 | Adrien Marie Legendre - Geometry - 1874 - 500 pages
...equal to AC*, and IDE2 to BD2 (P. Vin., C.) : hence, AE* + EC2 + CD2 + DA2 = AC2 + ED2. That is, the sum of the squares of the sides of a parallelogram, is equal to the sum of the squares of its diagonals. PROPOSITION XV. THEOREM. In any triangle, a line drawn parallel to the base... | |
 | William Alexander Willock - Circle - 1875 - 196 pages
...semipcrimeter (or half sum of the three sides) and the radius of its inscribed circle. 12. Prove that the sum of the squares of the sides of a parallelogram is equal to the sum of the squares of its diagonals. Verify this by the case of the square. 13. Prove that the sum of the squares... | |
 | Thomas Hunter - Geometry, Plane - 1878 - 142 pages
...2 +BC 2 be equal to For AC 2 =AD 2 +DC 2 + 2AD.DE (Prop. XIX.), DE PROPOSITION XXII.—THEOREM. The sum of the squares of the sides of a parallelogram is equal to the sum of the squares of the diagonals. Let ABCD be a parallelogram; then will the sum of the squares of AB, BD,... | |
 | W J. Dickinson - Geometry - 1879 - 44 pages
...BC. Then i. 47, n. 5.) 8. Enunciate (only) Props. 12 and 13 of Second Book. The sum of the squares on the sides of a parallelogram is equal to the sum of the squares on the diagonals. 9. If the square on the perpendicular from the vertex of a triangle to the... | |
 | Edward Harri Mathews - 1879 - 94 pages
...perpendicular let fall on it from the opposite angle, and the acute angle. The sum of the squares on the sides of a parallelogram is equal to the sum of the squares of the diagonals. Christmas 1874. EUCLID. Section I. 1. In what ways does Euclid classify triangles... | |
 | Joseph Wollman - 1879 - 120 pages
...on their difference is double the squares of the two straight lines. 49. The sum of the squares on the sides of a parallelogram is equal to the sum of the squares of the diagonals. 50. If a straight line be divided into any three parts, the square in the... | |
 | Isaac Todhunter - Euclid's Elements - 1880 - 426 pages
...is equal to the square on AB, together with twice the square on BC. 147. The sum of the squares on the sides of a parallelogram is equal to the sum of the squares on the diagonals. 148. The base of a triangle is given and is bisected by the centre of a given... | |
 | Education, Higher - 1884 - 538 pages
...and of the square on the line made up of the half and the part produced. 6. The sum of the squares on the sides of a parallelogram is equal to the sum of the squares on the diagonals. 8. If a straight line iouch a circle, and from the point of contact a straight... | |
 | Samuel Constable - Geometry - 1882 - 222 pages
...OBC, OCA, OAB. It will be found by addition that the squares OB, 00, OA cancel.] 2. Prove that the sum of the squares of the sides of a parallelogram is equal to the sum of the squares of its diagonals. [See Prop. 12. It is necessary, also, for the solution of this theorem and... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1883 - 428 pages
...is equal to the square on AB, together with twice the square on BC. 147. The sum of the squares on the sides of a parallelogram is equal to the sum of the squares on the diagonals. 148. The base of a triangle is given and is bisected by the centre of a given... | |
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The sum of the squares on the sides of a parallelogram is equal to the sum of the squares on the diagonals. 
