| Euclides - 1837 - 88 sider
...+ CB2 + figs. AG + GE, and that these are = AC* + CB8 + 2 AC x CB. D H M PROPOSITION V. Theorem. If **a straight line be divided into two equal parts, and also into two unequal parts, the rectangle** A contained by the unequal parts, I together with the square of the line between the points of section,... | |
| Euclides - 1838
...square on half the line. PROP. V THEOR. If a straight line be divided into two equal parts, and aim **into two unequal 'parts ; the rectangle contained...section, is equal to the square of half the line.** Let the straight line AB be divided into two equal parts in the point C, and into two unequal parts... | |
| Robert Simson (master of Colebrooke house acad, Islington.) - 1838
...square of the hypotenuse is equal to the sum of the squares of the other two sides. 14. If a right **line be divided into two equal parts, and also into two unequal parts,** what equations will result? 15. The base of a right-angled triangle is 300 feet, and the sum of the... | |
| Euclides - 1840
...half. PROP. V. THEOR. If a straight line (AB) be bisected (in c), and be also divided unequally (in D), **the rectangle contained by the unequal parts, together with the square of the** part intermediate between the points of section, is equal to the square of half the line. Upon AC describe... | |
| Euclides - 1840
...square of the half. PROP. V. THEOR. If a straight line be bisected, and be also divided unequally, **the rectangle contained by the unequal parts, together with the square of the** part intermediate between the points of section, is equal to the square of half the line. P E_ AD PROP.... | |
| 1840
...fancies about numbers. All even numbers (except the duad — two — which is simply two unities) may **be divided into two equal parts, and also into two unequal parts** But the ODD number is only divisible into uneven parts, &c. The Antients also remarked the monad to... | |
| Euclides - 1841 - 351 sider
...parallelograms about the diameter of a square are likewise squares. PROP. V. THEOR. If a straight fine **be divided into two equal parts, and also into two...section, is equal to the square of half the line.** Let the straight line AB be divided into two equal parts in the point C, and into two unequal parts... | |
| John Playfair - 1842 - 317 sider
...which this line is divided be denoted by a and b; then, (a-\-b)2 PROP. V. THEOR. If a straight line lie **divided into two equal parts, and also into two unequal...section, is equal to the square of half the line.** Let the straight line AB be divided into two equal parts in the point C, and into two unequal parts... | |
| Euclides - 1842
...manifest that the parallelograms about the diameter of a square are likewise squares. PROP. V. THEOR. IF **a straight line be divided into two equal parts, and...square of the line between the points of section, is** equivalent to the square of half the line. Let the straight line AB be divided into two equal parts... | |
| 1844
...same base, and between the same parallels, the parallelogram shall be double of the triangle. 6. If **a straight line be divided into two equal parts, and...section, is equal to the square of half the line.** 7. In obtuse angled-triangles, if a perpendicular be drawn from either of the acute angles to the opposite... | |
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