Angle f-^ D given to find the angles CDAandACD, the 
Complement whereof to a Semicircle is the angle S C A: 
Now in the Triangle S CA^ the Angle at C being foundjand 
at S obfervedj and given by Suppofition, the orher t A is 
]ikewi(e known, as being the complement of the two for^ 
mer to a Semicircle, and the fide A C given; hence the 
diftances C s ox AS may be found. 
Cafi 5^ If the place of Station be at fome Point within Fig 5^ 
thePlainofihe Triangle, made by the three Objeds, the 
Conftruftion and Calculation is the fame as in the laftj fa* ^ 
ving only that inftead of the obferved Angle AS the An- 
gle is equal to the Complement thereoftoa Seoiicir- 
ckj to wit^ it is equal to the Angle AS Dj both of them in- 
fifting on the fame Arch A D: And in like manner the Angle 
^ ADh equal to the Angle D S which is the Complement 
of the obferved C S 3^^ and in this Cafe the fum of the three 
Angles obferved^ is equal to four right Angles* 
In thefe three latter Cafes no ufe is made oCche Angle ob. 
fcrved between the two Objefts, as A and that are made 
the Bafe-line of the Conftrudion 3 Yet the fame is of ready 
ufe for finding the third diftance or laft fide fought, as in 
the fourth Schemej in the Triangle S A By there is given 
the diftance A- B^ its oppofite Angle equal to the fum of the 
two obferved Angles, and the Angle SAB attained^ a^in 
the fourth Cafe : Hence the third fide or lafl: diftance S B 
may be found. 
And here it may be noted^ that the three Angles C -A^Sj 
AsB^ S BC, are together equalto the Angle 5 for^ 
the two Angles C S B and C B s are equal to EC as being 
the Complement of S C B, to two right Angles 5 and the lik^ 
in the Triangle on the other fide. Ergo^ &c. 
Cafe 6> If the three Objeds be Aj B. c. and the Station pi^-, . 
at«y, a^ before, it may happen, according to the former ^ 
ConftruftionSj that the Points C and may fall ciofe toge- 
ther 3 and fo a right Line, joyning them, {hali be produced 
with uncertainty 5 in fuch cafe the Circle may be ccn:eivcd 
