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" ... the squares of the diagonals, is equal to the sum of the squares of the bisected sides together with four times the square of the line joining those points of bisection. "
Geometrical Problems Deducible from the First Six Books of Euclid, Arranged ... - Page xxv
by Miles Bland - 1819 - 377 pages
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Geometrical Problems Deducible from the First Six Books of Euclid, Arranged ...

Miles Bland - Euclid's Elements - 1819 - 442 pages
...sum of the squares of the two other sides, together with the squares of the diagonals, is equal to the sum of the squares of the bisected sides together...square of the line joining those points of bisection. Let AB, DC, two opposite sides of the trapezium ABCD, be bisected in E, .and F; join EF; and draw the...
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Solutions of the Cambridge Problems: From 1800 to 1820, Volume 2

John Martin Frederick Wright - Mathematics - 1825 - 798 pages
...to each other in the duplicate ratio of their homologous sides. 9. In any parallelogram, the sum of the squares of the diagonals is equal to the sum of the squares of the sides. 10. If two circles touch each other externally, any line drawn through the point...
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Elements of Geometry with Notes

John Radford Young - Geometry, Modern - 1833 - 238 pages
...stim of the squares of the two other sides, together with the squares of the diagonals, is equal to the sum of the squares of the bisected sides, together...square of the line joining those points of bisection. D Let AD, BC, two opposite sides of the trapezium ABCD, be bisected in E and F; join EF, and draw the...
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A complete treatise on practical land-surveying

Thomas Holliday - Surveying - 1838 - 404 pages
...the middle, and divide the area into two equal parts. 6. In any rectangled parallelogram, the sum of the squares of the diagonals is equal to the sum of the squares of all the sides. A rhombus has all its sides equal, but its angles are not right augles, as...
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845 - 546 pages
...sum of the squares of the two other sides, together with the squares of the diagonals, is equal to the sum of the squares of the bisected sides together with four times the square of the line, joining the points of bisection. 38. The squares of the diagonals of a trapezium are together double the squares...
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The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846 - 292 pages
...41. If two opposite sides of any quadrilateral be bisected, the sum of the squares of the other two sides, together with the squares of the diagonals, is equal to the sum of the squares of the sides bisected together with four times the square of the line joining the points of...
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The English Journal of Education, Volume 5

Education - 1851 - 502 pages
...In a circle the angle in a semicircle is a right angle. 3. Shew that in a parallelogram the sum of the squares of the diagonals is equal to the sum of the squares of all the sides. SECTION V.—Solve one of the following equations. 2x — 3 I0j; —4 —3—...
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Mechanics for the Millwright, Machinist, Engineer, Civil Engineer, Architect ...

Frederick Overman - Building - 1851 - 452 pages
...another as their bases, and those of equal bases are as their height. In a parallelogram, the sum of the squares of the diagonals is equal to the sum of the squares of all the four sides. The sum of the four internal angles of any quadrilateral figure is equal...
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A test-book for students; comprising sets of examination papers upon ...

Thomas Stantial - Examinations - 1859 - 356 pages
...line joining the point of its bisection with the opposite angle. 3. In a parallelogram, the sum of the squares of the diagonals is equal to the sum of the squares of the four sides. 4. The sum of the squares of two lines is never less than twice their rectangle....
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Mathematics for Practical Men: Being a Common-place Book of Principles ...

Olinthus Gregory - 1863 - 482 pages
...Parallelograms are to one another, as their bases and heights. 11. In any parallelogram the sum of the squares of the diagonals is equal to the sum of the squares of all the four sides. 12. The sum of the four internal angles of any quadrilateral figure,...
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