[123 3 ] 
fum'd, the fides gy, at ^), j?', wil be known; thenia 
the triangle y^&cp, the angle y^&cp with the legscty, 
ce-cp being known, the angles a>(py^ a,y(p with the fide 
<py will be known: then as for the reft of the 
work in the other figure, the triangle BCD having all 
its fides and angles known, and the angles B FC, B FD, 
^ being equal to the found fi(py, ^(pii; how to find 
FB, FC, FD by Calculation f'and alio Frotrailion) has 
becn,fliewn by Mr Collins (in FhiL TranfaUn. 6<) p. 
2093. ) as to all its cafes , which may therefore 
fuperlede my fhewing any other way. 
But here it muft be noted, that if the fumoftheob- 
ferved angles, BAE, A ED, is I go degrees: then A B 
and ED cannot meet, becaufe they are parallel, and 
confequently the given folution cannot take place > 
for which reafon I here lubjoin another. 
Another Solution, 
Upon BC f.) defcribe a legment BJC of a 
circle, fothat the angle of the legment, may be equal 
to the obferved l (icty, ("which as above quoted is 
fliewn J3. 3. Euclidj and upon CD defcribe a fegment 
CED of a circle, capable of an angle equal to the ob- 
ferved C ED I from C draw the diameters of thefe cir- 
cles CG, G H ; then upon CG defcribe a fegment of 
a circle GFC^ capable of an angle equal to the ob- 
ferved L jECy likewife upon f// defcribe a circles leg- 
ment CF H, capable of an angle equal to the obferv- 
ed CAE: fuppofe F the common ledtion of the two 
laft circles FIFC, GFC, join FH, cutting the circle 
HEC 'm E, join alfo FG, cutting the circle G AC in 
A: I fay that A, E, are the points required. 
Dem : 
For the L BAC\%^9>c^y by conftrucStion of the feg- 
ment, alfo the angles CEFl, CAG, are right, becauib 
each exifts in a femicircle: therefore a circle being de- 
fcribed upon as a diameter, wil pafs thro E, A, There- 
P p p 2 fore 
