| John Playfair - 1844 - 338 páginas
...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,... | |
| Euclid - 1845 - 218 páginas
...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...parts, shall 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, so that the rectangle... | |
| Great Britain. Council on Education - 1845 - 696 páginas
...rectangle 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...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... | |
| Euclides - 1845 - 546 páginas
...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 parts, so that...parts, shall be equal to 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... | |
| Alfred Wrigley - 1845 - 222 páginas
...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...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.... | |
| George Peacock - 1845 - 480 páginas
...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... | |
| Euclid, James Thomson - 1845 - 382 páginas
...expression, the first and third partu of whioh are, by the same curolla'y, tli» PROP. XI. PROB. — To divide a given straight line into two parts, so that...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... | |
| Euclides - 1846 - 292 páginas
...equal to 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...parts shall be equal to the square of the other part. Upon AB describe the square ACDB ; bisect AC in E, and join BE ; produce CA to F, and make EF equal... | |
| Euclid, John Playfair - 1846 - 334 páginas
...(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...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... | |
| Harvey Goodwin - 1846 - 500 páginas
...(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,... | |
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