| Euclides - 1864 - 262 pages
...— 2am + m'. Hence by adding these equals, .'. (a + m)' + (a - m)* = 2az + 2m*. That is, If a number **be divided into two equal parts, and also into two unequal parts, the** sum of the squares of the two unequal parts is equal to twice the square of half the number itself,... | |
| Euclides - 1865 - 402 pages
...Cor. The parallelograms about the diameter of a square are likewise squares. Prop. 5. If a straight **line be divided into two equal parts, and also into...contained by the unequal parts, together with the square** of the line between the noinls of section, is equal to the square of half the line. Cor. The difference... | |
| Robert Potts - 1865 - 528 pages
...1am + m*, Hence by adding these equals, .'. (a + m)t + (a — m)« = 2o* + 2m«. That is, If a number **be divided into two equal parts, and also into two unequal parts, the** sum of the squares of the two unequal parts, is equal to twice the square of half the number itself,... | |
| James McDowell - 1866 - 124 pages
...f- = tan - - - 1. 1 + tan|a \4 2/ If a + ft + 7 = ^, prove that cos a + cos /3 + cos 7 If an angle **be divided into two equal parts and also into two unequal parts, the rectangle** of the sines of the unequal parts, together with the square of the sine of the angle between the dividing... | |
| Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 424 pages
...parallellograms about the diameter of a square are likewise squares. PROPOSITION 5. THEOREM. If a straight **line be divided into two equal parts and also into two unequal parts, the rectangle contained by** iht unequal parts, together with the square on the line between the points of section, is equal to... | |
| Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...about the diameter of a square are likewise squares. PROPOSITION 5. THEOREM. If a straight line 1ie **divided into two equal parts and also into two unequal parts, the rectangle contained** l)y the unequal parts, together with the square on the line between the points of section, is equal... | |
| 1868 - 344 pages
...rectangular areas are represented by the product of two numerical symbols. SECTION VI. 1. If a straight **line be divided into two equal parts, and also into two unequal parts, the** rectal gle contained by the unequal parts, together with the square of the line between the points... | |
| Robert Potts - 1868 - 434 pages
...= a' — m*, to each of these equals add m* ; .'. (a + m) (a — m) + m' = a*. That is, if a number **be divided into two equal parts, and also into two unequal parts, the** product of the unequal parts together with the square of half their difference, is equal to the square... | |
| Euclides - 1870 - 270 pages
...&c. Psts. 2 and 3 ; 3. I. 10. I. To bisect a given finite st. line. Pst. 1. DEM. — 5. II. If a st. **line be divided into two equal parts, and also into...rectangle contained by the unequal parts together with the** squai e of the line between the points of section, equals the square of half the line. Def. 15 and... | |
| Cambridge univ, exam. papers - 1870 - 272 pages
...half the line and of the square on the line between the points of section. The square on half the line **together with the square on the line between the points of section** and the rectangle contained by the parts is equal to half the square on the line. 3. In equal circles,... | |
| |