| Euclid, James Thomson - 1845 - 382 páginas
...given lines are equal. PROP. XXIII. PROR. — To divide a given straight line into two parts, such that the rectangle contained by the whole and one of the parts may have a given ratio to the square of the other. Let AB (see the last figure) be the given line ; it... | |
| George Peacock - 1845 - 480 páginas
...the following problem. Its first case stated and solved. " To divide a given line into two such parts that the rectangle contained by the whole and one of the parts shall be equal to the square of the other." If we call x the greater of the two parts, and, therefore,... | |
| Euclides - 1846 - 292 páginas
...equal to the square of the other part. Let 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. Upon AB describe the square ACDB ; bisect AC in E,... | |
| Euclid, John Playfair - 1846 - 334 páginas
...equal to the square of the other part. Let 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. Upon AB describe (46. 1.) the square ABDC ; bisect... | |
| 1847 - 508 páginas
...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 side subtending... | |
| Great Britain. Committee on Education - 1847 - 606 páginas
...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 side subtending... | |
| Euclides - 1848 - 52 páginas
...bisected, and of the square of the line made up of the half and the part produced. PROP. XI. PROBLEM. To divide a given straight line into two parts, so...rectangle contained by the whole and one of the parts, shall be equal to the square of the other part. PROP. XII. THEOREM. In obtuse-angled triangles, if... | |
| J. Goodall, W. Hammond - 1848 - 390 páginas
...line intercepted without the triangle between the perpendicular and the obtuse angle. Section 4. 1. Divide a given straight line into two parts, so that...rectangle contained by the whole and one of the parts shall be equal to the square of the other part. 2. Describe a square that shall be double a given triangle.... | |
| Euclid, Thomas Tate - 1849 - 120 páginas
...squares of AC, CD: Wherefore, if a straight line, &c. QED Again, because EG F is EF PROP. XI. PROB. To divide a given straight line into two parts, so...-rectangle contained by the whole, and one of the parts, shall Tie equal to the square of the other part. Let AB be the given straight line; it is required... | |
| University of Cambridge - 1849 - 560 páginas
...upon the necessary homogeneity of algebraical equations, or any demonstration other than Euclid's ? 3. Divide a given straight line into two parts, so that...rectangle contained by the whole and one of the parts shall be equal to the square of the other part. Shew that in Euclid's figure four other lines, beside... | |
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