 | George Peacock - 1845 - 480 σελίδες
...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 - 222 σελίδες
...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 - 1846 - 334 σελίδες
...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 - 292 σελίδες
...'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... | |
 | 1847 - 508 σελίδες
...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... | |
 | Euclid - 1848 - 52 σελίδες
...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 - 388 σελίδες
...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 - 120 σελίδες
...&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 - 560 σελίδες
...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 - 942 σελίδες
...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... | |
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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. 
