Full text: Barrow, Isaac: Lectiones Opticæ & Geometricæ

& lt; CZ. BZ. dividendóque CB. BK& lt; CB. BZ. adeóque BK
& gt; BZ; hoc eſt punctum K magìs quàm Z à centro elongatur.

19.1.

Fig. 139.

3. Haud diſſimilis in aliis caſibus erìt _Demonſtratio_; ut in hoc, ubi
I & lt; R, ad convexas; eſt enim hîc (ut in præcedente) KB. AB& lt; KN. AN. adeóque (ſupra monſtratis inſiſtendo) CK. CZ& gt; KB. BZ. vel permutando CK. KB& gt; CZ. BZ. dividendóque
CB. KB& gt; CB. BZ. unde KB& lt; BZ. adeóque punctum K
centro ſemper vicinius eſt quàm Z.

19.1.

Fig. 140.

XVI. Hæc autem cùm, modo ſuo mutatis mutandis, ad omnes
caſus transferri poſſint, habentur indè determinati refractorum limites,
hoc eſt apparentia radiantium punctorum A loca, reſpectu oculi cen-
trum habentis in axe AC ſitum; juxta doctrinam à nobis toties in-
culcatam.

XVII. Id autem hîc in duobus caſibus (utroque nimirum ad circuli
cavas) peculiare venit obſervandum cùm ſit CB = CR, omnes
refractos in ipſo puncto Z (ut ſuprà definito) retrò protractos con-
gregari. Nam ob AB. BC : : AB. CR : : BZ. CZ. erit divi-
dendo AC. BC : : BC. CZ. quapropter ad punctum quodvis N
adſumptum connexis AN, ZN, erit ZN. AN : : (CZ. CN : : )
CZ. CR. unde ZN refractus erit incidentis AN.

XVIII. Hinc etiam ſi fuerit AB = CR, conſequetur punctum Z
à centro infinitè diſtare; quia nempe tum ob AB. CR : : BZ. CZ,
erit BZ = CZ; id quod fieri nequit, niſi punctum Z ità elongetur
infinitè.

19.1.

Fig. 141.

XIX. _Conſectantur_ & hæc: Si punctorum radiantium A, _a_ limites
ſint puncta Z, ζ, erit AC. AB + BZ. CZ = _a_ C. _a_B + Bζ. C ζ.

19.1.

Fig. 142,
143.

Nam è præmiſſis facilè conſtat eſſe
tam AC. AB + BZ. CZ = \q̇uam _a_ C. _a_ B + B ζ. C ζ = }I. R.

XX. Unde Cζ & gt; CZ. Nam ob BC. AB & lt; BC. _a_B. componendóque AC. AB & lt; _a_ C. _a_ B. erit BZ. CZ & gt; BC α B. Cζ. dividendóque BC. CZ & gt; BZ. Cζ. adeóque Cζ & gt; C Z.

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