| Education - 1844 - 688 pages
...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 - Euclid's Elements - 1844 - 338 pages
...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 - 544 pages
...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...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 to divide AB into two parts, so... | |
| Great Britain. Council on Education - 1845 - 700 pages
...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...and 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... | |
| Euclid - Geometry - 1845 - 218 pages
...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...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 to divide it into two parts, so... | |
| Alfred Wrigley - 1845 - 222 pages
...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 - Geometry - 1845 - 380 pages
...expression, the first and third partu of whioh are, by the same curolla'y, tliť 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 - 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, a - x the other, the equation... | |
| Euclides - 1846 - 292 pages
...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,... | |
| Euclid, John Playfair - Euclid's Elements - 1846 - 332 pages
...(2a+i)2+J2=2o2+2(a+4)2, and the proposition is evident from this algebraical equality. 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... | |
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