 | John Playfair - 1844 - 338 sider
...straight line ; it is required to divide it into two parts, so that the rectangle contained by Ji ^j. the whole, and one of the parts, shall be equal to the square of the other part. Upon AB describe (46. 1.) the square ABDC ; bisect (10. 1.) AC in E, and join BE ; produce CA to F,... | |
 | Euclides - 1845 - 546 sider
...the square of the other part. Let AB be the given straight line. It is required to divide AB into two parts, so that the rectangle contained by the whole...parts, shall be equal to the square of the other part. H KD Upon AB describe the square ACDB; (i. 46.) bisect AC in E, (i. 10.) and join BE, produce CA to... | |
 | Euclid - 1845 - 218 sider
...the square of the other part. Let AB be the given straight line; it is required to divide it into two parts, so that the rectangle contained by the whole...parts, shall be equal to the square of the other part. Upon AB describe* the square ABDC ; bisectf AC in • 46. i. E, and join BE; produce CA to F, and makeJ... | |
 | Great Britain. Council on Education - 1845 - 696 sider
...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,...parts, shall be equal to the square of the other part. 63. Show that if — B he substracted from A, the result is A + B. 64. Perform the operations indicated... | |
 | 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...parts shall be equal to the square of the other." If we call x the greater of the two parts, and, therefore, a - x the other, the equation will become... | |
 | Euclides, James Thomson - 1845 - 382 sider
...whioh are, by the same curolla'y, tli» 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 is required to... | |
 | Alfred Wrigley - 1845 - 222 sider
...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, iii.... | |
 | Harvey Goodwin - 1846 - 500 sider
...(l + n) ' ma ' na n (a> + mx) = Ex. 5. Divide the quantity a into two parts such that the product of the whole and one of the parts shall be equal to the square of the other part. Let a? = one part ; .-. a- n' = the other; .-. by the question, ax = (a — at): = o2 - Zax + a?2, x- -... | |
 | Euclid, John Playfair - 1846 - 334 sider
...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 is required to... | |
 | 1847 - 508 sider
...angle contained by these two sides is a light angle. SECTION Il. — 1. To divide a straight line, so that the rectangle contained by the whole and one...parts shall be equal to the square of the other part. 2. In every triangle the square of the side subtending either of the acute angles is less than the... | |
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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, may be equal to the square of the other part. 
