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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. "
Elements of Geometry - Page 54
by Adrien Marie Legendre - 1825 - 224 pages
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The Elements of Plane Geometry ...

Association for the improvement of geometrical teaching - Geometry, Modern - 1884 - 150 pages
...squares on AB and AC is double the sum of the squares on BD and DA. QED Ex. 23. The sum of the squares on the sides of a parallelogram is equal to the sum of the squares on the diagonals. Ex. 24. The sum of the squares on the sides of any quadrilateral 'WM ,'•...
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The elements of plane geometry, Volume 1

Mathematical association - 1884 - 146 pages
...squares on AB and AC is double the sum of the squares on BD and DA. QED Ex. 23. The sum of the squares on the sides of a parallelogram is equal to the sum of the squares on the diagonals. Ex. 24. The sum of the squares on the sides of any quadrilateral is greater...
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The First Six Books of the Elements of Euclid: And Propositions I-XXI of ...

Euclid, John Casey - Euclid's Elements - 1885 - 340 pages
...that prove that the middle point of AD is equally distant from B and C. 5. The sum of the squares on the sides of a parallelogram is equal to the sum of the squares on its diagonals. PEOP. XI.— PROBLEM. To divide a given finite line (AB) into two segments...
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The first six books of the Elements of Euclid, and propositions i.-xxi. of ...

Euclides - 1885 - 340 pages
...that prove that the middle point of AD is equally distant from B andC. 6. The sum of the squares on the sides of a parallelogram is equal to the sum of the squares on its diagonals. PEOP. XI.— PROBLEM. To divide a given finite line (AB) into two segments...
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A Synopsis of Elementary Results in Pure Mathematics: Containing ...

George Shoobridge Carr - Mathematics - 1886 - 1036 pages
...times the square of the line joining the middle points of the diagonals. (922, i.) 925 Сов. — The sum of the squares of the sides of a parallelogram is equal to the sum of the squares of the diagonals. 926 In a given line AG, to find a point X whose distance from a point P shall...
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The New York Examination Questions: Being the Questions Given at All the ...

New York (State). Department of Public Instruction - 1887 - 268 pages
...triangle, when the altitude, the vertical angle, and one of the sides are given. 4. Prove that the sura of the squares of the sides of a parallelogram is equal to the sum of the squares of the diagonals. 5. Describe a circle which shall pass through three given points not in the...
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Examinations Papers

1887 - 644 pages
...hase and on the line joining the vertex to the middle point of the base. The sum of the squares on the sides of a parallelogram is equal to the sum of the squares on the diagonals. 2. Angles in the same segment of a circle are equal to one another. Two chords...
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Exercise Manuals, Issue 3

George Albert Wentworth - 1889 - 276 pages
...to twice the product of the third side and the projection of the median upon the third side. 22. The sum of the squares of the sides of a parallelogram is equal to the sum of the squares of the diagonals (Ex. 19.) 23. The sum of the squares of the sides of any quadrilateral is...
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Wentworth & Hills's Exercise Manuals: Geometry, Issue 3

George Albert Wentworth - 1889 - 264 pages
...to twice the product of the third side and the projection of the median upon the third side. 22. The sum of the squares of the sides of a parallelogram is equal to the sum of the squares of the diagonals (Ex. 19.) 23. The sum of the squares of the sides of any quadrilateral is...
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Report of the Secretary for Public Instruction ...

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....
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