 | James Ryan, Robert Adrain - Algebra - 1824 - 542 pages
...sought. Ans. II, or 3], Prob. 22. It is required to divide 20 into two such parts, that the product of the whole and one of the parts, shall be equal to the square of the other. Ans. lOv/5 — 10, and 30— 10^/5, Prob. 23. A labourer dug two trenches, one of which... | |
 | Peter Nicholson - Mathematics - 1825 - 1046 pages
...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 parts, so that...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... | |
 | Daniel Cresswell - Euclid's Elements - 1825 - 616 pages
...produced, shall be to the square of the part produced, in a given ratio. VIII. PR. To divide a given finite 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... | |
 | John Bonnycastle - Algebra - 1825 - 336 pages
...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... | |
 | 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...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 - 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 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 - 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...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 - 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...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 - 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...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 ;... | |
| |
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. 
