 | Euclid - Geometry - 1890 - 442 pages
...which the quadrilateral is a parallelogram, when the Theorem becomes — The sum of the squares on the sides of a parallelogram is equal to the sum of the squares on its diagonals. THEOREM (13) — In any triangle three times the sum of the squares on its... | |
 | Queensland. Department of Public Instruction - Education - 1890 - 526 pages
...double the square on the other (Book I., and Props. 1 to 11 of Book II). (>. The sum of the squares on the sides of a parallelogram is equal to the sum of the squares on the diagonals (Book I., and Props. 1 to 14 of Book II). 7. Show that the proof of Prop.... | |
 | Rupert Deakin - Euclid's Elements - 1891 - 102 pages
...less, show that AH the greater segment is also divided in medial section. 6. The sum of the squares on the sides of a parallelogram is equal to the sum of the squares on the diagonals. LI. 1. If any four points A, B, C, D are taken in order along a straight... | |
 | Euclid - Geometry - 1892 - 460 pages
...cases in which AQ falls without the triangle, or coincides with A P. 25. The sum of the squares on the sides of a parallelogram is equal to the sum of the squares on the diagonals. 26. In any quadrilateral the squares on the diagonals are together equal... | |
 | Henry Martyn Taylor - Euclid's Elements - 1895 - 708 pages
...of the vertex, when the sum of the squares on the two sides is given. 3. The sum of the squares on the sides of a parallelogram is equal to the sum of the squares on the diagonals. 4. In any quadrilateral the squares on the diagonals are together equal to... | |
 | Joe Garner Estill - 1896 - 186 pages
...the third side is 8 ; what is the length of the third side ?—Mass. Inst. Tech. 63. Prove that the sum of the squares of the sides of a parallelogram is equal to the sum of the squares of its diagonals.—School of Mines. 64. In a triangle whose sides are 48, 36, and 50, where... | |
 | George D. Pettee - Geometry, Modern - 1896 - 272 pages
...rsubsti LProp. rsubstitute by | p.XIV, Case IJ r L sq. of AC = 4 times'! sq. of AF, etc. J 267. Cor. The sum of the squares of the sides of a parallelogram is equal to the sum of the squares of its diagonals. [The line joining the middle points of the diagonals equals zero.] FORMULAE... | |
 | Joe Garner Estill - Geometry - 1896 - 168 pages
...the third side is 8 ; what is the length of the third side ? — Mass. Inst. Tech. 63. Prove that the sum of the squares of the sides of a parallelogram is equal to the sum of the squares of its diagonals. — School of Mines. 64. In a triangle whose sides are 48, 36, and 50, where... | |
 | Lawrence Robert Dicksee - Accounting - 1897 - 122 pages
...if the square on one side is equal to the sum of the squares on the other two sides. Show that the sum of the squares of the sides of a parallelogram is equal to the sum of the squares of its diagonals. Q. 6.—Prove that, if a line be divided into any two parts, the rectangle... | |
 | Webster Wells - Geometry - 1898 - 264 pages
...§ 277, 2 ACx AE=Iff + AC* - BC 2 ; and in like manner a value may be found for 2 BC x BD.} 79. The sum of the squares of the sides of a parallelogram is equal to the sum of the squares of its diagonals. (§ 279, I.) 80. To construct a triangle similar to a given triangle, having... | |
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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. 
