 | Euclides - 1837 - 112 Seiten
...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... | |
 | Euclid - 1838 - 470 Seiten
...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 - 192 Seiten
...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 Seiten
...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.... | |
 | John Playfair - 1842 - 332 Seiten
...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 parts ;...equal parts in the 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,... | |
 | Euclides - 1842 - 316 Seiten
...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 two unequal parts,...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 - 688 Seiten
...parallels, the parallelogram shall be double of the triangle. 6. If a straight line be divided into two equal parts, and also into two unequal parts ;...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 - 1844 - 338 Seiten
...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 parts in the 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,... | |
 | Euclides - 1845 - 546 Seiten
...squares. PROPOSITION V. THEOREM. If a straight line be divided into two equal parts, and also into Iwo unequal parts ; the rectangle contained by the unequal...equal parts in the point C, and into two unequal parts in the point D. Then the rectangle AD, DB, together with the square of CD, shall be equal to the square... | |
 | Euclid, James Thomson - 1845 - 382 Seiten
...parts is 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 ;...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... | |
| |
If a straight line be divided into two equal parts, and also into two unequal parts ; the rectangle 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. 
