| John Playfair - Geometry - 1836 - 114 pages
...about the diagonal of a square are likewise squares. / G H / CPROP. XXI. THEOR. If a straight line lie **divided into two equal parts, and also into two unequal...points of section, is equal to the square of half the** line. Let the straight line AB be divided into two equal parts in the point C, and into two unequal... | |
| Euclid - Geometry - 1837 - 410 pages
...line being bisected, the rectangle of the parts is equal to the square of one of them. PROP. V. THEOR. **IF a straight line be divided into two equal parts,...points of section, is equal to the square of half the** line. Let the straight line AB be bisected in C, and divided unequally in D : the rectangle AD.DB,... | |
| Andrew Bell - Euclid's Elements - 1837 - 240 pages
...square of AB is 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,...points of section, is equal to the square of half the** line. Let the straight line AB he divided into two equal parts in the point C, and into two unequal... | |
| 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...points of section, is equal to the square of half the** line. Let the straight line AB be divided into two equal parts in the point C, and into two unequal... | |
| Euclides - Euclid's Elements - 1837 - 112 pages
...AC2 + CB2 + 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,... | |
| 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...points of section, is equal to the square of half the** line. Let the straight line AB be divided into two equal parts in the point C, and into two unequal... | |
| 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...points of section, is equal to 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... | |
| Robert Simson (master of Colebrooke house acad, Islington.) - 1838 - 206 pages
...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 - 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.... | |
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