of the Angle fubtended by Two Objects, &c. 
directly from S. That the conditions of the problem are ful- 
filled in the conftrudlion is demonftrated thus : 
ifl, The inclination of the reflectors B and C to the plane of 
motion was conflructed of the magnitude which is meafured by 
the arc KF. KC is perpendicular to the plane of motion. CF 
is perpendicular to the refledtor 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 ; 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 conftrufdon, the perpendiculars 
CF and Cl being parallel when, both, are fituated in. the plane of: 
the fame great circle DBQ. 
adly, KO: 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 confiruction, FY 
being a quadrant, 
^dly, Moreover, FD — FB, was eonfirudted equal to the con- - 
Rant angle of incidence at the fixed fpeculum ; CBR is the 
angle of incidence at the fixed fpeculum B, and it iscqual to the - 
angle BCF, becaufe CF and BR are parallel by ccnfirudtion ,and 
CB falls on therm; FB, or its equal FD ' therefore is truly con- 
ftructed the meafure of the given confiant. angle of incidence at 
the fixed fpeculum B. 
qthly, Becaufe it has been fhewn that CO; is the pofition of 
the radius CP,, when the reflectors are parallel, the arc OP is 
rightly confiructed the meafure. of the angular difiance of the. 
radius CP from that pofition. , 
It remains only to demonfirate that thefe four given ^quanti- 
ties,, KE, OP, XY, and DF, limit the. magnitude of the arc,: 
ED;: 
