54 Strong’s Problems. 
MATHEMATICS. 
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Art. V. Mathematical Problems, with Geometrical Con- 
structions and Demonstrations, by Professor THropore 
Strone, of Hamilton College. 
[For the figures, see the annexed Plate.] 
Prosiem I. 
"| HROUGH three given points which are not in thi 
same straight line, to describe a circle. 
Let A, B, C (fig. 1. pl. 1.) be 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. 
Construction. Join AB, BC, and AC. Then ABC is a 
triangle. Describe a circle about this triangle. (Sim. Eucl. 
IV. 5.) Then will the circumference of this circle pass 
through the points A, B, C._—Q. E. I. 
Prosuem II. 
Let there be three straight lines, which are not all parallel 
to each other, and do not cut each other in the same point, 
given, it is required to describe a circle, such that it shall 
touch each of them. sae 
Let AC, BC, BH, (Lig. 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 describe 
a circle such that it shall touch each of them. 
Const. Let AC, BC, produced if necessary, meet in C; 
and also CBand BHin 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 pomt 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 EF'G, which shall be the circle - 
required. 
