| Euclid, James Thomson - Geometry - 1837 - 410 pages
...HB, AD are equal. Then c B (II. 9.) HB2 + BD*, or AD2 + BD2= 5-a ' — 2CD2+2AC2.* 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 ; it... | |
| 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. Let AB be the given straight line: it... | |
| 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. Let AB be the given straight line; it... | |
| Euclides - 1842 - 316 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 part. Let AB be the given straight line... | |
| 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. Let AB be the given straight line ; it... | |
| Scotland free church, gen. assembly - 1847 - 554 pages
...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... | |
| Education - 1844 - 688 pages
...contained by 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... | |
| Euclides - 1845 - 546 pages
...AD, DB 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...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... | |
| 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 is less than the line to be divided.... | |
| 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. Let AB be the given straight line; it... | |
| |