| Euclides - 1842 - 320 pages
...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 part. Let AB be the given straight... | |
| Education - 1844 - 688 pages
...the whole and each of the parts are together equal to the square of the whole line. 7. 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. 8. If in a circle two straight... | |
| Euclid, James Thomson - Geometry - 1845 - 380 pages
...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. Let AB be the given straight line... | |
| Euclides - 1845 - 544 pages
...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. Let AB be the given straight... | |
| Euclid - Geometry - 1845 - 218 pages
...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. Let AB be the given straight... | |
| Great Britain. Council on Education - 1845 - 700 pages
...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. 63. Show that if — B he substracted... | |
| Alfred Wrigley, William Henry Johnstone - Mathematics - 1845 - 222 pages
...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 is less than the line to be... | |
| John Playfair - Euclid's Elements - 1846 - 332 pages
...2a+i)2+J2=2o2+2(a+4)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. Let AB be the given straight line... | |
| Euclides - 1848 - 52 pages
...square of the line made up of the half and the part produced. PROP. 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. PROP. XII. THEOREM. In obtuse-angled... | |
| J. Goodall, W. Hammond - 1848 - 388 pages
...intercepted without the triangle between the perpendicular and the obtuse angle. Section 4. 1. 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. 2. Describe a square that shall... | |
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