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" The sum of the squares of the sides of a quadrilateral is equal to the sum of the squares of the diagonals... "
Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ... - Page 29
by Euclides - 1860
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Elements of Plane Geometry According to Euclid

Andrew Bell - Euclid's Elements - 1837 - 240 pages
...points of a rectangle, the sums of the squares of those drawn to opposite angles are equal. 5. The sum of the squares of the sides of a quadrilateral is equal to the sum of the squares of its diagonals, and four times the square of the line joining their middle points. 6. The...
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The Elementary Geometry of the Right Line and Circle ... With Exercises

William Alexander Willock - Circle - 1875 - 196 pages
...the sum of the squares of its diagonals. Verify this by the case of the square. 13. Prove that the sum of the squares of the sides of a •quadrilateral is equal to the sum of the squares of its diagonals, with four times tlie square of the line joining their points of bisection....
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A Synopsis of Elementary Results in Pure and Applied ..., Volume 1, Part 1

George Shoobridge Carr - Mathematics - 1880
...equal to OA, the sum of the same squares is equal to 6ra. . MISCELLANEOUS PROPOSITIONS. 924 ТЬе sum of the squares of the sides of a quadrilateral is equal to the sum of the squares of the diagonals plus four times the square of the line joining the middle points of the diagonals....
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Geometrical Exercises for Beginners

Samuel Constable - Geometry - 1882 - 224 pages
...This the student can easily prove for himself. It is clearly a particular case of (II. 4.).] 3. The sum of the squares of the sides of a quadrilateral is equal to the sum of the squares of its diagonals, together with four squares of the line joining the middle points of the diagonals....
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A Synopsis of Elementary Results in Pure Mathematics: Containing ...

George Shoobridge Carr - Handbooks, vade-mecums, etc - 1886 - 1040 pages
...if r, the radius of the sphere, be equal to OA, the sum of the same squares is equal to or2. 924 The sum of the squares of the sides of a quadrilateral is equal to the sum of the squares of the diagonals plus four times the square of the line joining the middle points of the diagonals....
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Annual Reports of the War Department, Volume 1

United States. War Department - 1895 - 1000 pages
...coefficients and sum of the same coefficients with alternate signs. 3. Geometry. — No. 2 — The sum of the squares of the sides of a quadrilateral is equal to the sum of the squares of the diagonals, increased by four times the square of the segment which unites the middle...
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Military Schools in Europe, and Other Papers Selected for Publication

United States. Military Information Division. War Department - 1896 - 194 pages
...coefficients and sum of the same coefficients with alternate signs. 3. Geometry. — No. 2 — The sum of the squares of the sides of a quadrilateral is equal to the sum of the squares of the diagonals increased by four times the square of the segment which unites the middle...
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Plane Geometry

Edward Brooks - 1901 - 278 pages
...quadrilateral form a parallelogram. 3. The perimeter of the parallelogram formed by joining the middle points of the sides of a quadrilateral is equal to the sum of the diagonals of the quadrilateral. 4. The parallelogram formed by joining the middle points of the sides...
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Calendar, for the Year ...

1902
...might be included in this proposition 1 ANNUAL EXAMINATION. \. Shew that the sum of the squares on the sides of a quadrilateral is equal to the sum of the squares on the diagonals, together with four times the square on the line joining the middle points...
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School Science and Mathematics, Volume 21

Education - 1921 - 970 pages
...20F2 = 2421 -az/2 and EF- = 2a2-2846. It would seem that we could now find a by applying to ABOC the theorem: the sum of the squares of the sides of a quadrilateral equals the sum of the squares of the two diagonals, plus four times the square of the line (EF) joining...
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