| Scotland free church, gen. assembly - 1847
...the squares described on the other two sides, these sides contain a right angle. 3. Divide a given **line into two parts, so that the rectangle contained by the whole** line and one of the parts may be equal to the square of the other part. 4. The angle in a semicircle... | |
| 1844
...contained by the whole and each of the parts are together equal to the square of the whole line. 7. **Divide a given straight line into two parts, so that...and one of the parts shall be equal to the square of** the other part. 8. If in a circle two straight lines cut one another, which do not both pass through... | |
| John Playfair - 1844 - 317 páginas
...straight line ; it is required to divide it into two parts, so that the rectangle contained by Ji ^j. **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 (10. 1.) AC in E, and join BE ;... | |
| Euclides - 1845
...AD, DB are double of the squares of AC, CD. Wherefore, if a straight line, &c. QED PROPOSITION XI. **PROBLEM. To divide a given straight line into two...one of the parts, shall be equal to the square of** the other part. Let AB be the given straight line. It is required to divide AB into two parts, so that... | |
| Euclid - 1845 - 199 páginas
...are double of the squares of AC, CD. Wherefore, if a straight line, &c. QED PROPOSITION XI. PROB. — **To divide a given straight line into two parts, so...one of the parts, shall be 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... | |
| Great Britain. Council on Education - 1845
...the rectangle contained by the whole and that part, together with the square of the other part. 62. **To divide a given straight line into two parts, so...one of the parts, shall be equal to the square of** the other part. 63. Show that if — B he substracted from A, the result is A + B. 64. Perform the... | |
| Alfred Wrigley - 1845
...points of contact, and the diameter drawn from one of these points. (Euclid, iii. 18. Cape, ii. 38.) 59. **To divide a given straight line into two parts, so...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.... | |
| Euclid, James Thomson - 1845 - 352 páginas
...expression, the first and third partu of whioh are, by the same curolla'y, tli» PROP. XI. PROB. — **To divide a given straight line into two parts, so...rectangle contained by the whole and one of the parts,** may be equal to the square of the other part. Let AB be the given straight line ; it is required to... | |
| George Peacock - 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, a - x the other, the equation... | |
| Euclides - 1846
...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...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, and join BE ; produce CA to F, and... | |
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