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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*. "
The Solutions of the Geometrical Problems: Consisting Chiefly of Examples in ... - Página 28
de Thomas Gaskin - 1847 - 263 páginas
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The British Encyclopedia, Or Dictionary of Arts and Sciences ..., Volume 1

William Nicholson - 1809 - 716 páginas
...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...
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American Edition of the British Encyclopedia: Or, Dictionary of ..., Volume 1

William Nicholson - 1819 - 432 páginas
...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...
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Euclid's Elements of Geometry: The Six First Books. To which are Added ...

Rev. John Allen - 1822 - 516 páginas
...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...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1837 - 410 páginas
...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...
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The first principles of algebra, for the use of the boys of the Royal ...

Admiralty - 1845 - 152 páginas
...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=—...
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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1845 - 382 páginas
...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...
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The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846 - 292 páginas
...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...
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University of Durham

University of Durham - 1851 - 222 páginas
...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...
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Liber Cantabrigiensis, an account of the aids afforded to poor students, the ...

Robert Potts - 1855 - 1050 páginas
...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...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1860 - 380 páginas
...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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