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

Table of Notes

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          <p>
            <s xml:id="echoid-s7315" xml:space="preserve">Has inſtantias, facilitatis gratiâ, ità propoſuimus, quaſi punctum
              <lb/>
            A, unà cum duobus oculis O, P in plano exiſteret ad ſuperficiem in-
              <lb/>
            flectentem recto. </s>
            <s xml:id="echoid-s7316" xml:space="preserve">id quod utrùm in experiendo præcisè contingat
              <lb/>
            nécne, parùm refert; </s>
            <s xml:id="echoid-s7317" xml:space="preserve">duas utcunque ſpecies apparere liquet. </s>
            <s xml:id="echoid-s7318" xml:space="preserve">quin
              <lb/>
            facilè concipitur etiam eo poſito rem non aliter ſe habituram.</s>
            <s xml:id="echoid-s7319" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7320" xml:space="preserve">His prælibatis, illud diſcutiamus, quod innuimus, ψευ{δ ο}{γ ρ}άφημæ
              <lb/>
              <note position="left" xlink:label="note-0128-01" xlink:href="note-0128-01a" xml:space="preserve">_In Dioper._</note>
            quo nempe P. </s>
            <s xml:id="echoid-s7321" xml:space="preserve">_Herigonius_ propoſitionem hanc ſuam comprobatum it:
              <lb/>
            </s>
            <s xml:id="echoid-s7322" xml:space="preserve">“ Si oculus, & </s>
            <s xml:id="echoid-s7323" xml:space="preserve">aſpectabile ſint in diverſis mediis ſè mutuo contingen-
              <lb/>
            tibus, imago apparebit in concurſu catheti, & </s>
            <s xml:id="echoid-s7324" xml:space="preserve">radii ab oculo per
              <lb/>
            punctum refractionis directè producti.</s>
            <s xml:id="echoid-s7325" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7326" xml:space="preserve">Sit utique punctum Fin medio denſiori HLMN collocatum, quod
              <lb/>
              <note position="left" xlink:label="note-0128-02" xlink:href="note-0128-02a" xml:space="preserve">Fig. 181.</note>
            ad oculos A, B radios FEA, FDB emittat refractos ad E, & </s>
            <s xml:id="echoid-s7327" xml:space="preserve">D;
              <lb/>
            </s>
            <s xml:id="echoid-s7328" xml:space="preserve">& </s>
            <s xml:id="echoid-s7329" xml:space="preserve">rectæ AE, BD conveniant in C; </s>
            <s xml:id="echoid-s7330" xml:space="preserve">ſit autem ſuperficiei refringenti
              <lb/>
            perpendicularis recta FG; </s>
            <s xml:id="echoid-s7331" xml:space="preserve">erit (inquit) puncti F imago in recta
              <lb/>
            FG. </s>
            <s xml:id="echoid-s7332" xml:space="preserve">id quod ità demonſtrat: </s>
            <s xml:id="echoid-s7333" xml:space="preserve">Quoniam dicta imago tam in refracto
              <lb/>
            AE, quàm in refracto BD exiftit, ergò in horum interſectione C
              <lb/>
            exiſtet. </s>
            <s xml:id="echoid-s7334" xml:space="preserve">verùm interſectio C ìn recta FG exiſtet; </s>
            <s xml:id="echoid-s7335" xml:space="preserve">quoniam hæc
              <lb/>
            communis eſt ſectio planorum AEF, BDF ſuperficiei refringenti
              <lb/>
            rectorum. </s>
            <s xml:id="echoid-s7336" xml:space="preserve">ergò liquet propoſitum.</s>
            <s xml:id="echoid-s7337" xml:space="preserve"/>
          </p>
          <p>
            <s xml:id="echoid-s7338" xml:space="preserve">In hanc demonſtrationem adverto; </s>
            <s xml:id="echoid-s7339" xml:space="preserve">1. </s>
            <s xml:id="echoid-s7340" xml:space="preserve">Supponit ea refractos AE,
              <lb/>
            BD concurrere; </s>
            <s xml:id="echoid-s7341" xml:space="preserve">quod tamen falſum eſt, præterquam in uno vel al-
              <lb/>
            tero caſu; </s>
            <s xml:id="echoid-s7342" xml:space="preserve">quum nempe planum ABF in eodem exiſtit cum ipſa
              <lb/>
            recta FG plano; </s>
            <s xml:id="echoid-s7343" xml:space="preserve">vel, cùm puncta A, B ſunt in ſuperficie coni recti,
              <lb/>
            cujus axis eſt recta FG. </s>
            <s xml:id="echoid-s7344" xml:space="preserve">quod ſi prior caſus ponatur, è ſuprà demon-
              <lb/>
            ſtratis maniſeſtum eſt refractos AE, BD non in recta FG, ſed intra
              <lb/>
            angulum FGH convenire; </s>
            <s xml:id="echoid-s7345" xml:space="preserve">quod è principiis noſtris elicitum illum
              <lb/>
            ſaltem conſtringere debet, qui principia iſta admittit ac amplectitur.
              <lb/>
            </s>
            <s xml:id="echoid-s7346" xml:space="preserve">2. </s>
            <s xml:id="echoid-s7347" xml:space="preserve">Hinc, illa demonſtratio ipſam ſe perimit: </s>
            <s xml:id="echoid-s7348" xml:space="preserve">Nam, quoniam (in po-
              <lb/>
            ſito caſu) puncti F imago tam in recta AE, quàm in recta BD exiſtit,
              <lb/>
            adeóque in harum concurſu; </s>
            <s xml:id="echoid-s7349" xml:space="preserve">concurſus autem iſte non eſt in recta
              <lb/>
            FG; </s>
            <s xml:id="echoid-s7350" xml:space="preserve">ergò liquet dictam imaginem extra rectam FG verſari. </s>
            <s xml:id="echoid-s7351" xml:space="preserve">3. </s>
            <s xml:id="echoid-s7352" xml:space="preserve">Sup-
              <lb/>
            ponit iſte diſcurſus (ut & </s>
            <s xml:id="echoid-s7353" xml:space="preserve">ſuppar ille jamjam prolatus) puncti F uni-
              <lb/>
            cam oculo u@ique imaginem apparere; </s>
            <s xml:id="echoid-s7354" xml:space="preserve">quod πρῶγον ψεῦδ{ος} erat,
              <lb/>
            à nobis paullo ſupra refutatum. </s>
            <s xml:id="echoid-s7355" xml:space="preserve">Enimverò diverſi oculi ſunt reipsâ
              <lb/>
            diverſi ſpectatores. </s>
            <s xml:id="echoid-s7356" xml:space="preserve">hæc, opinor, ratiocinium illud ſatìs enervant.</s>
            <s xml:id="echoid-s7357" xml:space="preserve">‖</s>
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