 | Euclides - 1821 - 294 pàgines
...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... | |
 | 1844 - 456 pàgines
...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... | |
 | Philip Kelland - 1873 - 248 pàgines
...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,... | |
 | William Guy Peck - 1876 - 376 pàgines
...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... | |
 | Philip Kelland, Peter Guthrie Tait - 1882 - 310 pàgines
...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... | |
 | Hussein Tevfik (Pacha.) - 1882 - 98 pàgines
...« 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)... | |
 | John Casey - 1882 - 186 pàgines
...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... | |
 | Philip Kelland, Peter Guthrie Tait - 1882 - 288 pàgines
...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... | |
 | Dublin city, univ - 1883 - 510 pàgines
...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... | |
 | John Casey - 1886 - 262 pàgines
...and the sum of the squares of the sides in magnitude, the locus of the vertex is a 0 . Prop. 3. — The sum of the squares of the diagonals of a parallelogram is equal to the sum of the squares of its four Dem.— Let ABCD be the a. Draw CE || to BD ; £ produce AD to meet... | |
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The sum of the squares of the diagonals of a parallelogram is equal to the sum of the squares of its four Dem.— Let ABCD be the a. 
