| 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 - 444 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 - 1332 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 - 1048 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 - 198 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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