| Euclid, John Playfair - 1819 - 348 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 (46. 1.) the square ABDC ; bisect... | |
| Miles Bland - 1819 - 444 sider
...their squares may be equal to a given square, and their rectangle equal to a given rectangle. 9. To **divide a straight line into two parts, so that the rectangle contained by the whole** aud one of the parts may be equal to the square of a given line, which is less than the line to be... | |
| John Playfair - 1819 - 317 sider
...AD3+DB==2AC3+2CD3. Wherefore, if a straight line, &c. Q, ED PROP. XI, PROB. To divide a given straight line into too **parts, so that the rectangle contained by the whole, and one of the parts,** niay be equal to the square of the other part. Let AB be the given straight line ; it is required to... | |
| John Mason Good - 1819 - 740 sider
...made up of the half and the part produced. Prop. XI. Prob. To divide a given straight lint into tu'o **parts, so that the rectangle contained by the whole, and one of the parts,** shall be equal tu the fquare of the other part. Prop. XII. Theor. In obtuse angled triangles, if a... | |
| Daniel Cresswell - 1819 - 486 sider
...manifest from this proposition, and from E. 1O. 4., that if the semi-diameter of a circle be divided **into two parts, so that the rectangle contained by the whole and** the lesser part may be equal to the square of the greater part, the greater segment shall be equal... | |
| Miles Bland - 1821 - 438 sider
...given rectangle. Also the squares of AD, DB are equal to the square of AB, г. e. to the given square. **the 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. Let AB be the given line to be divided.... | |
| Euclid, Robert Simson - 1821 - 514 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** dne of the parts shall be equal to the square of the other part. Upon AB describe (46. 1.) the square... | |
| Peter Nicholson - 1825 - 372 sider
...squares of AC, CD. Wherefore, if a straight line, &c. QED Proposition Xf. 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 'o the square of the other part. Let AB be the given straight line ; it is required... | |
| Daniel Cresswell - 1825 - 582 sider
...produced, shall be to the square of the part produced, in a given ratio. VIII. PR. To divide a given finite **straight line into two parts, so that the rectangle, contained by the whole** line, and the difference of those two parts, shall be in a given ratio to the square of the less of... | |
| Miles Bland - 1827 - 458 sider
...rectangle contained by the whole line produced and the part produced may be equal to a given square. 9. To **divide a straight line into two parts, so that 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. 10. To divide a given line into two such... | |
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