 | William Nicholson - 1809 - 716 pagina’s
...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 - 1819 - 432 pagina’s
...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 - 1822 - 516 pagina’s
...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 - 1837 - 410 pagina’s
...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 pagina’s
...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 - 1845 - 382 pagina’s
...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 pagina’s
...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 - 1851 - 222 pagina’s
...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 pagina’s
...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 - 1860 - 380 pagina’s
...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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To divide a given straight line into two parts, so that the rectangle contained by the whole and one part may be equal to the square on the other part*. 
