L B JE is equal to that which was oMetved. Alfo 
the CB A C of the fegment, is by conftrudioa of the 
SegmeQt^ equal to the obfervd ^ ^^r. In like manner 
theconftradied angles^£/; and Z)^'/^, areequalto 
the correfpondent obferved angles DEF, there- 
fore^, £ are the points required. 
'The Calculation. 
In the Triangle BCM, the LBCM {upplement of 
BAE) and L BMC [=BJC) are given, with the fide 
B Cs thence MC may be found ; in like manner D N'm 
the A DNF may he found. But the z M CD)^ BCD 
"BGM) is known with its legs MC, CD, therefore its 
bale MDy and Z MDC may be known. Therefore 
the / MD N (=CDF^'CD M^-F D N) is known, with its 
legs M2>, DNi thence Af TV with the angles DMN, 
BNM, will be known. Then the Z (= z Z>MC 
DMN) is known, with the i MAC { = MAB 
j^B AC) and M C before found i therefore MA and AC 
wil be known. In like manner in the triangle EDN, 
the angles E, N, with the fide D N being known, the 
fides ENy ED will be known; therefore AE (=MN 
— MA"ENJ is known. Alfo in the triangle ABCythQ 
I A with its fides B C, C Ah€\x\% known, the fide AB 
will be known, with the / BCA-^ fo in the triangle 
EFD, the L £ with the fides, E D, DF being known, 
EF wil be found, with the lEDF. Laftly in the tri- 
angle ACD, the I A, CD (=BC D"BCA) with its legs 
AC, CD being known, the fidc^D wil be known, and 
in like manner £f in the triangle i? D C. 
Note that, in this problem, as alfo in the firft and 
fecond, if the two ftations fall in a right line with 
either of the given objedls ; the locus oi A, or £, be- 
ing a circle, the particular point of or cannot be 
decermioed from the things given. 
As to the other cafes of this third problem, wherein 
^</,and£, may fliift places, i. e. only 2>,i^,i? may bevi- 
P p p 3 fible 
