 | Euclid - 1908 - 456 sider
...Pythagoreans. The construction of this triangle depends upon n. n, or the problem of dividing a straight line so that the rectangle contained by the whole and one of the parts is equal to the square on the other part. This problem of course appears again in Eucl. vi. 30 as the... | |
 | Euclid - 1908 - 550 sider
...square on the remaining segment. Let AB be the given straight line ; thus it is required to cut AB so that the rectangle contained by the whole and one of the segments is equal to the square on the remaining segment. For let the square ABDC be described on AB... | |
 | Royal Military Academy, Woolwich - 1909 - 456 sider
...having a given area, that which has the least perimeter it isosceles. 3. Divide a given straight line into two parts so that the rectangle contained by the whole and one part may be equal to the square on the other part. If the line be divided so that nine times the rectangle... | |
 | 1911 - 1334 sider
...the doctor. GEOMETRY.— XI. 9 TO 11 AM, WEDNESDAY, STH JULY, 1911. 1. Divide a given straight line into two parts so that the rectangle contained by the whole and one part may be equal to the square on the other part. 2. If a straight line is divided internally in medial... | |
 | Great Britain. Board of Education - 1912 - 1044 sider
...middle points of BC, B'C', respectively, prove that AU is less than A'O1. 2. Divide a straight line so that the rectangle contained by the whole and one of the parts shall be equal to the square on the remaining part. Prove that the difference of the squares on the whole and on the remaining part... | |
 | Great Britain. Board of Education - 1912 - 632 sider
...used.) 1. Prove that the diagonals of a parallelogram bisect one another. 2. Divide a straight line so that the rectangle contained by the whole and one of the parts shall be equal to the square on the remaining part. Prove that the difference of the squares on the whole and on the remaining part... | |
 | F. A. Brining, D. N. Avasia - 1913 - 282 sider
...number of equal parts a given straight line which is too short to admit of distinct divisions. Let AB be the given straight line. It is required to divide it into 5 equal parts. At A erect a perpendicular AC, and on AC set off as many equal distances as there are... | |
 | Muḥammad ibn Mūsá Khuwārizmī - 1915 - 206 sider
...square on the remaining segment. " Let AB be the given straight line ; thus it is required to cut AB so that the rectangle contained by the whole and one of the segments is equal to the square on the remaining segment. 1 References and citations from the Elements... | |
 | Jay Hambidge - 1920 - 212 sider
...(who flourished about 300 BC), the following propositions occur: (i) "To cut a given straight line so that the rectangle contained by the whole and one of the segments is equal to the square on the remaining segment" (Book II, proposition II); (2) "To cut a... | |
 | David E. Smith - 1958 - 756 sider
...also gives in the Elements such geometric problems as the following : To cut a given straight line so that the rectangle contained by the whole and one of the segments shall be equal to the square on the remaining segment.3 This may be represented algebraically... | |
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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. 
