 | Miles Bland - 1819 - 442 σελίδες
...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 - 798 σελίδες
...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 - 238 σελίδες
...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 - 404 σελίδες
...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 - 546 σελίδες
...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 - 292 σελίδες
...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 - 502 σελίδες
...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 - 452 σελίδες
...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 - 352 σελίδες
...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 - 482 σελίδες
...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. 
