 | Peter Nicholson - 1825 - 1046 pagina’s
...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 to divide it into... | |
 | John Bonnycastle - 1825 - 336 pagina’s
...is required to divide a line, of 20 inches in length, into two such parts that the rectangle of (he whole and one of the parts shall be equal to the square of the other. Ans. 10^5-10, and 30—10^/5 6. It is required to divide the number 60 into two such... | |
 | Daniel Cresswell - 1825 - 616 pagina’s
...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... | |
 | Robert Simson - 1827 - 546 pagina’s
...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...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 divide .it into two parts,... | |
 | Miles Bland - 1827 - 462 pagina’s
...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. 10. To divide... | |
 | John Playfair - 1832 - 358 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, sha'l be equal to the square of the other part. Upon AB describe (40. 1.) the square ABDC;... | |
 | Euclid - 1835 - 540 pagina’s
...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...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 divide it into two parts, so... | |
 | 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...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 divide it into two part", so... | |
 | 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...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. 1.) AC in E, and join BE ;... | |
 | Euclides - 1837 - 112 pagina’s
...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 the rectangle contained...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 x FA + AE* = EF*, and that this... | |
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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, may be equal to the square of the other part. 
