| Euclides - 1837
...that this = AC* + CE* + EF! + FG", and that these = 2 AC* + 2 CD!. H PROPOSITION XI. E ._ Problem. To **divide a given straight line into two parts, so that...and one of the parts shall be equal to the square** of c KT~i the other part. Steps of the Demonstration. 1. Prove that CF x FA + AE* = EF*, and that this... | |
| Euclid - 1837 - 390 Seiten
...HB, AD are equal. Then c B (II. 9.) HB2 + BD*, or AD2 + BD2= 5-a ' — 2CD2+2AC2.* PROP. XI. PROB. To **divide a given straight line into two parts, so that...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... | |
| Euclides - 1838
...AD, DB are double of the squares of AC, CD. Wherefore, if a straight line, &c. QED PROP. XI. PROS. To **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. Let AB be the given straight line: it is required to divide it into two parts, so... | |
| Euclides - 1841
...DB are double of the squares of AC, CD. Wherefore, if a straight line, &c. QED PROP. XI. PROB. 1 To **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. Let AB be the given straight line; it is required to divide it into two parts, so... | |
| 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...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 - 1842 - 317 Seiten
...(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...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... | |
| 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 Seiten
...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... | |
| Robert Potts - 1845
...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 parts, so that...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... | |
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