| Charles Butler - Mathematics - 1814
...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,... | |
| Hirsh - 1827 - 304 pages
...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 - Trigonometry - 1827 - 264 pages
...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 - Geometry - 1830 - 272 pages
...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,... | |
| Mathematics - 1835
...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
...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
...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,... | |
| George Moody - 1847
...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 - School buildings - 1847
...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
...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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