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" To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, may be equal to the square of the other part. "
The Elements of Euclid; viz. the first six books, together with the eleventh ... - Page 3-16
by Euclides - 1814
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The Harpur Euclid: An Edition of Euclid's Elements

Edward Mann Langley, W. Seys Phillips - 1890 - 538 pages
...PROBLEM. To bisect a given finite straight line — that is, to divide it into two equal parts. Let AB be the given straight line; it is required to divide it into two equal parts. Describe on AB an equilateral A ABC. [I. 1. Bisect L AC B by the straight line CD, meeting...
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Euclid Revised: Containing the Essentials of the Elements of Plane Geometry ...

Euclid - Geometry - 1890 - 442 pages
...sq. on BX = 2 (sq. on AM + sq. on MX). 95 Proposition 11. PROBLEM — 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. Let AB be the given st. line. On AB describe the...
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Sandhurst Mathematical Papers for Admission Into the Royal Military College ...

Royal Military College, Sandhurst - Mathematics - 1890 - 144 pages
...whole and one of the parts may be equal to the square on the other part. Divide a given straight line into two parts, so that the rectangle contained by the whole and one part may be equal to the rectangle contained by the other part and another given straight line. 2....
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The Elements of Plane and Solid Geometry ...

Edward Albert Bowser - Geometry - 1890 - 414 pages
...equal. 59. Construct a square that shall be one-third of a given square. 60. Divide a straight line into two parts so that the rectangle contained by the whole and one part may be equal to a given square. 61. Produce AB to C so that the rectangle of AB and AC may be...
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Annual Report of the Chief Superintendent of Education

1891 - 718 pages
...equal to a given triangle, and have one of its angles equal to a given angle. 4. Divide a given line into two parts, so that the rectangle contained by the whole and one of the parts shall lie equal to the square of the other part. 5. Find a line the square of which shall be equal to the...
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The Educational Record of the Province of Quebec: The Medium ..., Volume 11

Education - 1891 - 442 pages
...part together with the square on the other part. Prove this proposition. 8. Divide a straight line into two parts so that the rectangle contained by the whole and one of the parts may be equal to the square on the other part. 9. If a straight line be divided into any two parts,...
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Plane and Solid Geometry

Seth Thayer Stewart - Geometry - 1891 - 428 pages
...squares may equal a given square, and their rectangle, a given rectangle. 19. Divide a straight line into two parts, so that the rectangle contained by the whole and one of the parts may equal the square of a line given less than the line to be divided. 20. Divide a given line into...
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A Higher Algebra

George Albert Wentworth - Algebra - 1891 - 550 pages
...area of which would be doubled by increasing its radius by 1 inch. 14. Divide a line 20 inches long into two parts so that the rectangle contained by the whole and one part may be equal to the square on the other part. 16. A can do some work in 9 hours less time than...
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Rider Papers on Euclid (books I. and II.)

Rupert Deakin - Euclid's Elements - 1891 - 102 pages
...the square on the line made up of the half and the part produced. 11. To divide a given straight line into two parts, so that the rectangle contained by the whole and one part shall be equal to the square on the other. 12. In obtuse-angled triangles, if a perpendicular...
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Exercises in Stewart's Plane and Solid Geometry: With Solutions for Teachers

Seth Thayer Stewart - Geometry - 1893 - 262 pages
...draw .L to diameter. Segments of diameter are sides of required CD. (P. x.) i9. Divide a straight line into two parts, so that the rectangle contained by the whole and one of the parts may equal the square of a line given less than the line to be divided. I. Erect a .L at one end of...
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