| Andrew Bell - Euclid's Elements - 1837 - 240 pages
...equal to the squares of AC, CB, and twice the rectangle AC-CB. PROPOSITION V. THEOREM. . If a straight **line be divided into two equal parts, and also into...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. Let the straight... | |
| Euclides - Euclid's Elements - 1837 - 112 pages
...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,... | |
| John Playfair - Geometry - 1837 - 332 pages
...(a+i)2 =a*+2a6+62. PROP. V. THEOR. If a straight line le divided into two equal parts, andalsointo **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. Let the straight... | |
| Robert Simson (master of Colebrooke house acad, Islington.) - 1838 - 206 pages
...triangle the 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 - 1838 - 264 pages
...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 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. Let the straight... | |
| Euclid - Geometry - 1838 - 478 pages
...demonstration it is manifest, that the parallelograms about the diameter of a square are likewise squares. **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. • Let the straight... | |
| 1840 - 288 pages
...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 - 378 pages
...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...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. Let the straight... | |
| Euclides - 1842 - 320 pages
...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 also into...contained by the unequal parts, together with the square** of the line between the points of section, is equivalent to the square of half the line. Let the straight... | |
| John Playfair - Euclid's Elements - 1842 - 332 pages
...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...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. Let the straight... | |
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