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. The English Journal of Education - Page 2721851Full view - About this book
| 1840
...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 - 1841 - 351 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...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 parts... | |
| John Playfair - 1842 - 317 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...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 parts... | |
| Euclides - 1842
...manifest that the parallelograms about the diameter of a square are likewise squares. PROP. V. THEOR. **IF a straight line be divided into two equal 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
...the same base, and between the same parallels, the parallelogram shall be double of the triangle. 6. **If a straight line be divided into two equal 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... | |
| Euclid, James Thomson - 1845 - 352 pages
...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,...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, together... | |
| Euclides - 1845
...that the parallelograms about the diameter of a square are likewise 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 parts, together with the square of the line... | |
| Scottish school-book assoc - 1845
...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 - 1846
...b, the proposition algebraically expressed is (a+b)*—a*-\-2ab + b*. PROP. XLIV. THEOR. 5 . 2 EU. **If a straight line be divided into two equal parts,...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 - 1846
...be a and b, the 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,...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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