 | Euclides - 1861 - 464 pagina’s
...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 - 140 pagina’s
...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 - 172 pagina’s
...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 - 316 pagina’s
...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 - 588 pagina’s
...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 - 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 - 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 - 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,...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 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,... | |
 | John Playfair - 1855 - 350 pagina’s
...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... | |
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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. 
