 | 1836 - 488 σελίδες
...parallelograms about 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 ;...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, James Thomson - 1837 - 410 σελίδες
...the 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... | |
 | Andrew Bell - 1837 - 290 σελίδες
...AC, CB, and twice the rectangle AC-CB. PROPOSITION V. THEOREM. . 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 he divided into two equal parts in the point C, and into two unequal parts at the point D ; the rectangle... | |
 | Euclides - 1837 - 112 σελίδες
...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 - 264 σελίδες
...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 - 470 σελίδες
...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 - 82 σελίδες
...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 - 1840 - 192 σελίδες
...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 - 1841 - 378 σελίδες
...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 unequal parts;...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... | |
 | Euclides - 1842 - 316 σελίδες
...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... | |
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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 of the line between the points of section, is equal to the square of half the line. 
