| Miles Bland - Euclid's Elements - 1819 - 442 pages
...equal to a given square, and their rectangle equal to a given rectangle. 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... | |
| Miles Bland - Euclid's Elements - 1819 - 444 pages
...DB are equal to the square of AB, ie to the given square. (9.) To divide a straight line into ttvo **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. L,etAB be the... | |
| John Playfair - Circle-squaring - 1819 - 350 pages
...PROP. X. PROB. To bisect a given finite straight line, that is, to divide it into two equal parts. Let **AB be the given straight line ; it is required to divide it into two** equal parts. Describe (1. 1.) upon it an equilateral triangle ABC, and bisect (9. 1.) the angle ACB... | |
| John Playfair - 1819 - 354 pages
...X. PROB. To bisect a given finite straight line, that is, to divide it into two equal parts. Let.AB **be the given straight line ; it is required to divide it into two** equal parts. Describe (1. 1.) upon it an equilateral triangle ABC, and bisect (9. 1.) the angle ACB... | |
| Daniel Cresswell - Geometry - 1819 - 446 pages
...> the L HAG ; and so on. . PROP. XXXIII. 47. PROBLEM. To trisect av given finite straight line. Let **AB be the given straight line: It is required to divide it into** three equal parts. Upon AB describe (E. 1.1.) the equilateral A CAB ; bisect (E. 9. 1.) the two equal... | |
| Daniel Cresswell - Geometry - 1819 - 486 pages
...manifest from this proposition, and from E. 1O. 4., that if the semi-diameter of a circle be divided **into two parts, so that the rectangle contained by the whole and** the lesser part may be equal to the square of the greater part, the greater segment shall be equal... | |
| 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
...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 - 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... | |
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