dene triangles |3 yet, ^Bye, ]o\nJE, and the thing is ma- 
nifeftly done. 
The Calculation. 
Affuming of any number of parts, in the trian- 
gles ctjSg, cty€, the angles being given, the fides cf.(i, 
y* 2/3/^7 i^^y be found by Trigonometry ; then in 
the Triangle jScty, having the angle P^*y, and the 
legs fit 18, cty, we may find /3y. Then ^y. BCr-ficc. 
BJ:: ^g. y^. CA:.yi. CE. 
The Jecond Problem ("Fig. 3 & 4.^ 
Three objeds 5, C, A are given, or ("which is the 
fame) the fides, and confequently angles of the trian- 
gle BCD are given; alfo there are 2 points or fta- 
tions J,E, fuch, that at A may be leen the three 
points B,C,Ei but not Z) ; and at the ftation, £, may 
be leen JyC/o, but not 5, that is the angles B A C, 
BAE, AECAED, ("and confequently £^^^^^,^£0 
are known by obfervation ; to find the lines -^5, AC^ 
AE, EC, ED. 
ConjiruBian, 
Take any line «tg at pleafure, and at its extremrtys 
make the angles e cty, gtftjS, c^g y, c6gJ\„ equal to the 
correlpondent obferved angles^ AC.EAB, AE C, AE D. 
Produce A oti A g> til they meet in (p, join (py, then 
upon CB defcribe ("according to 33. 3. Eucl) a Seg- 
ment of a circle, that may contain an angle = ycp ^ ; 
and upon CD defcribe a Segment of a circle capa- 
ble oi an angle =y^? A; luppofe F the common fe- 
dtion of thele 2 circles s join FB, FCy FD; then from 
the point draw forth the lines CA, CE, fo that the 
angle FCA, m^y be = (pya.^ snidF CE--'^(py s ', io A, E, 
the common fe<aions of CA, CE. with FB, FD, will 
be the points required, from, whence the reft is eafily 
deduced. The Calculation. 
Aifuming ctg of any number, in the triangles ct y e,. 
^,4)g, all the angles being given, with the fide af- 
fum'd^ 
