| John Playfair - Euclid's Elements - 1844 - 338 pages
...rectangle contained by the whole, and one of the parts, may be equal to the square of the other part. Let **AB be the given straight line ; it is required to...into two parts, so that the rectangle contained by** Ji ^j. the whole, and one of the parts, shall be equal to the square of the other part. Upon AB describe... | |
| Great Britain. Council on Education - 1845 - 696 pages
...whole and that part, together with the square of the other part. 62. To divide a given straight line **into two parts, so that the rectangle contained by...parts, shall be equal to the square of the other part.** 63. Show that if — B he substracted from A, the result is A + B. 64. Perform the operations indicated... | |
| Euclides - 1845 - 546 pages
...equal to the square of the other part. Let AB be the given straight line. It is required to divide AB **into two parts, so that the rectangle contained by...parts, shall be equal to the square of the other part.** H KD Upon AB describe the square ACDB; (i. 46.) bisect AC in E, (i. 10.) and join BE, produce CA to... | |
| George Peacock - Algebra - 1845 - 480 pages
...the following problem. Its first case stated and solved. " To divide a given line into two such parts **that the rectangle contained by the whole and one...parts shall be equal to the square of the other."** If we call x the greater of the two parts, and, therefore, a - x the other, the equation will become... | |
| Alfred Wrigley - 1845 - 222 pages
...drawn from one of these points. (Euclid, iii. 18. Cape, ii. 38.) 59. 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 a given line, which is less than the line to be divided. (Euclid, iii.... | |
| Euclid - Geometry - 1845 - 218 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. 14 t 24 Def. Constr. 4. 1. • 3. 1. t 1. 1. I Constr. || 24 Def. § 8. 1. 10 Def. \ D... | |
| Euclid, James Thomson - Geometry - 1845 - 380 pages
...was to be done. PROP. XXX. PROB. — To divide a given straight line in extreme and mean ratio. Let **AB be the given straight line ; it is required to divide it** in extreme and mean ratio. Divide AB (II. 11 ) in the point C, so that the rectangle AB.BO may be equal... | |
| Euclides - 1846 - 292 pages
...rectangle contained by the whole 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...parts shall be equal to the square of the other part.** Upon AB describe the square ACDB ; bisect AC in E, and join BE ; produce CA to F, and make EF equal... | |
| Harvey Goodwin - Mathematics - 1846 - 500 pages
...(l + n) ' ma ' na n (a> + mx) = Ex. 5. Divide the quantity a into two parts such that the product of **the whole and one of the parts shall be equal to the square of the other part.** Let a? = one part ; .-. a- n' = the other; .-. by the question, ax = (a — at): = o2 - Zax + a?2,... | |
| John Playfair - Euclid's Elements - 1846 - 334 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... | |
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