| Robert Potts - 1865 - 528 pages
...squares on AC, CD. Wherefore, if a straight liue, &c. QED PROPOSITION XI. PROBLEM. To divitfe a given straight line into two parts, so that the rectangle contained by the whole and one of the parts, shall be equal to the square on the otlier part. Let AB be the given straight... | |
| Euclides - 1865 - 402 pages
...the squares of AC, CD. Wherefore, if a straight line, &c, QED PROP. XL— PROBLEM, To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts shall be equal to the square of the other part. (References — Prop. 1 3, 10,... | |
| Charles Alfred Jones, Charles Hartwell Horne Cheyne - Algebra - 1867 - 176 pages
...geometric series of which the sum is 2 j1^ and the second term — - ? 7. If a straight line be divided into two parts so that the rectangle contained by the whole line and one part is equal to six times the square of the other part ; find the ratio of the parts. EXERCISE LXII.... | |
| Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...squares on AC, CD. Wherefore, if a straight line &c. QED H PROPOSITION 11. PROBLEM. To divide a. given straight line into two parts, so that the rectangle contained by the whole and one of the parts may be equal to the square on the other part. Let AB be the given straight line... | |
| 1867 - 224 pages
...by those two sides is a right angle. 9. Define rectangle ; gnomon. '••/£: , 10. Divide a given straight line into two parts so that the rectangle contained by the whole and one part may be equal to the square on the other part, jj yi . 1 1. Give construction only for... | |
| Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 424 pages
...squares on AC, CD. Wherefore, if a straight line &c. QED PROPOSITION 11. PROBLEM. To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts may lie equal to the square on the other part. Let AB be the given straight line... | |
| Washington Hudson - 1868 - 78 pages
...required ratio, which is represented by the squares с b г/and ach i. Fi«. 104. То divide a given straight line into two parts, so that the rectangle contained by the whole line and lesser part, shall be equal to the square on the other. Let AB be the given line. On AB as a side,... | |
| 1868 - 876 pages
...square of the straight line which is made up of the half and the part produced 25 5. Divide a given straight line into two parts, so that the rectangle contained by the whole mid one of the pails shall be equal to the square of the other part 25 100 B. Latt of Pupils recommended... | |
| Robert Potts - 1868 - 434 pages
...squares on AC, CD ; but DG is equal to DB; BOOK II. PROP. XI. PROPOSITION XI. PROBLEM. To divide a given straight line into two parts* so that the rectangle contained by the whole and one of the parts, shall be equal to the square on the other part, Let AB be the given straight... | |
| Edinburgh univ - 1868 - 334 pages
...upon the same base, and upon the same side of it, are between the same parallels. 4. To divide a given 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. 5. The angles in the same segment... | |
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