| Euclides - 1816 - 528 páginas
...straight line, &c. QED PROP. VIII. THEOfc. IF a straight line be divided into any two parts, four, times **the rectangle contained by the whole line, and one of the parts,** together with the square of the other part, is equal to the square of the straight line, which is made... | |
| Daniel Cresswell - 1817 - 436 páginas
...equally distant from the four sides of the given rectangle. (XXVII.) To divide a given straight line **into two parts, such, that the rectangle contained by the whole line and one of** its parts, shall have a given ratio to the square of the other part. (XXVIII.) The base, the vertical... | |
| John Bonnycastle - 1818 - 260 páginas
...required to divide a line, of 20 inches in length, into two such parts that the rectangle of the whole **and one of the parts shall be equal to the square of the other.** Ans. 10^/5-10 5. It is required to divide the number 60 into two such parts, that their product shall... | |
| Daniel Cresswell - 1819 - 410 páginas
...ratio ; .-. PQ is to PR in the given ratio. PKOP. XLII. 51. PROBLEM. To divide a given straight line **into two parts, such, that the rectangle contained by the whole line and one of** its parts, shall have a given ratio to the square of the other part. Let AB be the given straight line... | |
| John Playfair - 1819 - 333 páginas
...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 (46. 1.) the square ABDC ; bisect (10. 1.) AC in E, and join BE ; produce CA to F,... | |
| Miles Bland - 1819 - 377 páginas
...square of AC, ie to the square of the given line. (10.) To divide a given line into two such parts **that the rectangle contained by the whole line and one of the parts** may be (m) times the square of the other part, m being whole or fractional. Let AB be the given line,... | |
| Miles Bland - 1819 - 377 páginas
...square of AC, ie to the square of the given line. (10.) To divide a given line into two such parts **that the rectangle contained by the whole line and one of the parts** may be (m) times the square of the other part, m being whole or fractional. Let AB be the given line,... | |
| John Playfair - 1819 - 317 páginas
...difference of the lines." PROP. VIII. THEOR. If a straight line be divided into any two parts, fouf times **the rectangle contained by the whole line, and one of the parts,** together with the square of the other fart, is equal to the square of the straight line which is made... | |
| Euclid, Robert Simson - 1821 - 516 páginas
...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 ABDC; bisect (10. 1.) AC in E, and join BE; produce CA to F, and... | |
| James Ryan, Robert Adrain - 1824 - 516 páginas
..., 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— lOy/5. Prob. 23. A labourer dug two trenches, one of which was 6 yards... | |
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