 | John Playfair - 1806 - 320 páginas
...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 - 1806 - 546 páginas
...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 páginas
...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 - 1819 - 350 páginas
...+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 - 1819 - 442 páginas
...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 - 1819 - 486 páginas
...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 - 1819 - 444 páginas
...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 - 1821 - 514 páginas
...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 - 1046 páginas
...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 - 1825 - 616 páginas
...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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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 on the other part. 
