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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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Solutions of the Problems and Riders Proposed in the Senate-house ...

William Walton, Charles Frederick Mackenzie - Education - 1854 - 266 pages
...BD the other diameter, the difference of the parallelograms is equal to twice the triangle BSD. 2. Divide a given straight line into two parts so that the rectangle contained by the whole line and one of the parts shall be equal to the square of the other part. Produce a given straight...
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Solutions of the problems and riders proposed in the Senate-house ...

Cambridge univ, exam. papers - 1854 - 284 pages
...BD the other diameter, the difference of the parallelograms is equal to twice the triangle BKD. 2. Divide a given straight line into two parts so that the rectangle contained by the whole line and one of the parts shall be equal to the square of the other part. Produce a given straight...
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Orr's Circle of the Sciences: Organic nature, vols. 1-3 (1854-1856)

William Somerville Orr - Science - 1854 - 534 pages
...the remarks at the end of this book. PROPOSITION XI.— PROBLEM. To divide a given straight line (AB) into two parts, so that the rectangle contained by the whole, and от of the parts, shall be equal to the square of the other part. From A draw AC perpendicular and...
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Liber Cantabrigiensis, an account of the aids afforded to poor students, the ...

Robert Potts - 1855 - 1050 pages
...that iSj divides them into two equal parts. Prove also that the two diameters bisect each other. 3. Divide a given straight line into two parts, so that...and one of the parts, shall be equal to the square of the other part Solve the same problem algebraically, and give the geometrical interpretation of...
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Minutes of the Committee of Council on Education

Great Britain. Committee on Education - School buildings - 1855 - 976 pages
...upon the other two sides of it, the angle contained by those two sides is a right angle. 3. Divide a straight line into two parts, so that the rectangle...and one of the parts shall be equal to the square of the other part. Section 3. 1. The angles in the same segment of a circle are equal. 2. If from a...
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Elements of Geometry: Containing the First Six Books of Euclid with a ...

John Playfair - Geometry - 1855 - 334 pages
..., and the proposition is evident from this algebraical equality. PROP. XI. PROB. To divide a givrn 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. I Let AB be the given straight line; it is required to...
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1855 - 270 pages
...the square of the straight line which joins the points of the bisection of the diagonals. . PROP. D. PROBLEM. — To divide a given straight line into two parts so that the rectangle contained by its segments shall be equal to a given square, not greater than the square of half the given straight...
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Cambridge examination papers: a suppl. to the University calendar, 1856-59

Cambridge univ, exam. papers - 1856 - 200 pages
...contained by the whole and each of the parts are together equal to the square of the whole line. 7. To divide a given straight line into two parts, so...and one of the parts shall be equal to the square of the other part. 8. If a straight line drawn through the centre of a circle bisect a straight line...
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Cambridge examination papers: a suppl. to the University calendar, 1856-59

Cambridge univ, exam. papers - 1856 - 252 pages
...contained by the whole and each of the parts, are together equal to the square of the whole line. 7. Divide a given straight line into two parts, so that...and one of the parts, shall be equal to the square of the other part. 8. If two circles cut one another, they shall not have the same centre. 9. If two...
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Guide to the civil service examinations [by H. White].

Henry White - 1856 - 168 pages
...one side of it are either two right angles, or are together equal to two right angles. 18 Divide a straight line into two parts, so that the rectangle contained by the whole and ono of the parts shall be equal to the square of the other part. 19 If two circles cut each other,...
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