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

& demittatur NQ ad AC perpendicularis, erit CQ = F - E. ‖
Nam (ut ſuprà) eft CA. CK: : F. E. quare dividendo erit CA
- CK. CK: : F - E. E. Item hîc erit ANq - ACq =
2 AC x CQ + CNq. adeóque 2 AC x CQ + CNq. CNq
: : AC. CK. hoc eſt, (ob CNq = 2 AC x E.) 2 AC x CQ
+ 2 AC x E. 2 AC x E: : AC. CK. hoc eſt CQ + E. E: :
AC. CK. quare dividendo CQ. E: : AC - CK. CK. ergo
F - E = CQ: Q. E. D.

IX. porrò, ſi duorum quorumvis radiorum AN, AR reflexi
NK, RL axem ſecent punctis K, L; erit CK. CL: : ARq -
ACq. ANq - ACq. Nam ob CK. AC: : CNq. ANq
- ACq. & AC. CL: : ARq - ACq. CNq. erit ex æquo
perturbatè CK. CL: : ARq - ACq. ANq - ACq.

X. Hinc ſi radius AR ſit ipſo AN obliquior; erit CK & lt; CL. Nam ARq - ACq & lt; ANq - ACq.

XI. Hinc palàm eſt reflexos NK, RL ſeſe priùs quàm axem
decuſſare.

XII. Accipiantur porrò bini pares arcus NR, RX; & inciden-
tium AN, AR, AX reflexi cum axe conveniant punctis K, L, M; dico ſpatium LM, obliquiorum occurſibus interjectum, majus eſſe
ſpatio LK, quod rectiorum continetur occurſibus. Nam è ſuprà
monſtratis conſtat eſſe ANq + AXq & lt; 2 ARq. proindeque fo-
re ANq + AXq - 2 ACq & lt; 2 ARq - 2 ACq. ac indè
ANq. - ACq. ARq - ACq & lt; ARq - ACq. AXq -
ACq. hoc eſt CL. CK & lt; CM. CL. vel CM. CL & gt; CL. CK. quare CM + CK & gt; 2 CL. & ideò LM & gt; KL.

### 19.1.

Fig. 102;

XIII. Hinc rectiùs ingruens lux à reflectione verſus axem conden-

XIV. Quidnì demùm rurſus ex his inferatur, viſibilis A imaginem
@irca reflexorum metam Z, oculo uſpiam in AZ conſtituto, appa-
rere?

XV. Adverſatur ſaltem (id quod experiendo deprehendetur) ocu-
lo uſpiam in ZB collocato confuſiorem apparentiam objici; quippe

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