| William Nicholson - Natural history - 1809 - 716 pages
...QUADRATIC EQUATIONS. Prob. 1. To divide a line of 20 inches into two such parts, that the rectangle under **the whole and one part, may be equal to the square of the other.** Let ,r be the greater part, then will 20 — x be the less, «nd x1 = 20— x. 20 = 400 — 20 x by... | |
| William Nicholson - Arts - 1819 - 432 pages
...PROHLEMS EQUATIONS. Prob. 1. To divide aline of 20 inches into two such parts, that the rectangle under **the whole and one part may be equal to the square of the other.** Let x be the greater part, then will 20 — or be the less. and x> = (20 — x) . 20 - 400 — 20 x... | |
| Rev. John Allen - Astronomy - 1822 - 516 pages
...PROP. XI. PROB. To divide a given Jlnite right line (AB) so into two parts, that the rectangle under **the whole and one part, may be equal to the square of the other** part. At A draw AC perpendicular and equal f! 1C n to AB (11 and 3. 1), bisect AC in E, join EB, and... | |
| Euclid, James Thomson - Geometry - 1837 - 410 pages
...this problem in which the given lines are equal. PROP. XXIII. PROB. To divide a given straight line **into two parts, such. that the rectangle contained by the whole and one** of the parts may have a given ratio to the square of the other. Let AB (see the last figure) be the... | |
| Admiralty - 1845 - 152 pages
...Ex. 2. Divide a line 20 inches in length into two such parts, that the product, or rectangle under **the whole and one part, may be equal to the square of the other** part. Let ж=опе part, then 20 — ж=the other by the question ж*=20 X (20 -x) ж+ 100=500 x=—... | |
| Euclid, James Thomson - Geometry - 1845 - 382 pages
...this problem m which the given lines are equal. PROP. XXIII. PROR. — To divide a given straight line **into two parts, such that the rectangle contained by the whole and one** of the parts may have a given ratio to the square of the other. Let AB (see the last figure) be the... | |
| Euclides - 1846 - 292 pages
...C. 18. ABCD is a trapezium, AD parallel to BC : shew that AC2-BD2 : AB2-CD2 :: BC+AD : BC^ AD. 19. **Divide algebraically a given line a into two parts, such that the rectangle** of the whole and one part may be equal to the square of the other part. Deduce Euclid's construction... | |
| University of Durham - Education, Higher - 1851 - 222 pages
...parts together with twice the rectangle contained by the parts. 5. To divide a given straight line **into two parts, such that the rectangle contained by the whole and one** of the parts shall be equal to the square of the other part. 6. If two circles cut one another they... | |
| Robert Potts - 1855 - 1050 pages
...opposite to them are also equal. 3. Divide a straight line into two parts, so that the rectangle under **the whole, and one part, may be equal to the square of the other** part. If the diagonals of a quadrilateral be equal and also a pair of opposite sides; shew that the... | |
| Robert Potts - Geometry, Plane - 1860 - 380 pages
...circumstance. 30. How may a series of lines be found similarly divided to the line AB inEuc. n. 11 ? 31. **Divide Algebraically a given line (a) into two parts,...and one part may be equal to the square of the other** part. Deduce Euclid's construction from one solution, and explain the other. 32. Given the lesser segment... | |
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