 | 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 - 550 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 was 6 yards... | |
 | 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 was 6 yards... | |
 | Peter Nicholson - Mathematics - 1825 - 1046 pages
...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 parts, so...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 - 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 parts that their... | |
 | 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... | |
 | 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 - 546 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...parts, shall be equal to the square of the other part. Upon AB describe* the square ABDC; bisect* AC in E, ahd join BE : produce CA to F, and make* EF equal... | |
 | 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;... | |
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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. 
