 | Euclid - Geometry - 1845 - 218 pages
...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... | |
 | Euclides - 1845 - 546 pages
...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...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 AB into two parts, so... | |
 | Alfred Wrigley - 1845 - 222 pages
...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.... | |
 | Euclid, James Thomson - Geometry - 1845 - 382 pages
...expression, the first and third partu of whioh are, by the same curolla'y, tliť 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... | |
 | George Peacock - Algebra - 1845 - 480 pages
...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 - 292 pages
...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,... | |
 | Euclid, John Playfair - Euclid's Elements - 1846 - 334 pages
...(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 - Mathematics - 1846 - 500 pages
...(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):... | |
 | Great Britain. Committee on Education - School buildings - 1847 - 606 pages
...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... | |
 | Education - 1847 - 508 pages
...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... | |
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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. 
