 | Euclid - 1908 - 550 σελίδες
...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 σελίδες
...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 σελίδες
...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 - 632 σελίδες
...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... | |
 | Great Britain. Board of Education - 1912 - 1044 σελίδες
...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... | |
 | F. A. Brining, D. N. Avasia - 1913 - 282 σελίδες
...required 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 σελίδες
...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 σελίδες
...(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 σελίδες
...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... | |
 | Saskatchewan. Department of Education - 1910 - 260 σελίδες
...the longer diagonal is three times the square on the shorter. 4. (a) 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 on the other part. II. 11. (6) Divide a given straight line externally in... | |
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AB be the given straight line ; it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part. 
