Full text: Barrow, Isaac: Lectiones Opticæ & Geometricæ

_XI._ Ad lentem convexo-convexam diverg.

Fig. 158,

_XII._ Ad lentem concavo-concavam converg.

1. Si AB & gt; {R/I} AC, facto AB - {R/I} AC. AB : : BC. BZ; & {I/R} KZ - DZ : : DK. DY; puncta Z, Y adverſus Acadunt.

2. Si AB = {R/I} AC, fac I - R. R : : DK. DY; & cape DY
adverſus A.

3. Si AB & lt; {R/I} AC; fac {R/I} AC - AB. AB : : BC. BZ; & ſume BZ verſus A. Jam cùm Z cadit extra DK, ſi primò ſit
{I/R} KZ & gt; DZ, fac {I/R} KZ - DZ. DZ : : DK. DY; & ſume
DY adverſus A

4. Secundò, ſi {I/R} KZ = DZ, imago diſtabit infini è.

5. Tertiò, ſi {I/R} KZ & lt; DZ, fac DZ - {I/R} KZ. DZ : : DK. DY; & ſume DY verſus A.

6. Quum denuò cadit Z inter D, & K, fiat DZ + {I/R} KZ. DZ : :
DK. DY; ſumatúrque DY verſus A.

Corol. Ad in regram Sphæram diυerg.

1. Si AB + AC & gt; {2R/I} AC; fiat AB + AC - {2R/I} AC. AC : : BC. CY; & cape CY adverſus A.

2. Si AB + AC = {2R/I} AC; imago in infinitum abit.

3. Si AB + AC & lt; {2R/I} AC; fiat {2R/I} AC - AC - AB. AC : : BC. CY; capiatúrque CY verſus A.

_XIII._ Ad lentem concavc-concavam diverg.

Fig. 159.

_XIV._ Ad lentem convexo-convexam converg.


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