 | Euclides - 1862 - 140 pages
...about the diagonal of a square are likewise squares. PROPOSITION 5.— THEOREM. If a straight line be divided into two equal parts, and also into two...contained by the unequal parts, together with the square on the line between the points of section, ^s equal to the square on half the line. (References—... | |
 | Euclides - 1862 - 172 pages
...parallelograms about the diameter of a square are likewise squares. PROP. V.— THEOREM. //' a straight line be divided into two equal parts, and also into two unequal parts ; then the rectangle contained by the unequal parts, together with the square of the line between the... | |
 | University of Oxford - Education, Higher - 1863 - 316 pages
...given triangle and have one of its angles equal to a given rectilineal angle. 8. If a straight line be divided into two equal parts, and also into two...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. 9. If a straight... | |
 | Woolwich roy. military acad - 1864 - 588 pages
...arranged, under the restriction that the tvco vowels e shall never stand together 1 10. If a straight line be divided into two equal parts, and also into two...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. Hence show that... | |
 | 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 - 1864 - 448 pages
...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 pages
...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 two...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 of the squares of two... | |
 | 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,... | |
 | John Playfair - Geometry - 1855 - 350 pages
...which this jine is divided be denoted by </ and b ; then, (u+4)1 PROP. V. THEOR. If a straight Itnelf divided into two equal parts, and also into two unequal...by the unequal parts, together with the square of tAt line between the points of section, is equal to the square of half the line. Let the straight line... | |
 | James M'Dowell - 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... | |
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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 of the line between the points of section, is equal to the square of half the line. 
