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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. "
The first six books of the Elements of Euclid, with numerous exercises - Σελίδα 42
των Euclides - 1853 - 147 σελίδες
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Annual Report of the Department of Education of the Province of Alberta, Τόμος 5

Alberta. Department of Education - 1911
...is equal to the difference of the squares on the two straight lines. 9 8. To divide a given straight line into two parts so that the rectangle contained by the whole line and one part may be equal to the square on the other part. 11 — II. Values. 8 10. If any two...

The Dublin University Calendar, Τόμος 1

Trinity College (Dublin, Ireland) - 1911
...another the angle subtended by the first is greater than that subtended by the second. 5. Divide a line into two parts so that the rectangle contained by the whole line and one part shall be equal to the square of the other part. 6. Prove that the rectangle contained...

Special Reports on Educational Subjects, Τόμοι 26-27

Great Britain. Board of Education - 1912
...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...

The Teaching of Mathematics in the United Kingdom

Great Britain. Board of Education - 1912
...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...

Manual of Drawing and Surveying: Designed Especially for the Use of Students ...

F. A. Brining, D. N. Avasia - 1913 - 238 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...

Robert of Chester's Latin translation of the Algebra of al-Khowarizmi

Muḥammad ibn Mūsá Khuwārizmī - 1915 - 164 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...

Elementary Algebra: First[-second] Year Course, Τόμος 1

Florian Cajori, Letitia Rebekah Odell - 1915 - 240 σελίδες
...of Book II, of the Elements, Euclid solved by drawing lines the problem : To divide a given straight line into two parts, so that the rectangle contained by the whole line and one part of it may be equal to the square on the other part. In algebra, this problem demands...

Dynamic Symmetry: The Greek Vase

Jay Hambidge - 1920 - 161 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...

History of Mathematics, Τόμος 2

David E. Smith - 1958 - 736 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...
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Annual Report

Saskatchewan. Department of Education - 1910
...on 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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