| Robert Potts - 1855
...iSj divides them into two equal parts. Prove also that the two diameters bisect each other. 3. Divide **a given straight line into two parts, so that the...parts, shall be equal to the square of the other part** Solve the same problem algebraically, and give the geometrical interpretation of the result. 4. The... | |
| Great Britain. Committee on Education - School buildings - 1855
...upon the other two sides of it, the angle contained by those two sides is a right angle. 3. Divide a **straight line into two parts, so that the rectangle...parts shall be equal to the square of the other part.** Section 3. 1. The angles in the same segment of a circle are equal. 2. If from a point without a circle... | |
| John Playfair - Geometry - 1855 - 318 pages
..., and the proposition is evident from this algebraical equality. PROP. XI. PROB. To divide a givrn **straight line into two parts, so that the rectangle contained by the whole, and one of the parts,** may be equal to the square of the other part. I Let AB be the given straight line; it is required to... | |
| Euclides - 1855
...straight line which joins the points of the bisection of the diagonals. . PROP. D. PROBLEM. — To divide **a given straight line into two parts so that the rectangle contained by** its segments shall be equal to a given square, not greater than the square of half the given straight... | |
| Cambridge univ, exam. papers - 1856
...equal to a given triangle, and have one of its angles equal to a given rectilineal angle. 9. Divide **a given straight line into two parts, so that the...parts, shall be equal to the square of the other part.** 10. If two circles touch one another internally, they shall not have the same centre. 11. The diameter... | |
| Henry White - 1856
...one side of it are either two right angles, or are together equal to two right angles. 18 Divide a **straight line into two parts, so that the rectangle contained by the whole and** ono of the parts shall be equal to the square of the other part. 19 If two circles cut each other,... | |
| Henry Latham - 1857 - 59 pages
...thus formed shall pass through the same point. 3. Shew by diagram that a (b + c} = ab + ac. To divide **a given straight line into two parts so that the rectangle...parts shall be equal to the square of the other part.** Give the full construction. 4. Define a decimal fraction. Prove the rule for pointing in the multiplication... | |
| Archibald Montgomerie - Algebra - 1857 - 95 pages
...of sheep, and the price of each. Ans. 100 at 30s. (25.) Divide a given line a, into two such parts **that the rectangle contained by the whole and one of the parts** may be equal to the square of the other. , 3+ ^'5 , 3— 4/5 Ans. a — ^— , and a — ~— . (26.)... | |
| Euclides - 1858
...exercises for the learner. " — LARDNEB'S Euclid, pp. 79 and 80. PROP. 11. — PROB. To divide a given **line into two parts, so that the rectangle contained...parts shall be equal to the square of the other part.** SOL. — 46. I. To describe a square on a given line. 10. I. To bisect a given finite st. line. 3.... | |
| Euclides - 1858
...ijivru. ihr .«'iķe». o;' the reetnnt/lii e,m be found. BOOK II. 105 PRоP. XI. PRоB. To divide a **line into two parts, so that the rectangle contained...parts shall be equal to the square of the other part.** SoL. 46. I, 10. I, 3. I. Pat i. 2. DEM. 6. II, 47. I, Ax. 3. 1, Dei. 8U. 1. E». i Dat. Quœs. CON.... | |
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