| 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,... | |
| Euclides - 1845 - 546 páginas
...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 páginas
...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 páginas
...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 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... | |
| Euclides, James Thomson - 1845 - 382 páginas
...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 páginas
...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 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, x- -... | |
| Euclid, John Playfair - 1846 - 334 páginas
...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 páginas
...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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