 | 1840 - 288 pages
...fancies about numbers. All even numbers (except the duad — two — which is simply two unities) may be divided into two equal parts, and also into two unequal parts But the ODD number is only divisible into uneven parts, &c. The Antients also remarked the monad to... | |
 | Euclides - Geometry - 1841 - 378 pages
...parallelograms 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...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 parts at the point D; the rectangle... | |
 | John Playfair - Euclid's Elements - 1842 - 332 pages
...which this line 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...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 parts in the point D ; the... | |
 | Euclides - 1842 - 316 pages
...parallelograms 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...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
...between the same parallels, the parallelogram shall be double of the triangle. 6. If a straight line be divided into two equal parts, and also into two...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... | |
 | Euclid, James Thomson - Geometry - 1845 - 382 pages
...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, and also into two...the 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... | |
 | Euclides - 1845 - 546 pages
...= a2 — ma, to each of these equals add m* ; .-. (a + m) (a — m) + m' = a'. That is, if a number be divided into two equal parts, and also into two unequal parts, the product of the unequal parts and the square of half their difference, is equal to the square of half... | |
 | Scottish school-book assoc - 1845 - 444 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),... | |
 | Great Britain. Admiralty - Geometry - 1846 - 128 pages
...algebraically expressed is (a+b)*—a*-\-2ab + b*. PROP. XLIV. THEOR. 5 . 2 EU. If a straight line be divided into two equal parts, and also into two...points of section, is equal to the square of half the whole line. Let the str. line AB be divided into two equal parts at the pt. C, and into two unequal... | |
 | Great Britain. Admiralty - Geometry - 1846 - 128 pages
...proposition algebraically expressed is (a+by=a8+2ab+b8. PROP. XLIV. THEOR. 5. 2 Eu. If a straight line be divided into two equal parts, and also into two...points of section, is equal to the square of half the whole line. Let the str. line AB be divided into two equal parts at the pt. C, and into two unequal... | |
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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. 
