 | Education - 1844 - 688 pages
...contained by the whole and each of the parts are together equal to the square of the whole line. 7. 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. 8. If in a circle two straight lines cut one another, which do not both pass through... | |
 | John Playfair - Euclid's Elements - 1844 - 338 pages
...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... | |
 | Euclides - 1845 - 544 pages
...AD, DB are 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...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... | |
 | Great Britain. Council on Education - 1845 - 700 pages
...the 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...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... | |
 | Euclid - Geometry - 1845 - 218 pages
...are 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...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... | |
 | Alfred Wrigley - 1845 - 222 pages
...points 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...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 - 380 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...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
...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 - 332 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...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... | |
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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. 
