118100
159.
_XI._
Ad lentem convexo-convexam diverg.
11Fig. 158, 159.
_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.
& {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.
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
& 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.
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.
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.
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.
AC : : BC. CY; capiatúrque CY verſus A.
_XIII._
Ad lentem concavc-concavam diverg.
22Fig. 159.
_XIV._
Ad lentem convexo-convexam converg.