116 S. L. Penfield — Stereographic Projection. 



Case <2.— Given an angle A = 24° 9' and a side h = 70° 14/ 

 of a right triangle, figure 16. On the diameter x, locate the 

 point p 24° 9 ; from the divided circle, using protractor No. I ; 

 then making use of scale No. 1, figure 3, construct the great 

 circle A p. Likewise on the diameter y locate p' 70° 14/ from 



A, and making use of scale No. 2, figure 3, construct the small 

 circle which intersects the great circle previously constructed 

 at B. Through B draw a diameter, thus locating the right 

 angle 0, and completing the triangle. The side a is measured 

 by protractor No. I, the side b by the graduation of the divided 

 circle, and the angle B on the great circle 3, by means of pro- 

 tractor No. II, page 18. 



The results are as follows : 







Calculated. 

 a = 22° 39' 

 b = 68 30 

 B = 81 23 



Plotted. 

 22° 40 

 68 25 

 81 25 



Error 

 1' 

 5 

 2 



Case 3. — Given the three sides of an oblique triangle, a — 

 94° 26', b = 78° 42 ; , and c = 72° 36', figure 17. On the 

 divided circle, lay off the side a, and thus locate the angles B 

 and C. On the diameters x and y locate the points p and p', 

 respectively 78° 42' and 72° 36' from C and B, using pro- 

 tractor No. I. Now making use of scale No. 2, figure 3, con- 

 struct small circles through p and j/, and their intersection 

 locates the angle A. Construct the great circles through C and 

 A, and B and A, and the sides a, b, and c, of the triangle are 

 plotted. The angles B and C are measured on the diameters?' 

 and y\ at 90° from B and C, respectively, using protractor 



