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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. "
Elements of geometry, based on Euclid, books i-iii - Page 71
by Edward Atkins - 1876 - 119 pages
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Rider Papers on Euclid: Books i and Ii, Graduated and Arranged in Order of ...

Rupert Deakin - Euclid's Elements - 1891 - 102 pages
...parallel to BC meeting AB and AC in D and E. Prove that DE is equal to the sum of BD and CE. 4. Show how to divide a given straight line into two parts so that the square of one part may be equal to three times the square of the other part. 5. In the figure of Prop....
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A Text-book of Geometrical Deductions: Book I [-II] Corresponding to ..., Book 2

James Andrew Blaikie, William Thomson - Geometry - 1892 - 74 pages
...to the line. CHAPTER II. PROBLEMS. 39. Problems which follow directly from known propositions. 1. Divide a given straight line into two parts so that the rectangle contained by the parts shall be equal to a given square. This is a converse problem to Euc. II. 14, and the following...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - Geometry - 1892 - 460 pages
...its parallel sides. PROBLEMS. 37. Construct a rectangle equal to the difference of two squares. 38. Divide a given straight line into two parts so that the rectangle contained by them may be equal to the square described on a given straight line which is less than half the straight...
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Annual Report of the Department of Education

New Brunswick. Board of Education, New Brunswick. Department of Education - Education - 1893 - 800 pages
...sum of squares on one pair of opposite sides is equal to the sum of squares on the other pair. 4- (a) 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 part, (b) Show that when a line is divided as in this...
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Annual Report of the Department of Education

New Brunswick. Board of Education, New Brunswick. Department of Education - Education - 1893 - 804 pages
...sum of squares on one pair of opposite sides is equal to the sum of squares on the other pair. 4. (a) 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 part, (b) Show that when a line is divided as in this...
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Exercises in Stewart's Plane and Solid Geometry: With Solutions for Teachers

Seth Thayer Stewart - Geometry - 1893 - 256 pages
...intersection with О 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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Euclid's Elements of Geometry, Books 1-6

Henry Martyn Taylor - 1893 - 486 pages
...a chord, one of whose segments shall be four times as long as the other. 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. 5. A, B, C are three points on a circle, D is the middle point...
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Examination Papers for Science Schools and Classes

Great Britain. Education Department. Department of Science and Art - 1894 - 892 pages
...the four walls "would be 116 square yards ; find the dimensions of the room. (25.) B. 27. Show how to divide a given straight line into two parts, so...rectangle contained by the whole and one of the parts may be equal to the square on the other part. Given a line AB, show how to produce it to a point P,...
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The Manitoba School Question

Frederick Coate Wade - Church and state - 1895 - 168 pages
...square on half the line. Construct a rectangle equal to the difference between two given squares. 5. To divide a given straight line into two parts, so...rectangle contained by the whole and one of the parts may be equal to the square on the other part. If one side of a triangle be bisected, the sum of the...
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Euclid's Elements of Geometry, Books 1-6; Book 11

Henry Martyn Taylor - Euclid's Elements - 1895 - 708 pages
...a chord, one of whose segments shall be four times as long as the other. 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. 5. A, B, C are three points on a circle, D is the middle point...
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