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

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Si A cadat extra BC, fiat AB - {R/I} AC. AB : : BC. BZ; ſin A
11Fig. 159. cadat inter B, C; fiat AB + {R/I} AC. AB : : BC. BZ; deinde fac
{I/R} KZ - DZ. DZ : : DK. DY.
Coroll- Adintegram Sphæram converg.
Si punctum A extra BC ponatur, fiat AB + {I-2R/I} AC : : BC.
CY. ſin A cadat inter B, & C; fiat AB+{2R-I/I} AC. AC : :
BC. CY; & cape CY ad partes centri verſus A.
_XV._ Ad lentera convexo-concavam diverg.
22Fig. 160,
161.
_XVI._ Ad lentem concavo convexam converg.
1. Si AB & lt; {R/I} AC; puncta Z, & Y verſus A cadunt, facto
{R/I} AC - AB. AB : : BC. BZ; & {I/R} KZ - DZ. DZ : : DK. DY.
2. Si AB = {R/I} AC; fac I - R. R : : DK. DY; & cape DY
verſus A.
3. Si AB & gt; {R/I} AC; fac AB - {R/I} AC. AB : : BC. BZ; &
cape BZ adverſus A. Jam quum Z cadit extra DK, tum primò ſi
{I/R} KZ & gt; DZ, fac {I/R} KZ - DZ. DZ : : DK. DY; & cape DY
verſus A.
4. Secundò, ſi {I/R} KZ = DZ, imago infinitè diſtabit.
5. Tertiò, ſi {I/R} KZ & lt; DZ, fac DZ - {I/R} KZ. DZ : : DK.
DY, & ſume DY adverſus A.
6. Sed quando Z inter D, & K cadit; fiat DZ + {I/R} KZ. DZ : :
DK. DY; & ſumatur DY adverſus A.

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