[ 73 ] . 
the intended fegments j but, if the angle, corre-* 
fponding to the intended fegment, is to be neither 
greater or lefs than 90°, the point A, which bifects 
the line B C, will be the centre of the intended 
fegment. 
Thus, if I would have the angle in the intended 
fegment, to confift of 120'', 1 conftitute upon 
B C, at the point C, the angle D C B equal to 
30°, the difference between 120° and 90°, and on 
the oppofite fide of C B from its correfponding 
fegment, becaufe it exceeds 90°, Then with the 
centre D, and radius D C, I defcribe the fegment 
C 120 B, in every part of which the two points 
C and B will fubtend an angle of 120°. 
In like manner, if I would have the angle in the 
intended fegment to conlifl of 80°, I conftitute upon 
B C, at the point C, the angle BCG equal to 10°, 
the difference between 80° and 90"", and becaufe the 
intended angle is now lefs than 90°, I place G on 
the fame fide of B C with its correfponding feg- 
ment. Then with the centre G, and radius G C, 
I defcribe the fegment C 80 B, in every part of 
which the two points C and B will fubtend an angle 
of 80®. 
Laftly, if I would have the angle, in the intended 
fegment, to confifl of 90°, with the centre A and 
radius A C, I defcribe the femicircle C 90 B, in 
every part of which the two points C and B will 
fubtend an angle of 90° 
* If we want a fegment, the angle in which is to be the half 
of one we have got before, the centre is already found to our 
hands j for it will be the point of interfedlion of the former 
fegment with the perpendicular line DE. Thus the point, 
VoL. LV. L The 
