| Euclid - 1845 - 199 Seiten
...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...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 divide it into two parts, so... | |
| Great Britain. Council on Education - 1845
...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...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 is A + B. 64. Perform the... | |
| James Thomson - 1845 - 358 Seiten
...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... | |
| 1845
...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
...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, a - x the other, the equation... | |
| Euclides - 1846
...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...and one of the 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,... | |
| John Playfair - 1846 - 317 Seiten
...(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 - 468 Seiten
...(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):... | |
| George Moody - 1847
...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 of the 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... | |
| Great Britain. Committee on Education - 1847
...the angle contained by these two sides is a right angle. SECTION II. 1. To divide a straight line, **so that the rectangle contained by the whole and one of the 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... | |
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