...CAE, .-. BC2 is less than DC2 by four rectangles under CA,AE or CA,AF. Cor. 2. Hence it is evident the sum of the squares of the diagonals of a parallelogram is equal to the sum of the squares of the sides. PROP. 14. PROB. i To describe a square equal to a given rectilineal...

...a semicircle is a right angle ; that in a greater segment less ; and that in a smaller greater. 2. The sum of the squares of the diagonals of a parallelogram is equal to the sum of the squares of its sides. 3. Construct a parallelogram that shall be equal, both in area...

...Fay; ie (21. 3) abe sin С = ace sin B, or 6 sin C = с sin B ; ie ó : с : : sin B : sin С. Ex. 3. The sum of the squares of the diagonals of a parallelogram is equal to the sum of the squares of the sides. Retaining the notation and figure of Ex. 1, Art. 7, DA=a-ß; and,...

...by twice the square of the line drawn from the middle of the third side to the opposite vertex. 4°. The sum of the squares of the diagonals of a parallelogram is equal to the sum of the squares of its sides. BOOK IV. 105 ties of one diagonal is equal to the sum of the squares...

...Fay; L e. (21. 3) abf sin C = act sin B, or b sin C = c sin B ; ie 6 : c :: sin A' ; sin C". Ex. 3. The sum of the squares of the diagonals of a parallelogram is equal to the sum of the squares of the sides. Retaining the notation and figure of Ex. 1, Art. 7, and, changing...

...« ß' -+• ß a', which is not less important than the two preceding ones. 67. Examples. Ex. 1 . The sum of the squares of the diagonals of a parallelogram is equal to the sum of the squares of the sides. с Let the side AB = <x, the side AD = ß, then (Arts. 15, 16)...

...and the sum of the squares of the sides in magnitude, the locus of the vertex is a O. Prop. 3.—The sum of the squares of the diagonals of a parallelogram is equal to the B sum of the squares of its four Dem.—Let ABCD be the a. Draw CE || to BD ; A" produce AD to...

...ie (21.3) abe sin G = act sin B, or 6 sin C = c sin .B ; ie b : c : : sin B : sin C. Ex. 3. TAe swm of the squares of the diagonals of a parallelogram is equal to the sum of the squares of the sides. Retaining the notation and figure of Ex. 1, Art. 7, and, changing...

...so that the rectangle under BO and a given line DE shall be equal to the square of AC. 9. Prove that the sum of the squares of the diagonals of a parallelogram is equal to the sum of the squares of its four sides. 10. Reduce 1 1 . Find the square root of and also the square...

...the sine. (i) Find в when 2 sin1 в + ^2 cos в = 2. 8. Obtain the formula a» =63+c2 -2bc cos в. The sum of the squares of the diagonals of a parallelogram is equal to the sum of the squares of the four sides. 9. Define a plane — a ruled surface. The intersection of...