| Euclides - Euclid's Elements - 1837 - 112 pages
...that this = AC* + CE* + EF! + FG", and that these = 2 AC* + 2 CD!. H PROPOSITION XI. E ._ 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 c KT~i the other... | |
| Euclides - 1838 - 264 pages
...AD, DB are double of the squares of AC, CD. Wherefore, if a straight line, &c. QED PROP. XI. PROS. **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.... | |
| Euclides - Geometry - 1841 - 378 pages
...AD, DB are double of the squares of AC, CD. Wherefore, if a straight line, &c. QED PROP. XI. PROB. 1 **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.... | |
| Euclides - 1842 - 320 pages
...are equivalent to double the squares of AC, CD. If therefore a straight line, &c. QED PROP. XI. PROB. **To divide a given straight line into two parts, so that the** rectangle contained by the whole, and one of the parts, shall be equivalent to the square of the other... | |
| John Playfair - Euclid's Elements - 1842 - 332 pages
...(2a-f*)2+*2=2a2+2(a+i)2, and the proposition is evident from this algebraical equality. PROP. XI. PROB. **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.... | |
| Alfred Wrigley - 1845 - 222 pages
...points of contact, and the diameter drawn from one of these points. (Euclid, iii. 18. Cape, ii. 38.) 59. **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 a given line, which... | |
| Euclid, James Thomson - Geometry - 1845 - 380 pages
...expression, the first and third partu of whioh are, by the same curolla'y, tliť PROP. XI. PROB. — **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.... | |
| Euclides - 1845 - 546 pages
...are double of the squares of AC, CD. Wherefore, if a straight line, &c. QED 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 of the other part.... | |
| Great Britain. Council on Education - 1845 - 696 pages
...the rectangle contained by the whole and that part, together with the square of the other part. 62. **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.... | |
| Euclid - Geometry - 1845 - 218 pages
...are double of the squares of AC, CD. Wherefore, if a straight line, &c. QED PROPOSITION XI. PROB. — **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.... | |
| |