| Andrew Bell - Euclid's Elements - 1837 - 240 pages
...points of a rectangle, the sums of the squares of those drawn to opposite angles are equal. 5. The **sum of the squares of the sides of a quadrilateral is equal to the sum of the** squares of its diagonals, and four times the square of the line joining their middle points. 6. The... | |
| William Alexander Willock - Circle - 1875 - 196 pages
...the sum of the squares of its diagonals. Verify this by the case of the square. 13. Prove that the **sum of the squares of the sides of a •quadrilateral is equal to the sum of the** squares of its diagonals, with four times tlie square of the line joining their points of bisection.... | |
| George Shoobridge Carr - Mathematics - 1880
...equal to OA, the sum of the same squares is equal to 6ra. . MISCELLANEOUS PROPOSITIONS. 924 ТЬе **sum of the squares of the sides of a quadrilateral is equal to the sum of the** squares of the diagonals plus four times the square of the line joining the middle points of the diagonals.... | |
| Samuel Constable - Geometry - 1882 - 224 pages
...This the student can easily prove for himself. It is clearly a particular case of (II. 4.).] 3. The **sum of the squares of the sides of a quadrilateral is equal to the sum of the** squares of its diagonals, together with four squares of the line joining the middle points of the diagonals.... | |
| George Shoobridge Carr - Handbooks, vade-mecums, etc - 1886 - 1040 pages
...if r, the radius of the sphere, be equal to OA, the sum of the same squares is equal to or2. 924 The **sum of the squares of the sides of a quadrilateral is equal to the sum of the** squares of the diagonals plus four times the square of the line joining the middle points of the diagonals.... | |
| United States. War Department - 1895 - 1000 pages
...coefficients and sum of the same coefficients with alternate signs. 3. Geometry. — No. 2 — The **sum of the squares of the sides of a quadrilateral is equal to the sum of the** squares of the diagonals, increased by four times the square of the segment which unites the middle... | |
| United States. Military Information Division. War Department - 1896 - 194 pages
...coefficients and sum of the same coefficients with alternate signs. 3. Geometry. — No. 2 — The **sum of the squares of the sides of a quadrilateral is equal to the sum of the** squares of the diagonals increased by four times the square of the segment which unites the middle... | |
| Edward Brooks - 1901 - 278 pages
...quadrilateral form a parallelogram. 3. The perimeter of the parallelogram formed by joining the middle points **of the sides of a quadrilateral is equal to the sum of the** diagonals of the quadrilateral. 4. The parallelogram formed by joining the middle points of the sides... | |
| 1902
...might be included in this proposition 1 ANNUAL EXAMINATION. \. Shew that the sum of the squares on **the sides of a quadrilateral is equal to the sum of the** squares on the diagonals, together with four times the square on the line joining the middle points... | |
| Education - 1921 - 970 pages
...20F2 = 2421 -az/2 and EF- = 2a2-2846. It would seem that we could now find a by applying to ABOC the **theorem: the sum of the squares of the sides of a quadrilateral** equals the sum of the squares of the two diagonals, plus four times the square of the line (EF) joining... | |
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