| Euclid, Robert Simson - Geometry - 1821 - 514 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** dne of the parts shall be equal to the square of the other part. Upon AB describe (46. 1.) the square... | |
| James Ryan - Algebra - 1824 - 552 pages
...sought. Ans. 1 1 , 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... | |
| 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 - 372 pages
...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...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 - Algebra - 1825 - 312 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... | |
| Daniel Cresswell - Euclid's Elements - 1825 - 582 pages
...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 - Euclid's Elements - 1826 - 326 pages
...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 - Trigonometry - 1827 - 513 pages
...•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...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 - Geometry - 1827 - 458 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 - 333 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;... | |
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