 | Miles Bland - Euclid's Elements - 1827 - 462 pages
...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...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... | |
 | Robert Simson - Trigonometry - 1827 - 546 pages
...« 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...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 - Euclid's Elements - 1832 - 358 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 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 pages
...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...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 - Trigonometry - 1835 - 544 pages
...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 - Geometry - 1836 - 148 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 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 - Euclid's Elements - 1837 - 112 pages
...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 parts, so that...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, James Thomson - Geometry - 1837 - 410 pages
...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 - Algebra - 1837 - 584 pages
...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 pages
...AD, DB are double 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...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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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. 
