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

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9476 in axe capiatur CK = CG; connectatúrque recta NK, fore NK
ipſius MNPrefractum. Connectantur enim rectæ FG, BG; &
quoniam eſt BZ. CZ: : (I. R: :) FZ. FC; erit permutando
BZ. FZ: : CZ. FC. dividendóque BF. FZ: : FZ.
11Fig. 109. FC. itaque patet triangula BF G, GFC(latera ſcilicet habentia
circa communem angulum GFCproportionalia) ſimilia fore.
quamobrem erit BG. GF: : GC. CF. ſeu permutatim BG. GC
: : GF. CF. hoc eſt BG. GC: : FZ. CF: : I. R. verum in tri-
angulis BC G, NCKeſt BC = CN, & CG = CK; & ang.
BCG = NCK; adeóque BG. GC: : NK. CK. quare erit quo-
que NK. CK: : I. R. ergò, ſecundum generatim antehac 22_Lect. 3. nu-_
_mero. 10._ liquet NK ipſius MN refractum exiſtere.

_Coroll._ Adnotetur eſſe triangula BFG, GFCſimilia; ac eſſe
BG. CC: : I. R; & ang. BG F = GC F; & eſſe BF, FG,
FC {. ./. .}& c.

III. Ex hoc (ſanè pulchro, perutilíque _Theoremate_) cùm particu-
laris exoritur methodus hujuſmodi quotcunque refractos expeditiſſimè
ſeu delineandi, ſeu computandi; tum ipſorum præcipua _ſymptomata_
facilimè diſcernuntur ac demonſtrantur. qualia ſunt, quæ in ſubjectis
exhibentur _Corollariis._

IV. Patet hinc punctum Z eſſe limitem ultra quem (reſpectu cen-
tri) nullus axem interſecat refractus; ſeu perpendicularis ipſius AB
(vel ei ſaltem quàm proximè adjacentis radii) refractum ad Z termi-
33Fig. 110. nari. quia nimirum eſt CZ & gt; CG, vel CR.

V. Conſequitur etiam, ſi duorum incidentium MN, QR (quorum
QR ſit obliquior) refracti conveniant cum axe punctis K, L, fore
CK& gt; CL. Etenim ſi rectæ NC, RC ad circulum refractarium
44Fig. 111. (itâ circulum EGZmeritò ſubinde nominabimus) producantur, ut
ipſum ſecent punctis G, H; liquet eſſe CG & gt; CH; adeóque CK
& gt; CL. Hinc

VI. Ad eaſdem partes incidentium refracti ſeſe priùs interſecant
quàm axem; (veluti puta refracti NK, RL ſeſe decuſſant in X.)

VII. Quinetiam, ſi in primo caſu per centrum C dueatur recta
55Fig. 111. VI ad BZ perpendicularis, dictóque circulo refractario occurrens
ad I; & fiat CY = CI, patet punctum Y eſſe limitem

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