 | Henry William Watson - Geometry - 1871 - 320 pages
...sum of the squares of AP and BP is equal to the sum of the squares of AQ and BQ. 9. Prove that the sum of the squares of the sides of a parallelogram is equal to that of the squares of its two diagonals. 10. Prove that if any point within a parallelogram be joined... | |
 | 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... | |
 | 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... | |
 | 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... | |
 | 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... | |
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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. 
