| Robert Simson - 1827 - 513 sider
...•6.2. t Constr. • 47. 1. t 3 Ax. t 30 Def. t lAx. t 3 Ax. t 30 Def. PROP. XL PROB. 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. Let AB be the given straight line ; it is required... | |
| John Playfair - 1832 - 333 sider
...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 the whole, and one of** the_parts, sha'l be equal to the square of the other part. Upon AB describe (40. 1.) the square ABDC;... | |
| Euclid - 1835 - 540 sider
...the squares of AC, CD. Wherefore, " if a straight line," &c. QED 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 be equal to the square of the other part. Let AB be the given straight line; it is required to... | |
| Robert Simson - 1835 - 513 sider
...CD. Wherefore, " if a straiglit line," &.c. QED PROP. XI. PROB. To divide a given straight line info **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. Let AB be the given straight Hue; it is required to... | |
| John Playfair - 1836 - 114 sider
...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 the whole and one of the parts** shall be equal to the square of the other part. Upon AB describe (16. 2.) the square ABDC; bisect (8.... | |
| Euclides - 1837 - 112 sider
...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 the rectangle contained by the whole 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... | |
| Euclid - 1837 - 410 sider
...the given lines are equal. PROP. XXIII. PROB. To divide a given straight line into two parts, such. **that the rectangle contained by the whole and one of the parts may** have a given ratio to the square of the other. Let AB (see the last figure) be the given line; it is... | |
| John Hind - 1837 - 539 sider
...which answer the symbolical condition. • Ex. 3. Divide 20 into two parts, so that the product of **the whole and one of the parts, may be equal to the square** of the other part. Let a? = one part : .-. 20 - as = the other : whence, 20a? = (20 - off = 400 - 40a?... | |
| Euclides - 1838 - 264 sider
...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 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 to... | |
| Euclides - 1841 - 378 sider
...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 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 to... | |
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