 | John Casey - Geometry - 1888 - 279 pages
...CF2) + 4FB* - 4AE2 + 4EP +4FB2 = AC2 +BD2 + 4EE2. Prop. 5. — Three times the sum of the squares of the sides of a triangle is equal to four times the sum of the squares of the lines bisecting the sides of the triangle. Dem. — Let D, E, F be the middle points of the... | |
 | 1890 - 608 pages
...of the squares on half the base and on the line joining the vertex to the middle point of the base. Three times the sum of the squares on the sides of...equal to four times the sum of the squares on the lines drawn from the vertices to the middle points of the opposite sides. 3. If a chord of a circle... | |
 | Edward Mann Langley, W. Seys Phillips - 1890 - 538 pages
...Show that the locus of D is a circle whose centre is the mid.pt. (C) of their join (AB). Ex. 205. — Three times the sum of the squares on the sides of...triangle is equal to four times the sum of the squares on its medians. Ex. 206. — The sq. on the distance of a point ( D) from a given point (A) is double... | |
 | Euclid - Geometry - 1890 - 442 pages
...sides of any triangle, and their comers joined ; then the sum of the squares on the hexagon thus formed is equal to four times the sum of the squares on the sides of the triangle. NOTE — Use preceding Exercise. 20. The sum of the squares on the diagonals... | |
 | Rupert Deakin - Euclid's Elements - 1891 - 102 pages
...squares on AB and BC is equal to three times the square on AC. 6. Three times the sum of the squares of the sides of a triangle is equal to four times the sum of the squares of its three medians. 1. In any quadrilateral figure the squares on the diagonals are together equal... | |
 | Euclid - Geometry - 1892 - 460 pages
...the hypotenuse is equal to five times the square on the line between the points of trisection. 33. Three times the sum of the squares on the sides of...equal to four times the sum of the squares on the medians. 34. ABC is a triangle, and O the point of intersection of its medians : shew that AB2+BC2... | |
 | James Blaikie - 1892 - 74 pages
...parallelogram, I and J coincide with O. 5. In any triangle, three times the sum of the squares on the sides is equal to four times the sum of the squares on the medians. A s Apply Ex. 1 to each pair of sides, and add results. 6. If G be the point of intersection... | |
 | Nathan Fellowes Dupuis - Geometry, Solid - 1893 - 268 pages
...3 2a2 - 2a^. QED 93. Theorem. In any tetrahedron, nine times the sum of the squares on the medians is equal to four times the sum of the squares on the edges. Proof. Let mj, m2,' ms, m4 denote the medians. Then from 86, Das vertex, 9wii2 = 3a2 + 362 +3c2... | |
 | William James Milne - Geometry - 1899 - 404 pages
...the diagonals of a parallelogram is equivalent to the sum of the squares on its four sides. Ex. 582. Three times the sum of the squares on the sides of a triangle is equivalent to four times the sum of the squares on the medians of the triangle. Ex. 583. Two sides... | |
 | William James Milne - Geometry - 1899 - 326 pages
...ZD2«=4 AE2 + 4 BE1. Now AG = 2 AE ; .: AC2 ** 4 ÄE2 ; similarly, Ш? ** 4 BU?, and Hence, Ex. 582. Three times the sum of the squares on the sides of a triangle is equivalent to four times the sum of the squares on the medians of the triangle. Data : Д ЛВC and... | |
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Prove that three times the sum of the squares on the sides of a triangle is equal to four times the sum of the squares on the lines drawn from the vertices to the middle points of the opposite sides. 
