...from the vertex to the middle of the base, being given; to determine the triangle. PKOB. xxxv. Given the three lines drawn from the angles of a triangle to the opposite sides, dividing each of these angles into two equal parts; to determine the triangle. PROB....

...Triangles continued. VOL. XVII. X Prop. 2. El. b. vi. as far a* it extends to commensurable lines. The three lines drawn from the angles of a triangle to the middle points of the opposite sides have a common point of intersection. Also, the three lines bisecting the angles of a triangle. Prop....

...it would be greater by four times the square of the line E F. (303) If lines be drawn from the three angles of a triangle to the middle points of the opposite sides, three times the sum of the squares of the sides is equal to four times that of the bisectors. Let A,...

...is l-4th of the height. In the human body it is in the pelvis, between the hips. The intersection of three lines, drawn from the angles of a triangle, to the middle of the opposite sides, is its centre of gravity and percussion. If the lines bisect the angles, it...

...the circumference of a certain circle, and is also in a certain straight line. PROR. xxxv. — Given the three lines drawn from the angles of a triangle to the opposite sides, dividing each of these angles into two equal parts ; to determine the triangle. PROR,...

...Straight Line which joins the Origin and the Point in which two Lines MN', NM' meet ............... ib. The three Lines drawn from the Angles of a Triangle to the Middle Points of the opposite Sides meet in the same Point ................ ib. The Lines bisecting the three Angles of any Triangle meet...

...therefore AP passes through the middle point of MN. / Hence the three lines drawn from the angles of any triangle to the middle points of the opposite sides intersect in the same point. COR. 2. Let MN', NM' be supposed to bisect the angles M, N. Then by Euc. vi. 3, ri m n-ri MN and m...

...and the line drawn I'rom the vertex to the middle of the base, to determine the triangle. 12. Given the three lines drawn from the angles of a triangle to the middle of each of the opposite sides, to determine the triangle. 13. Given the base of a triangle, and the...

...rectangle contained by whose sides may be equal to the square of their difference. 93- Given the lengths of the three lines drawn from the angles of a triangle to the points of bisection of the opposite sides , construct the triangle. 94. Describe a triangle whose sides...

...squares of the sides. Equation [10] gives this THEOREM. Sixteen times the sum of the fourth powers of the lines drawn from the angles of a triangle to the middle points of the opposite sides, is equal to nine times the sum of the fourth powers of the sides. Equations [11], [12] and [13] would...