 | Euclides - 1864 - 262 pagina’s
...— 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 - 1864 - 448 pagina’s
...2am + at'. Hence by adding these equals, .-. (a + m)* + (o — m)' = 2aa + 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 pagina’s
...by the parts. Cor. The parallelograms about the diameter of a square are likewise squares. Prop. 5. If a straight line be divided into two equal parts,...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 pagina’s
...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 M'Dowell - 1866 - 124 pagina’s
...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 - 1867 - 426 pagina’s
...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 pagina’s
...explain how 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 pagina’s
...= 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 pagina’s
...&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 pagina’s
...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,... | |
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If a straight line be divided into two equal parts, and also into two unequal parts, the rectangle contained by the unequal parts, together with the square on the line between the points of section, is equal to the square on half the line. 
