| Euclides - Geometry - 1841 - 351 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...parts, shall be equal to the square of the other part.** Upon AB describe* the square ABDC; bisect* AC * 46. 1. in E, and join BE; produce CA to F, making*... | |
| Euclides - 1842
...equivalent to double the squares of AC, CD. If therefore a straight line, &c. QED PROP. XI. PROB. To divide **a given straight line into two parts, so that the...contained by the whole, and one of the parts, shall be** equivalent to the square of the other part. Let AB be the given straight line : it is required to divide... | |
| John Playfair - Euclid's Elements - 1842 - 317 pages
...(2a-f*)2+*2=2a2+2(a+i)2, and the proposition is evident from this algebraical equality. 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,** may be equal to the square of the other part. Let AB be the given straight line ; it is required to... | |
| 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... | |
| Education - 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 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 the centre, they... | |
| John Playfair - Euclid's Elements - 1844 - 317 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 ; produce CA to F,... | |
| Great Britain. Council on Education - 1845
...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 that 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 operations indicated... | |
| Euclid - Geometry - 1845 - 199 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...parts, shall be equal to the square of the other part.** Upon AB describe* the square ABDC ; bisectf AC in • 46. i. E, and join BE; produce CA to F, and makeJ... | |
| Euclides - 1845
...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 the rectangle contained by...parts, shall be equal to the square of the other part.** H KD Upon AB describe the square ACDB; (i. 46.) bisect AC in E, (i. 10.) and join BE, produce CA 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...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 will become... | |
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