            &</s>
            <s xml:id="echoid-s3721" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s3722" xml:space="preserve">CE + CG; </s>
            <s xml:id="echoid-s3723" xml:space="preserve">unde 4 AC x CF &</s>
            <s xml:id="echoid-s3724" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s3725" xml:space="preserve">2 AC x CE + 2 AC x
              <lb/>
            CG atqui eſt ANq = ACq + CNq - 2 AC x CE. </s>
            <s xml:id="echoid-s3726" xml:space="preserve">& </s>
            <s xml:id="echoid-s3727" xml:space="preserve">AXq
              <lb/>
            = ACq + CNq - 2 AC x CG. </s>
            <s xml:id="echoid-s3728" xml:space="preserve">& </s>
            <s xml:id="echoid-s3729" xml:space="preserve">2 ARq = 2 ACq +
              <lb/>
            2 CNq - 4 AC x CF. </s>
            <s xml:id="echoid-s3730" xml:space="preserve">ergo ANq + AXq &</s>
            <s xml:id="echoid-s3731" xml:space="preserve">gt; </s>
            <s xml:id="echoid-s3732" xml:space="preserve">2 ARq.</s>
            <s xml:id="echoid-s3733" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3734" xml:space="preserve">Addo, ſequentium gratià, ſi punctum A ſumatur ad alteras (inſra
              <lb/>
            centrum) partes; </s>
            <s xml:id="echoid-s3735" xml:space="preserve">& </s>
            <s xml:id="echoid-s3736" xml:space="preserve">reliqua ſimiliter apparentur; </s>
            <s xml:id="echoid-s3737" xml:space="preserve">fore contrà, tum
              <lb/>
            ANq + AXq &</s>
            <s xml:id="echoid-s3738" xml:space="preserve">lt; </s>
            <s xml:id="echoid-s3739" xml:space="preserve">2 ARq. </s>
            <s xml:id="echoid-s3740" xml:space="preserve">nam in eo caſu eſt ANq + AXq
              <lb/>
            = 2 ACq + 2 CNq + 2 AC x CE + 2 AC x CG. </s>
            <s xml:id="echoid-s3741" xml:space="preserve">& </s>
            <s xml:id="echoid-s3742" xml:space="preserve">
              <lb/>
            2 ARq = 2 ACq + 2 CNq + 4 AC x CF. </s>
            <s xml:id="echoid-s3743" xml:space="preserve">unde liquet pro-
              <lb/>
            poſitum.</s>
            <s xml:id="echoid-s3744" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s3745" xml:space="preserve">XVII. </s>
            <s xml:id="echoid-s3746" xml:space="preserve">Sint jam ad eaſdem axis partes duo quilibet æquales </s>
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