| John Playfair - Mathematics - 1806 - 320 pages
...AD2+DB2=2AC2+ 2CD2. Wherefore, if a straight line, &c, QE D, 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... | |
| Robert Simson - Trigonometry - 1806 - 546 pages
...squares of AC, CD. Wherefore, wr a straight line, &c. QED PROP. XI. PROB. TO clivjde 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... | |
| Euclides - 1816 - 588 pages
...CD. Wherefore, if a straight line, £c. QED "46. 1 Ho. 1 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... | |
| John Playfair - Circle-squaring - 1819 - 350 pages
...+DB3=2AC3+2CD3. Wherefore, if a straight line, &c. Q, ED . . 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... | |
| Miles Bland - Euclid's Elements - 1819 - 442 pages
...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 and one** of the parts may be equal to the square of a given line, which is less than the line to be divided.... | |
| Daniel Cresswell - Geometry - 1819 - 486 pages
...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 - Euclid's Elements - 1819 - 444 pages
...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... | |
| Euclid, Robert Simson - Geometry - 1821 - 514 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 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 - Mathematics - 1825 - 1046 pages
...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... | |
| Daniel Cresswell - Euclid's Elements - 1825 - 616 pages
...therefore (dividendo), : BC* :: AB : BD. PROP. VIII. 8. PROBLEM. To divide a given Jinite 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... | |
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