_- TWO TABLES 
— rn 
~~ 
OF THE VARIETIES IN THE FIRST AND SECOND CASES OF 
OBLIQUE SPHERICS. 
By WILLIAM CROSWELL, a. m. 
—- rig a letter to the Honorable John Davis, Esq. 
Se Sa 4 — 
Of the —- in the first case of ob spherics, in het: are given 
two sides, and an angle opposite to one of those sides 
Cliven /|CGiv.sid 
|Z 
Side adjacent to given angle [Zop.adj.s)1 
i | acute. 
1| acute | acute jequal to opposite eside — 
2| acute | acute fless than opposite side — 
3} acute | acute ieee than opposite side 
| 4| acute |greate pithan gaposiic © ot 
a = 3 acute a an Se less 1an AD joe os 
8| acute aan greater than 08 opp. side obtu: 
9 
10) 
obtuse acute - less than 
f obtuse obt ; than op opposite 
111] obtuse | obtuse {equal to ‘opposite sid 
412} obtuse | obtuse jgreater t si onieetiiet side 
13! obtuse | mixed jobtuse ae than supp. opp. Si ide 
14} obtuse | mixed {acute equal to supp. opposite side 
15] obtuse | mixed jacute less than supp. opposite side 
116] obtuse | mixed acute greater than supp: ed 
Tt appears : : s above ove » that only four varieties in tl 
ma iaewe ambiguous. 
Let the sides be 114” 30’ and 56° 40’, and let the angle opposite to — : 
114° 30’ be 125° 20’... The angle narra to 56° 40’ is found ida cal 
culation to be 48° 31’, oF 1312 29 
Robertson, from whom this €xample ake: eaeties dinteat 
fection must be determined by construction. 
This example belongs to the 15th variety in the Table, whence the | 
angle concerned is found to be acute ; meh eaectons of the other 
required parts are determined. 
In constructing the ambiguous varieties, two triangles are odie 
ed, equally agreeing with the example ; and the uncertainty continues 
