| Euclides - Geometry - 1853 - 176 pages
...С d. Wherefore, if a straight line, &c. QED PROPOSITION XI. — PROBLEM. To divide a given straigM line into two parts, so that the rectangle contained...and one of the parts shall be equal to the square of the other part. LET ab be the given straight line ; it is required to divide it into two parts, so... | |
| Euclides - Geometry - 1853 - 334 pages
...To divide a given straight line into two such parts, that the rectangle contained by the whole line and one of the parts shall be equal to the square of the other part. Let AB be the given straight line. It is required to divide it into two such parts,... | |
| Royal Military Academy, Woolwich - Mathematics - 1853 - 476 pages
...divide a line of 20 inches in length into two parts such that the rectangle contained by the whole line and one of the parts shall be equal to the square of the other part. Let x = the greater part ; then 20 — x = the less part, and hence by the question... | |
| Cambridge univ, exam. papers - 1854 - 284 pages
...BD the other diameter, the difference of the parallelograms is equal to twice the triangle BKD. 2. Divide a given straight line into two parts so that the rectangle contained by the whole line and one of the parts shall be equal to the square of the other part. Produce a given straight... | |
| William Walton, Charles Frederick Mackenzie - Education - 1854 - 266 pages
...BD the other diameter, the difference of the parallelograms is equal to twice the triangle BSD. 2. Divide a given straight line into two parts so that the rectangle contained by the whole line and one of the parts shall be equal to the square of the other part. Produce a given straight... | |
| William Somerville Orr - Science - 1854 - 534 pages
...the remarks at the end of this book. PROPOSITION XI.— PROBLEM. To divide a given straight line (AB) into two parts, so that the rectangle contained by the whole, and от of the parts, shall be equal to the square of the other part. From A draw AC perpendicular and... | |
| Robert Potts - 1855 - 1050 pages
...that 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...one of the parts, shall be equal to the square of the other part Solve the same problem algebraically, and give the geometrical interpretation of the... | |
| Great Britain. Committee on Education - School buildings - 1855 - 976 pages
...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...and one of the 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... | |
| John Playfair - Geometry - 1855 - 334 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 - 270 pages
...the square of the 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... | |
| |