of the Angle fubt ended by Two ObjeZls, &c. 40 3 
direCtly from S. That the conditions of the problem are ful- 
filled in the conflxuCtion is demonftrated thus : 
lift. The inclination of the reflectors B and C to the plane of 
motion wasconftructed of the magnitude which ismeafured by 
the arc KF. KC is perpendicular to the plane of motion. CF 
is perpendicular to the refleCior C, and the inclination of thefe 
two lines CK, CF, is meafured by the arc KF ; but the incli- 
nation of any two planes is the fame as the inclination of 
two lines which are perpendicular to them - y the inclination 
therefore of the refleCtor C to the plane of motion is meafured 
by the arc KF, and the fpeculum B is equally inclined to the 
plane of motion with C by the conftruCtion, the perpendiculars 
CF and Cl being parallel when both are fituated in the plane of 
the fame great circle DBQ. 
2dly, KQ being the fecondary to which the pofition of the 
fixed plane of reflection DFB at the fpeculum B was referred, 
that given inclination will be equal to the angle OFB* which 
is meafured by the arc XY according to the conflrucHon, FY 
being a quadrant* 
3dly, Moreover, FD = FB, was conftruCted equal to the com- 
Rant angle of incidence at the fixed fpeculum ; CBR u the 
angle of incidence at the fixed fpeculum B, and it is equal to the 
angle BCF, beeaufe CF and BR are parallel by conftruCiion, and 
CB falls on them ; FB, or its equal FD therefore is truly con- 
ftruCled the meafure of the given conftant angle of incidence at 
the fixed fpeculum B* 
4thly, Beeaufe it has been fhewn that CO is the pofition of 
the radius CP* when the refleClors are parallel, the arc OP is 
rightly conftruCted the meafure of the angular diftance of the 
radius CP from that pofition.. 
It remains only to demonftrate that thefe four given quanti- 
ties, KF, OP, XY, and DF, limit the magnitude of the arc 
ED t: 
