 | W. J. C. Miller - Mathematics - 1874 - 118 pages
...various triangles of the figure the following theorem : — The squares on two sides of a triangle are equal to twice the square on. half the third side, together with twice the square on the medial line to that side from the opposite angle.] III. Solution by the PROPOSER. Since O is at the... | |
 | Euclid - Geometry - 1890 - 442 pages
...fig. (i) 2MN = BN ~ CN. In fig. (2) zMN = BN + CN. AlsoAB2~AC3 = BN^CN", ADDENDA THEOREM (n) — /« any triangle the sum of the squares on two sides is...with twice the square on the median which bisects that side. B NC In A ABC let AD be the median from A. Draw AN JL to BC. Then, unless AN coincides with... | |
 | Rupert Deakin - Euclid's Elements - 1891 - 102 pages
...equation. Solve it and explain the two solutions. 6. In any triangle the sum of the squares on two s'des is equal to twice the square on half the third side together with twice the square on the median waich bisects the third side. LIII. 1. State and prove geometrically that (a+6+e)2= 2. Of all rectangles... | |
 | Euclid - Geometry - 1892 - 460 pages
...point D in AC perpendicular to AB: shew that the rectangle AB, AE is equal to the rectangle AC, AD. 24. In any triangle the sum of the squares on two sides...with twice the square on the median which bisects the third side. QC Let ABC be a triangle, and AP the median bisecting the side BC. Then shall AB. +... | |
 | Great Britain. Education Department. Department of Science and Art - 1894 - 894 pages
...rectangle. What is the least length that the given perimeter mav havel (20.)" 28. In any triangle, show that the sum of the squares on two sides is equal to twice...the third side together with twice the square on the straight line drawn from the middle point of that side to the opposite vertex. In the circle ABCD,... | |
 | Euclid, Henry Sinclair Hall, Frederick Haller Stevens - Euclid's Elements - 1900 - 330 pages
...D in AC perpendicular to AB : shew that the rectangle AB, AE is equal to the rectangle AC, AD, 24. In any triangle the sum of the squares on two sides...with twice the square on the median which bisects the third side. BPQC Let ABC be a triangle, and AP the median bisecting the side BC. Then shall AB2... | |
 | 1904 - 226 pages
...angular points of a given polygon of n sides, but none of whose sides are sides of the polygon. 7. (a) In any triangle the sum of the squares on two sides...with twice the square on the median which bisects the third side. (6) If from any point on the circumference of the circle circumscribed about a triangle,... | |
 | Euclid - Euclid's Elements - 1904 - 488 pages
...is equal to the sum of the rectangles AB, BF and AC, CE. 24. In any triangle the sum of the sqitares on two sides is equal to twice the square on half...with twice the square on the median which bisects the third side. BPQC Let ABC be a triangle, and AP the median bisecting the side BC. Then shall AB2... | |
 | Levi Leonard Conant - Geometry - 1905 - 140 pages
...fixed points on the circle shall be a minimum. HINT. Prove by means of the theorem which states that in any triangle the sum of the squares on two sides...is equal to twice the square on half the third side plus twice the square on the median drawn to the third side. 286. Given the base and the opposite angle... | |
 | Henry Sinclair Hall - 1908 - 286 pages
...rectangle contained by one of those sides and the projection of the other side upon it. 227 THEOREM 56. In any triangle the sum of the squares on two sides...together with twice the square on the median which bisectu the third side. 229 Rectangles in connection with Circles. THEOREM 57. [Euc. III. 35.] If two... | |
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In any triangle the sum of the squares on two sides is equal to twice the square on half the third side together with twice the square on the median which bisects the third side. 
