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" When is this possible? 4. Divide a given straight line into two parts, so that the rectangle contained by the parts may be equal to a given rectangle. "
Principles of the Differential and Integral Calculus: Familiarly Illustrated ... - 51. lappuse
autors: William Ritchie - 1836 - 174 lapas
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An Elementary Treatise on the Differential and Integral Calculus

Jean-Louis Boucharlat - 1828 - 398 lapas
...the line, to which that root corresponds. Fig- 2' Ex. 2. To dhidf a given straight line AB (fig. 2) into two parts, so that the rectangle contained by the parts may be equal to a given square. Let c be a side of the square, a the given line, x one of the parts, and therefore...
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Skeleton propositions &c. of Euclid, books i and ii, with ..., 2. sējums

Euclides - 1858
...beinij ijivru. ihr .«'iíe». o;' the reetnnt/lii e,m be found. BOOK II. 105 PRоP. XI. PRоB. To divide a line into two parts, so that the rectangle contained by the whole and one of the parts shall be equal to the square of the other part. SoL. 46. I, 10. I, 3. I....
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Mathews' Euclid examination papers ... on Euc. i.-iv

Edward Harri Mathews - 1879
...the line between the points of section is equal to .the square on half the line. Hence show how to divide a line into two parts so that the rectangle contained by them may be a maximum. 3. In every triangle the square on the side subtending an acute angle is less...
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(Report).

Elizabethan club - 1880
...parts together with twice the rectangle contained by the parts. Express this also algebraically. 5. Divide a line into two parts, so that the rectangle contained by the whole and one part shall be equal to the square on the other part. 6. If a =- 2, b = 3, c = o, what...
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Elements of Algebra

George Albert Wentworth - 1881 - 380 lapas
...the sum of the squares on these two parts may be the least possible. 11. Divide a line 20 in. long into two parts so that the rectangle contained by the parts may be the greatest possible. 12. Find the fraction which has the greatest excess over its square. 235. Two...
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Geometry for schools, comprising books i. and ii. of Euclid, with some ...

Euclides - 1883 - 96 lapas
...made up of the half and the part produced. — (En. II. 6.) 9. Divide a given straight line internally into two parts so that the rectangle contained by the parts may be a maximum (ie, the greatest possible). 10. How should a straight line be divided into two parts so that the sum...
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Differential calculus for beginners

Alexander Knox (B.A.) - 1884
...minimum. 107. We will conclude this part of the subject with one more example. " Divide a straight line into two parts, so that the rectangle contained by the parts may be a maximum." Let « be the straight line, and x one of the parts, a - #=other part, and the rectangle = (a — x(* or...
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Differential Calculus for Beginners: With a Selection of Easy Examples

Alexander Knox - 1884 - 112 lapas
...variation of function =J rate of variation of angle *,=4, cos ^ = *, .'. angle = 60°. 4. Divide a straight line into two parts, so that the rectangle contained by the parts may be the greatest possible. Let o = the line, #=one of the parts, . '. a - .r = other part, then rectangle...
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Examination Papers

Queen's University (Kingston, Ont.) - 1886
...in D. Prove that С A* - CD* = AD.DB, and show in what sense this relation is universally true. 2. Divide a line into two parts so that the rectangle contained by the parts may be equal to the differences of the squares upon the parts. 3. If a chord be drawn from the point of contact...
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Elementary Algebra

Walter William Rouse Ball - 1890 - 486 lapas
...Find the least value which the expression a?-6.v+W can have for any real value of x. Let x* Ex. 2. Divide a line into two parts so that the rectangle contained by them shall be a maximum. Let the length of the line be a ; that is, suppose that it contains a units...
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