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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. "
Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ... - Page 26
by Euclides - 1860
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The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich - Mathematics - 1853
...together with double the square on half the base. 8. Three times the sum of the squares on the three sides of a triangle is equal to four times the sum of the squares of the Hues drawn from the angles to bisect the opposite sides. 9. The difference between the squares...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - Geometry, Plane - 1860 - 361 pages
...of the squares be joined ; the sum of the squares on the sides of the hexagonal figure thus formed is equal to four times the sum of the squares on the sides of the triangle. VII. 54. Find the side of a square equal to a given equilateral triangle. 55....
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The school edition. Euclid's Elements of geometry, the first six books, by R ...

Euclides - 1864 - 448 pages
...of the squares be joined ; the sum of the squares on the sides of the hexagonal figure thus formed is equal to four times the sum of the squares on the sides of the triangle. vn. 54. Find the side of a square equal to a given equilateral triangle. 55....
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Euclid's Elements of geometry, the first four books, by R. Potts. Corrected ...

Euclides - 1864 - 262 pages
...of the squares be joined ; the sum of the squares on the sides of the hexagonal figure thus formed is equal to four times the sum of the squares on the sides of the triangle. VII. 54. Find the side of a square equal to a given equilateral triangle. 55....
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson ...

Robert Potts - 1865 - 528 pages
...of the squares be joined ; the sum of the squares on the sides of the hexagonal figure thus formed is equal to four times the sum of the squares on the sides of the triangle. vn. 62. Find the side of a square equal to a given equilateral triangle. 63....
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An Elementary Course of Plane Geometry

Richard Wormell - Geometry, Modern - 1868 - 286 pages
...the difference of the squares of A B. BC, is equal to the difference of the squares of AD, DC. 10. Three times the sum of the squares on the sides of...triangle is equal to four times the sum of the squares of the lines joining the middle point of each side with the opposite angles. 1 1 . The squares of the...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1868 - 434 pages
...of the squares be joined ; the sum of the squares on the sides of the hexagonal figure thus formed is equal to four times the sum of the squares on the sides of the triangle. TIL 54. Find the side of a square equal to a given equilateral triangle. 55....
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An Elementary Course of Plane Geometry

Richard Wormell - Geometry, Plane - 1870 - 304 pages
...the difference of the squares of AB, BC, is equal to the difference of the squares of AD, D C. 10. Three times the sum of the squares on the sides of...triangle is equal to four times the sum of the squares of the lines joining the middle point of each side with the opposite angles. 1 1 . The squares of the...
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The Bombay university calendar, Volume 1

Bombay city, univ - 1873
...tangle contained by the whole and one of the parts may be equal to the square on the other part. 5. The sum of the squares on the sides of a triangle is 11 ual to twice the square on half the bass together with twice tVie square on the straight line which...
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The Elements of Euclid, containing the first six books, with a selection of ...

Euclides - 1874 - 342 pages
...the segments into which it is divided is equal to the square on the other side. 63. The difference of the squares on the sides of a triangle is equal to the difference of the squares on the segments of the base made by a perpendicular from the opposite...
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