 | Euclides - 1842 - 316 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 - 382 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 - 546 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 - 696 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 - 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... | |
 | Euclid, John Playfair - Euclid's Elements - 1846 - 334 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 - 390 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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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. 
