54 Strong’s Problems. 
MATHEMATICS. 
RE Ae 
Arr. V. Mathematical Problems, with Geometrical Con- 
structions and Demonstrations, by Professor Turopore 
Srrone, of Hamilton College. , 
[For the figures, see the annexed Plate.] 
Prosiem [. 
Tt HROUGH three given pane which are not in the 
same straight line, to describe a 
Let A, B, C (Fig. 1. pl. 1 ) ris the three given points 
which are not in the same straight line, it is required to de- 
scribe a circle the circumference of which shall pass through 
these points. : sae * eg ae eee 
onstruction. Join AB, BC, and AC. Then ABC is a 
triangle. Describe a circle about this triangle. (Sim. Euel. 
IV. 5.) Then will the circumference of this circle pass 
through the points A, Q. E. 1. 
Prosiem II. 
Let there be three straight lines, w to arenot all parallel 
to each other, and do not cut each other in the same point, 
given, it is required to describe a idecls. such that it shall 
touch each of them 
Let AC, BC, BH, (Fig. 2.) be three given straight lines 
which are not all parallel to each other and which do not 
cut each other in the same point, it is required to depoaibe 
a circle such ay it shall touch each of them. 
t , BC, produced if necessary, meet in C; 
_and also CB ea BH in B. Bisect the angle ACB by the 
straight line CD, and also the angle CBH by the straight 
line BD. Let them meet in D. From the point D draw 
DG, at right angles to BC, DF at right angles to AC, and 
DE at right angles to BH. From D as a centre, with ra- 
dius DF, describe the circle EFG, which shall be the circle 
required. 
