| Euclides - 1861
...III. 47, I. Axs. 1, 2, 3, I. 36, 1. Parlms. upon eq. bases and between the same ||s are equal. 5, II. **If a straight line be divided into two equal parts, and also into two** uneq. parts, the rcct. contained by the nneq. parts, together with the square of the line between the... | |
| Euclides - 1862
...the parallelograms about the diagonal of a square are likewise squares. PROPOSITION 5.— THEOREM. **If a straight line be divided into two equal parts,...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
...that the 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 - 1863
...one another, and the diameter bisects the parallelogram, that is, divides it into two equal parts. **7. Describe a parallelogram that shall be equal to...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
...Chelsea be 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,...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
...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 - 1864
...— 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
...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,...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... | |
| John Playfair - 1855 - 317 sider
...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 McDowell - 1866
...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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