# Full text: Barrow, Isaac: Lectiones Opticæ & Geometricæ

biſecat angulum ANK; erit AN. NK : : AT. TK. & lt; AB. BK. quare BZ. AB + AN. NK & lt; BZ. AB + AB. BK
(communem adſciſcendo rationem BZ ad AB). eſt autem BZ. AB + AN. NK = CZ. AC + AC. CK = CZ. CK & BZ. AB + AB. BK = BZ. BK. ergo CZ. CK & lt; BZ. BK. permutandóque CZ. BZ & lt; CK. BK. quin & componendo CB. BZ & lt; CB. BK. ideóque BZ & gt; BK; quare punctum Z centro
propinquius eſt, quàm ipſum K: Q. E. D.

_Coroll_. Hinc ſi puncta Z, ζ fuerint limites punctorum radiantium
A, _a_ (quorum A fit à fpeculo remotiùs, quàm _a_) erit CZ & lt; C ζ. Nam eſt BC. AB & lt; BC, _a_ B. adeóque compoſitè AC. AB & lt; _a_ C. _a_ B. hoc eſt CZ. BZ & lt; C ζ. B ζ. quare componendo
BC. BZ & lt; BC. B ζ. & indè BZ & gt; B ζ.

IX. Porrò, conſectatur è præmiſſis, quòd ſi duorum quorumvis
incidentium AN, AR reflexi GN, HR axem interſecent punctis
K, L; erit CL, CK : : ACq - ANq. ACq - ARq. ‖ Nam
quoniam eſt AC. CK : : ACq - ANq. CBq. itémque CL. AC : : CBq. ACq - ARq. erit ex æquo perturbatè CL. CK : : ACq - ANq. ACq - ARq.

X. Simili planè diſcurſu, ſi fuerit AC. AB : : CZ. ZB. erit CZ. CK : : ACq - ANq. ACq - ABq. & CL. CZ : :
ACq - ARq. ACq - ABq.

XI. Hinc perſpicuum eſt obliquioris reflexi concurſum à centro
magìs elongari quam rectioris; quod nempe ſit CL & gt; CK. Cùm
enim ſit ACq - ANq & gt; ACq - ARq; erit CL & gt; CK.

XII. Hinc neceſſariò duo quilibet ad eaſdem axis partes incidentium
reflexi (quales NK, RL) ſeſe priùs quàm axem interſecabunt, puta

XIII. Adnotari poteſt angulum GXH vel KXL (à reflexis oc-
currentibus incluſum) æquari angulo NCR unà cum differentia angu-
lorum incidentiæ; vel, duplo angulo NCR unà cum ang. NAR. ‖ Etenim
ang. KXL = ang. ALR - AKN = ang. ACR + CRL -: ang. ACN + CNK = ang. ACR - ACN + : ang. CRL -
CNK = ang NCR +: ang CRS - CNP. ‖ Quinetiam ang. CRS - CNP = ang. RCA + CAR -: ang. NCA +

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