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" ... by four times the square of the line joining the middle points of the diagonals. "
Elements of Geometry, Theoretical and Practical: Containing a Full ... - Page 75
by George Clinton Whitlock - 1848 - 324 pages
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Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - Geometry - 1830 - 584 pages
...Therefore, &c. PROP. 41. The squares of the four sides tf a quadrilateral are together greater than the squares of its diagonals, by four times the square of the straight line which joins the middle points of the diagonals. Let А В С D be a quadrilateral, and...
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Library of Useful Knowledge: Geometry plane, solid, and spherical [by Pierce ...

Mathematics - 1835 - 684 pages
...Therefore, SEC. PROP. 41. The squares of the four sides of a quadrilateral are together greater than the squares of its diagonals, by four times the square of the straight line which joins the middle points of the diagonals. Let А В С D be a quadrilateral, and...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1852 - 436 pages
...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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Mathematical Dictionary and Cyclopedia of Mathematical Science: Comprising ...

Charles Davies, William Guy Peck - Mathematics - 1855 - 628 pages
...the squares of the two diagonals is equivalent to the sum of the squares of the four sides diminished by four times the square of the line joining the middle points of .he diagonals ; that is, AC* + BD»o AB» + BC1 + CD3 + DA1 - 4EF1. If the quadrilateral is a parallelogram,...
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Examination papers used at the examinations for direct commissions [&c.].

War office - 1858 - 578 pages
...(2*-3)0-5) = 103. 3. Show that the squares of the sides of a quadrilateral figure are greater than the squares of its diagonals by four times the square...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 - Logarithms - 1858 - 292 pages
...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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The geometry of the circle and mathematics as applied to geometry by ...

James Smith - 1869 - 490 pages
...of the squares of the four sides is equal to the sum of the squares of the diagonals, together with four times the square of the line joining the middle points of the diagonals" Now, when the diameter of the circle Z=8,then, — £---* = — = 7, and this is the length of the...
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The Geometry of the Circle and Mathematics as Applied to Geometry by ...

James Smith - Circle-squaring - 1869 - 459 pages
...the squares of the four sides is equal to the sum of the squares of the diagonals •, together with four times the square of the line joining the middle points of the diaOA 4- AH gonals? Now, when the diameter of the circle Z = 8,then, - — 4—+_3 — L ="7 and this...
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The ratio between diameter and circumference in a circle demonstrated by ...

James Smith - 1870 - 634 pages
...of the squares of the four sides, is equal to the sum of the squares of the diagonals, together with four times the square of the line joining the middle points of the diagonals^ JM Wilson, Mathematical Master of Rugby School, and the most recent author of a Treatise on " Elementary...
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Chambers's Encyclopædia: A Dictionary of Universal Knowledge for ..., Volume 9

Ephraim Chambers - Encyclopedias and dictionaries - 1870 - 872 pages
...sum of the squares of its diagonals is equal to the sum of the squares of the sides, together with four times the square of the line joining the middle points of the diagonals ; if it can Ъе inscribed in a circle (ie, if its four corners are in the circumference of any circle),...
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