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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: The Errors, by which Theon, Or Others, Have Long Ago ... - Page 60
by Robert Simson - 1806 - 518 pages
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Liber Cantabrigiensis, an account of the aids afforded to poor students, the ...

Robert Potts - 1855
...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 the...parts, shall be equal to the square of the other part Solve the same problem algebraically, and give the geometrical interpretation of the result. 4. The...
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Minutes of the Committee of Council on Education

Great Britain. Committee on Education - School buildings - 1855
...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...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 point without a circle...
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Elements of Geometry: Containing the First Six Books of Euclid with a ...

John Playfair - Geometry - 1855 - 318 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
...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
...equal to a given triangle, and have one of its angles equal to a given rectilineal angle. 9. Divide a given straight line into two parts, so that the...parts, shall be equal to the square of the other part. 10. If two circles touch one another internally, they shall not have the same centre. 11. The diameter...
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Guide to the civil service examinations [by H. White]. By H. White

Henry White - 1856
...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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Considerations on the Suggestions of the University Commissioners with ...

Henry Latham - 1857 - 59 pages
...thus formed shall pass through the same point. 3. Shew by diagram that a (b + c} = ab + ac. To divide a given straight line into two parts so that the rectangle...parts shall be equal to the square of the other part. Give the full construction. 4. Define a decimal fraction. Prove the rule for pointing in the multiplication...
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The elements of algebra

Archibald Montgomerie - Algebra - 1857 - 95 pages
...of sheep, and the price of each. Ans. 100 at 30s. (25.) Divide a given line a, into two such parts that the rectangle contained by the whole and one of the parts may be equal to the square of the other. , 3+ ^'5 , 3— 4/5 Ans. a — ^— , and a — ~— . (26.)...
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Gradations in Euclid : books i. and ii., with an explanatory preface [&c ...

Euclides - 1858
...exercises for the learner. " — LARDNEB'S Euclid, pp. 79 and 80. PROP. 11. — PROB. To divide a given line into two parts, so that the rectangle contained...parts shall be equal to the square of the other part. SOL. — 46. I. To describe a square on a given line. 10. I. To bisect a given finite st. line. 3....
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Skeleton propositions &c. of Euclid, books i and ii, with ..., Volume 2

Euclides - 1858
...ijivru. ihr .«'iķe». o;' the reetnnt/lii e,m be found. BOOK II. 105 PRоP. XI. PRоB. To divide a line into two parts, so that the rectangle contained...parts shall be equal to the square of the other part. SoL. 46. I, 10. I, 3. I. Pat i. 2. DEM. 6. II, 47. I, Ax. 3. 1, Dei. 8U. 1. E». i Dat. Quœs. CON....
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