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" The sum of the squares of the 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 middle points of the diagonals. "
A Treatise on Elementary Geometry: With Appendices Containing a Collection ... - Pagina 117
door William Chauvenet - 1872 - 368 pagina’s
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The Elements of geometry [Euclid book 1-3] in general terms, with notes &c ...

Euclides - 1821 - 294 pagina’s
...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 pagina’s
...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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Elemento of Geometry, Theoretical and Practical: Containing a Full ...

George Clinton Whitlock - 1848 - 338 pagina’s
...squares- of the sides of a (138) quadrilateral, exceeds the sum of the squares of its diagonals by four times the square of the line joining the middle points of the diagonals. Cor. 4. The sum of the squares of the sides of a parallele- (139) gram, is equal to the sum of the...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - 1852 - 436 pagina’s
...quadrilateral, the sum of the squares of the four sides is equivalent to the sum of the squares of the two diagonals, plus four times the square of the line joining the middle points of the diagonals. Let ABCD be a quadrilateral, AC, BD, the diagonals, and EF a line join- D^ ing the middle points E...
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Five Years in an English University, Volume 2

Charles Astor Bristed - 1852 - 470 pagina’s
...THE squares of the sides of a quadrilateral figure are greater than the squares of its diagonals by four times the square of the line joining the middle points of the diagonals. 2. The coefficient of x' in the expansion of (1 -fx) (l+cz) (1 + c'x) (1 + c'x)..., the number of factors...
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Mathematical Dictionary and Cyclopedia of Mathematical Science: Comprising ...

Charles Davies, William Guy Peck - 1855 - 628 pagina’s
...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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Examination papers used at the examinations for direct commissions [&c.].

War office - 1858 - 578 pagina’s
...the squares of the sides of a quadrilateral figure are greater than the squares of its diagonals by four times the square of the line joining the middle points of the diagonals. 4. The faces of a pyramid on a square base are equilateral triangles, and each side of the base is...
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A Treatise on Plane and Spherical Trigonometry, and on Trigonometrical ...

John Hymers - 1858 - 292 pagina’s
...sides of a quadrilateral figure is greater than the sum of the squares of its diagonals by TRIO. 20 four times the square of the line joining the middle points of the diagonals. 61. When a quadrilateral is capable of having both a circle inscribed in it and one circumscribed about...
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Elements of Plane and Spherical Trigonometry: With Practical Applications

Benjamin Greenleaf - 1862 - 532 pagina’s
...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 - 1863 - 504 pagina’s
...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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