 | Miles Bland - 1819 - Liczba stron: 442
...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... | |
 | John Martin Frederick Wright - 1825 - Liczba stron: 798
...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... | |
 | John Radford Young - 1833 - Liczba stron: 238
...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... | |
 | Thomas Holliday - 1838 - Liczba stron: 404
...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... | |
 | Euclides - 1845 - Liczba stron: 546
...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... | |
 | Euclides - 1846 - Liczba stron: 292
...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... | |
 | 1851 - Liczba stron: 502
...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—... | |
 | Frederick Overman - 1851 - Liczba stron: 452
...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... | |
 | Thomas Stantial - 1859 - Liczba stron: 352
...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.... | |
 | Olinthus Gregory - 1863 - Liczba stron: 482
...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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... 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. 
