...before, AB2=BC2+ AC2— 2BC X CD. THEOREM. 192. In any triangle, having an obtuse angle, the square of the side opposite the obtuse angle, is greater than the sum of the squares of the sides containing it, by twice the rectangle contained by either of the latter sides, and the...

...AB2=BC2 + AC2 —SBC x CD. PROPOSITION XIII. THEOREM. .In every obtuse angled triangle, the square of the side opposite the obtuse angle is greater than the sum of the squares of the other two sides by twice the rectangle contained by the base and the distance from the obtuse...

...any triangle, the square of the side subtending an acute angle, is less than the squares of the other sides, by twice the rectangle contained by either of those sides, and the straight line intercepted between the acute angle and the perpendicular drawn to that side from the...

...the square of the side subtending either of the acute angles, is less than the sum of the squares of the other two sides, by twice the rectangle contained by either of these sides and the straight line intercepted between the perpendicular let fall upon it from the opposite...

...any triangle, the square of a side subtending an acute angle, is less than the squares of the other sides, by twice the rectangle contained by either of those sides, and the straight line intercepted between the acute angle and the perpendicular drawn to that side from the...

...=BC 2 +AC 2 —2BCxCD. D DB PROPOSITION XIII. THEOREM. In every obtuse angled triangle, the square of the side opposite the obtuse angle is greater than the sum of the squares of the other two sides by twice the rectangle contained by the base and the distance from the obtuse...

...obtuse-angled triangle (ABC) to the opposite side (BC) produced, the square on the side (AB) subtending the obtuse angle is greater than the sum of the squares on the two sides (BC and CA), which contain the obtuse angle, by double the rectangle under the side (BC),...

...sides about the right angle. THEOREM XL. In any obtuse-angled triangle, the square on the side opposiie the obtuse angle is greater than the sum of the squares...sides, by twice the rectangle contained by either side about the obtuse angle, and the part of this side produced to meet the perpendicular drawn to...

...the square root of the sum of the squares of the two sides about the right angle. THEOREM XL. In any obtuse-angled triangle, the square on the side opposite...sides, by twice the rectangle contained by either side about the obtuse angle, and the part of this side produced to meet the perpendicular drawn to...

...of the equal sides. 600. Find the obtuse angle of a triangle when the square on the side opposite to the obtuse angle is greater than the sum of the squares on the sides containing it, by the rectangle of the sides. 501. Construct a rectangle equal to a given square...