 | Charles Butler - 1814 - 582 σελίδες
...introduced under a different form in another part of the Elements, (viz. 11.2.) there, we have merely to divide a straight line, so that the rectangle contained by the whole and the less segment, may equal the square of the greater ; we have to determine the properties of a figure,... | |
 | Hirsch - 1827 - 690 σελίδες
...ACB; further, ACL = \AQL = AOE = GDE ; consequently ABC - ACB = GDE. QE I). SECTION LXXII. Рков. To divide a straight line, so that the rectangle contained by the two parts may be equal to a given square. SOLDT. The given line AB = a (ßg. 85) is required to be... | |
 | Meyer Hirsch - 1827 - 288 σελίδες
...ABC - ACB; further, ACL = $AOL = AOE = GDE ; consequently ABC - ACB = GDE. QED SECTION LXXII. PROB. To divide a straight line, so that the rectangle contained by the two parts may be equal to a given square. SOLUT. The given line AB = a (ßg. 85) is required to be... | |
 | Pierce Morton - 1830 - 584 σελίδες
...required value of y. Hence AD, and therefore AC and А В are found, and the triangle is determined. 18. To divide a straight line, so that the rectangle contained by the two parts may be equal to the square upon a given line 6. Let А В = a AP = x Then the rectangle AP,... | |
 | 1835 - 684 σελίδες
...required value of y. Hence AD, and therefore А С and AB are found, and the triangle is determined. 18. To divide a straight line, so that the rectangle contained by the two parts may be equal to the square upon a given line b. L,et AB =¿ a д p — - у Then the rectangle... | |
 | Euclides - 1840 - 192 σελίδες
...expressed in numbers ; in other words, there is no number capable of being divided so that the product of the whole and one part, shall be equal to the square of the other part. When a line is thus divided (in extreme and mean ratio, as it is termed in the Sixth Book), the rectangle... | |
 | Euclides - 1846 - 272 σελίδες
...PROBLEM. To divide a given finite right line ( AB) so that the rectangle contained under the whole line and one part, shall be equal to the square of the other part. From A draw AC, perpendicular to the given line AB, and let AC be equal to AB, and bisect it in E,... | |
 | 1847 - 508 σελίδες
...the other two sides of it, the angle contained by these two sides is a light angle. SECTION Il. — 1. To divide a straight line, so that the rectangle contained by the whole and one of the parts shall be equal to the square of the other part. 2. In every triangle the square of the... | |
 | Great Britain. Committee on Education - 1847 - 606 σελίδες
...upon the other two sides of it, the angle contained by these two sides is a right angle. SECTION II. 1. To divide a straight line, so that the rectangle contained by the whole and one of the parts shall be equal to the square of the other part. 2. In every triangle the square of the... | |
 | Cork city, univ. coll - 1851 - 208 σελίδες
...Trigonometry. 1. Show geometrically how to divide a straight line so that the rectangle of the whole line and one part shall be equal to the square of the other part. Deduce the same method also by algebra. Explain why the line thus divided is said to be divided in... | |
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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. 
