| 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...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 - 194 pages
...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 - 82 pages
...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 - 378 pages
...likewise squares. PROP. V. THEOR. If a straight fine be divided into two equal parts, and also into two **unequal parts; the rectangle contained by the unequal...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 - Euclid's Elements - 1842 - 332 pages
...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 by the unequal...point C, and 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=... | |
| Euclides - 1842 - 320 pages
...likewise squares. PROP. V. THEOR. IF a straight line be divided into two equal parts, and also into two **unequal parts, the rectangle contained by the unequal...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... | |
| Education - 1844 - 688 pages
...be double of the triangle. 6. If a straight line be divided into two equal parts, and also into two **unequal parts ; the rectangle contained by the unequal...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... | |
| John Playfair - Euclid's Elements - 1844 - 338 pages
...For, let the two parts into which this line is divided be denoted by a and 6 ; then, PROP. V. THEOR. **Let the straight line AB be divided into two equal...point C, and 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+CD 2... | |
| Euclid, James Thomson - Geometry - 1845 - 380 pages
...of them. PROP. V. THEOR. — If a straight line be divided into two equal parts, and also into two **unequal parts ; the rectangle contained by the unequal...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... | |
| Scottish school-book assoc - 1845 - 434 pages
...be bisected in C, and divided unequally in D, 1 the rectangle AD-DB. together with the square on CD, **the line between the points of section is equal to the square** on (AC or CB) half the line. For AB2=AD-' + DB-+2AD-DB, (Prop. 37), but AB"=4AC2, (Prop. 37, Cor. 2),... | |
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