| 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 - 700 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
...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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