| Euclides - 1861 - 464 pages
...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 pages
...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 pages
...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 - Education, Higher - 1863 - 328 pages
...their other angles shall be equal, each to each, namely those to which the equal sides are opposite. 3. **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. 4. Bisect a given... | |
| Woolwich roy. military acad - 1864 - 588 pages
...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 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 - 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
...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 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 - 358 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... | |
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