| 1836 - 472 sider
...the diameter of a square are likewise squares. V. If a straight line be divided into two equal parts, **and also into two unequal parts ; the rectangle contained...section, is equal to the square of half the line.** COR. From this proposition it is manifest, that the difference of the squares of two unequal lines... | |
| Euclid - 1837 - 390 sider
...equal to the square of one of them. PROP. V. THEOR. IF a straight line be divided into two equal parts, **and also into two unequal parts ; the rectangle contained...square of half the line. Let the straight line AB be** bisected in C, and divided unequally in D : the rectangle AD.DB, together with the square of CD, is... | |
| Andrew Bell - 1837 - 240 sider
...the rectangle AC-CB. PROPOSITION V. THEOREM. . If a straight line be divided into two equal parts, **and also into two unequal parts, the rectangle contained...square of half the line. Let the straight line AB** he divided into two equal parts in the point C, and into two unequal parts at the point D ; the rectangle... | |
| Euclides - 1837
...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...section, is equal to the square of half the line.** Proved by showing that BC* = figs. CM + HG +LF; and that these = figs. AH + LF ; and these = AD x DB... | |
| 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...equal parts in the point C, and into two unequal parts** at the point D : the rectangle AD'DB, together with the square of CD, shall be equal to the square... | |
| Euclid - 1838 - 416 sider
...demonstration it is manifest, that the parallelograms about the diameter of a square are likewise squares. **two unequal parts: the rectangle contained by the...square of half the line. • Let the straight line** AH be divided into two equal parts in the point C, and into two unequal parts at the point D ; 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.... | |
| Euclides - 1841
...a square are likewise squares. PROP. V. THEOR. If a straight fine be divided into two equal parts, **and also into two unequal parts; the rectangle contained...equal parts in the point C, and into two unequal parts** at the point D; the rectangle AD, DB, together with the square of CD, shall be equal to the square... | |
| John Playfair - 1842 - 317 sider
...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 parts ; the rectangle contained...into two unequal parts in the point D ; the rectangle** AD.DB, together with the square of CD, is equal to the square of CB, or AD.DB+CD2= CB2. Upon CB describe... | |
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