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" Iff a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other... "
Arithmetic, algebra, differential and integral calculus, by W. Rutherford ... - Página 153
por Royal Military Academy, Woolwich - 1853
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Solutions to the questions of the general examination at Easter, 1848 ...

J. Goodall, W. Hammond - 1848
...Section 4. 1. Divide a given straight 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. 2. Describe a square that shall be double a given triangle. 3. Prove that the diagonals of a parallelogram...
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The definitions, postulates, axioms, and enunciations of the propositions of ...

Euclides - 1848
...of the other part. PROP. VIII. THEOREM. If a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line, which is made...
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An Elementary Course of Mathematics: Designed Principally for Students of ...

Harvey Goodwin - 1849 - 528 páginas
...n (,» + mx) = 1 +» 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 x = one part ; .•. a - a: = the other; .•. by the question, CLX = (ffl — ai)z mi a* — 2aa> +...
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Register

University of Cambridge - 1849
...Euclid's ? 3. Divide a given straight 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. Shew that in Euclid's figure four other lines, beside the given line, are divided in the required manner....
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The first three books of Euclid's Elements of geometry, with theorems and ...

Euclides, Thomas Tate - 1849 - 108 páginas
...straight line, &c. QED PROP. VIII. THEOR. If a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made...
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An elementary course of practical mathematics, Parte2

James Elliot - 1850
...the half of its square by § ? 3. Divide 100 into two such parts, that the product of the whole by one of the parts shall be equal to the square of the other part. 4. A horse-dealer bought a number of young horses at a fair, all at the same price, for the sum of...
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University of Durham

University of Durham - 1851
...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 cannot have the same centre. 7. Equal straight lines in a circle...
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THE PRINCIPLES OF THE SOLUTION OF SENATE-HOUSE 'RIDERS'

FRANCIS J. JAMESON - 1851
...1849. (A). Divide a given straight 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. (ii. 11.) (B). Shew that in Euclid's figure, four other lines, beside the given line, are divided in...
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A Collection of Problems and Examples Adapted to the "Elementary Course of ...

Harvey Goodwin - 1851 - 173 páginas
...Euclid's ? 3. Divide a given straight 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. Shew that in Euclid's figure four other lines, beside the given line, are divided in the required manner....
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BONNYCASTLE'S INTRODUCTION TO ALGEBRA; CONTAINING THE INDETERMINATE AND ...

JAMES RYAN - 1851
...to divide a line y of 20 inches in length, into two such parts that the rectangle of the whole arid one of the parts shall be equal to the square of the other. Ans. 10^/5 — 10, and 30— 10 ^5. 5. It is required to divide the number 60 into two such parts,...
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