| George Peacock - Algebra - 1845
...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,... | |
| Alfred Wrigley - 1845
...these points. (Euclid, iii. 18. Cape, ii. 38.) 59. 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 a given line, which is less than the line to be divided. (Euclid, iii.... | |
| John Playfair - Euclid's Elements - 1846 - 317 pages
...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... | |
| Euclides - 1846
...'Wherefore, If a straight line %c. PROP. XI. PROII. To divide a yifen straight line into tioo parts, so **that the rectangle contained by the whole and one of the parts** shall be equal to the square of the other part. Let AB be the given straight line : it is required... | |
| Education - 1847
...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... | |
| Euclides - 1848
...the half and the part produced. PROP. XI. PROBLEM. To divide a given straight line 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. PROP. XII. THEOREM. In obtuse-angled triangles, if... | |
| J. Goodall, W. Hammond - 1848
...the perpendicular and the obtuse angle. Section 4. 1. Divide a given straight line 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. 2. Describe a square that shall be double a given triangle.... | |
| Euclid, Thomas Tate - 1849 - 108 pages
...&c. QED Again, because EG F is EF PROP. XI. PROB. To divide a given straight line into two parts, so **that the -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
...equations, or any demonstration other than Euclid's ? 3. Divide a given straight line 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. Shew that in Euclid's figure four other lines, beside... | |
| Great Britain. Committee on Education - 1850
...equal to one another. 3. Solve Euc. II. 11. To divide a given finite straight line into two parts, so **that the rectangle contained by the whole and one of the parts** may be equal to the squire of the other part. 4. Prove Euc. III. 22. The opposite angles of any quadrilateral... | |
| |