 | John Playfair - 1842 - 332 sider
...a-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...whole, and one of the parts, may 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,... | |
 | Euclides - 1842 - 320 sider
...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 line : it is required... | |
 | Scotland free church, gen. assembly - 1847 - 552 sider
...the squares described on the other two sides, these sides contain a right angle. 3. Divide a given line into two parts, so that the rectangle contained by the whole line and one of the parts may be equal to the square of the other part. 4. The angle in a semicircle... | |
 | 1844 - 688 sider
...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 lines cut one another,... | |
 | Alfred Wrigley - 1845 - 222 sider
...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...whole and one of the parts may be equal to the square of a given line, which is less than the line to be divided. (Euclid, iii. 1 6, 36. Cape, ii. 38 and... | |
 | Great Britain. Council on Education - 1845 - 696 sider
...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 from A, the result... | |
 | Euclid - 1845 - 218 sider
...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 line; it is required to... | |
 | Euclides - 1845 - 544 sider
...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 line. It is required to... | |
 | Euclid, James Thomson - 1845 - 380 sider
...given lines are equal. PROP. XXIII. PROR. — To divide a given straight line into two parts, such that the rectangle contained by the whole and one of the parts may have a given ratio to the square of the other. Let AB (see the last figure) be the given line ; it... | |
 | George Peacock - 1845 - 480 sider
...the following problem. Its first case stated and solved. " To divide a given line into two such parts that the rectangle contained by the whole and one of the parts shall be equal to the square of the other." If we call x the greater of the two parts, and, therefore,... | |
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AB be the given straight line ; it is required to divide it 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. 
