 | Euclid, Robert Simson - 1821 - 514 pagina’s
...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 pagina’s
...AD, DB, are double of the squares of AC, CD. Wherefore, if a straight line, &c. QED Proposition Xf. Problem. To divide a given straight line into two...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 pagina’s
...none of which lies within another, the tangents so drawn shall be equal to one another. LXXXI. PR. To divide a given straight line into two parts, so that the square of the one shall be equal to the rectangle contained by the other and a given straight line.... | |
 | Euclid, John Playfair - 1826 - 326 pagina’s
...DG=DB: Therefore, AD3-fDBi)==2AC»-|r'2CD>3< Wherefore, if a straight line, &e. QBD H B PROP, XI. PROB. To divide a given straight line into two parts, so that the reetangle eontained by the whole, and one of the parts, may be equal to the square of the other part.... | |
 | Robert Simson - 1827 - 546 pagina’s
...•3.1. « 46. 1. •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... | |
 | Miles Bland - 1827 - 462 pagina’s
...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 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.... | |
 | Euclid - 1835 - 540 pagina’s
...AD, DB are double 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... | |
 | Robert Simson - 1835 - 544 pagina’s
...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... | |
 | John Playfair - 1836 - 148 pagina’s
...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;... | |
 | Euclides - 1837 - 112 pagina’s
...AG"; and 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...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.... | |
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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. 
