| Euclides - 1853 - 147 páginas
...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 - 1853
...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 - 1853
...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
...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 - 1854 - 225 páginas
...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 - 1854
...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
...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 - 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...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 - 1855 - 318 páginas
..., 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
...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... | |
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