(κ). II. 3.
Through a given point, without a given Line, a Line may be drawn such that the two Lines are equally inclined to any transversal.
Take a second point, on the same side of the given Line and at the same distance from it; and join the 2 points.
Then the Line, so drawn, and the given Line, are equally inclined to any transversal. [(θ).
Therefore through a given point, &c. Q. E. D.
(λ). II. 18 (b).
The angles of a Triangle are together equal to two right angles.
Let ABC be a Triangle. It is to be proved that its 3 angles are together equal to 2 right angles.
Through A let DAE be drawn, such that DAE, BC are equally inclined to any transversal. [(κ).
Then ∠B = ∠DAB, and ∠C = ∠EAC;
∴ ∠s B, C, BAC = ∠s DAB, EAC, BAC;
= 2 rt ∠s. [Euc. I. 13.
Therefore the angles &c. Q. E. D.
(μ). II. 4.
A Pair of Lines, which are equally inclined to a certain transversal, are so to any transversal.
