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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. "
Euclid's Elements [book 1-6] with corrections, by J.R. Young - Page 70
by Euclides - 1838
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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 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...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 in it, which does...
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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...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 circles touch each...
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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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Considerations on the Suggestions of the University Commissioners with ...

Henry Latham - 1857 - 390 pages
...parallelograms 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...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 - 116 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 - 248 pages
...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 - 136 pages
...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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Examination papers used at the examinations for direct commissions [&c.].

War office - 1858 - 578 pages
...contained by the parts. If the line be bisected, what do the rectangles contained by the parts become ? 4. 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. NATURAL SCIENCES. By MAJOR-GEN....
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