 | Euclid, Dionysius Lardner - Euclid's Elements - 1828 - 542 pages
...rectangle under the sum and difference of the segments (207). (250) COR. 6. — The difference, between the squares of the sides of a triangle is equal to twice the rectangle under the base and the distance of the perpendicular from the middle point. For if the perpendicular... | |
 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...the rectangle is a maximum when the line is bisected. Cor. 4. Since (I. 47. cor. 4.) the difference of the squares of the sides of a triangle is equal to the difference of the squares of the segments of the base, it follows, from the first corollary above,... | |
 | Samuel Earnshaw - Statics - 1845 - 290 pages
...Consequently, in the case of the triangle (Art. 147), EC- + AC? + AB* = 3. (AGP + BG* + CCP). Hence the sum of the squares of the sides of a triangle is equal to three times the sum of the squares of the distances of its angular points from its centre of gravity.... | |
 | Euclid, James Thomson - Geometry - 1845 - 382 pages
...the rectangle is a maximum when the line is bisected. Cor. 4. Since (I. 47, cor. 4) the difference of the squares of the sides of a triangle is equal to the difference of the squares of the segments of the base, it follows, from the first corollary above,... | |
 | Euclides - 1858 - 248 pages
...equal to the rectangle under the sum and difference of the segments. — 6. The difference between the squares of the sides of a triangle, is equal to twice the rectangle under the base and the distance of the perpendicular from the middle point. — These Corollaries... | |
 | Woolwich roy. military acad - 1861 - 572 pages
...opposite angle and the acute angle. In any triangle shew that the sum of the squares of the two sides is equal to twice the square of half the base, together with twice the square of the line which joins the vertex to the middle point of the base. 9. Investigate the expression for the... | |
 | Euclides - 1862 - 140 pages
...or more given squares; and also one equal to the difference of two given squares. 49. The difference of the squares of the sides of a triangle is equal to the difference of the squares of the segments of the base made by a perpendicular from the opposite... | |
 | Euclid, James Bryce, David Munn (F.R.S.E.) - Geometry - 1874 - 236 pages
...C; then the square on BC will be the difference of the given squares. Cor. 3. — a. The difference of the squares of the sides of a triangle is equal to the difference of the squares of the segments of the base made by a perpendicular. For the square of... | |
 | William Alexander Willock - Circle - 1875 - 196 pages
...four times tlie square of the line joining their points of bisection. 14. Prove that 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 bisectors of the sides drawn from the vertices of the triangle.... | |
 | William Guy Peck - Conic sections - 1876 - 412 pages
...difference of two lines is equal to the difference of their squares. 3°. The sum of the squares of two sides of a triangle is equal to twice the square of half the third side, increased ly twice the square of the line drawn from the middle of the third side to the... | |
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The sum of the squares of two sides of a triangle is equal to twice the square of half the third side increased by twice the square of the median upon that side. 
