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" The sum of the squares of the four sides of any quadrilateral is equal to the sum of the squares of the diagonals plus four times the square of the line joining the mid-points of the diagonals. "
A Synopsis of Elementary Results in Pure Mathematics: Containing ... - Page 187
by George Shoobridge Carr - 1886 - 935 pages
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The Elements of geometry [Euclid book 1-3] in general terms, with notes &c ...

Euclides - 1821 - 294 pages
...PROP, 11. THEOR, In every quadrilateral Jigure (ABCD) the sum of the squares of the sides is equal to the sum of the squares of the diagonals, plus four times the square of the fine (EF) joining the points of bisection of the did' gonals. .. 23. Join EA, ED. Then the sum of the...
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The Elements of geometry [Euclid book 1-3] in general terms, with notes &c ...

Euclides - 1833 - 304 pages
...PROP. 11. THEOR. In every quadrilateral figure (ABCD) the sum of the squares of the sides is equal to the sum of the squares of the diagonals, plus four times the square of the line (EF) joining the points of bisection of the diagonals. Fig. 23. Join EA and ED. Then the sum of the...
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Elements of Plane Geometry According to Euclid

Andrew Bell - Euclid's Elements - 1837 - 290 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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Mathematical Dictionary and Cyclopedia of Mathematical Science: Comprising ...

Charles Davies, William Guy Peck - Mathematics - 1855 - 628 pages
...AC X BD sin AOD. 5. In any quadrilateral, the sum of the squares of the four sides is equivalent to the sum of the squares of the diagonals, plus four times the square of the distance between the middle points of the diagonals ; that is, If the quadrilateral is a parallelogram,...
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Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ...

Euclides - 1860 - 142 pages
...former, we obtain DE2 + DF2 + FG= + GH2 + HK2 + KE2 = 3BC2 + 5BC2 = 8BC2. EXERCISE XVII. — THEOREM. 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. Let ABCD...
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Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ...

Euclides - 1860 - 288 pages
...to eight times the square on the hypotenuse of the original triangle. 17. The sum of the squares on the sides of a quadrilateral is equal to the sum of the squares on its diagonals, and four times the square on the line joining their middle points. 18. The...
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Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - Geometry - 1862 - 532 pages
...PROPOSITION XVI. — THEOREM. 249. In any quadrilateral the sum of the squares of the sides is equivalent to the sum of the squares of the diagonals, plus four times the square of the straight line that joins the middle points of the diagonals. Let А В С D be any quadrilateral, the...
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Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - Geometry - 1863 - 504 pages
...PROPOSITION XVI. — THEOREM. 249. In any quadrilateral the sum of the squares of the sides is equivalent to the sum of the squares of the diagonals, plus four times the square of the straight line that joins the middle points of the diagonals. Let ABCD be any quadrilateral, the _C...
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Elements of Geometry: With Practical Applications to Mensuration

Benjamin Greenleaf - Geometry - 1868 - 340 pages
...PROPOSITION XVI. — THEOREM. 249. In any quadrilateral the sum of the squares of the sides is equivalent to the sum of the squares of the diagonals, plus four times the square of the straight line that joins the middle points of the diagonals. Let ABCD be any quadrilateral, the diagonals...
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Elements of Geometry and Trigonometry: With Practical Applications

Benjamin Greenleaf - 1869 - 516 pages
...PROPOSITION XVI. — THEOREM. 249. In any quadrilateral the sum of the squares of the sides is equivalent to the sum of the squares of the diagonals, plus four times the square of the straight line that joins the middle points of the diagonals. Let ABCD be any quadrilateral, the diagonals...
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