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" AB be the given straight line ; it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part. "
Elements of geometry: consisting of the first four,and the sixth, books of ... - Page 53
by Euclides - 1842
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Liber Cantabrigiensis, an account of the aids afforded to poor students, the ...

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

Great Britain. Committee on Education - School buildings - 1855 - 976 pages
...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 contained by the whole 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...
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1855 - 262 pages
...that the rectangle contained by the whole and one of the parts, shall be equal to the square oflhe other part. Let AB be the given straight line. It is required to divide AB into two parts, so that the rectangle contained by the whole and one of tLe parts, shall be equal...
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Cambridge examination papers: a suppl. to the University calendar, 1856-59

Cambridge univ, exam. papers - 1856 - 252 pages
...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 the rectangle contained by the whole, 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...
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Guide to the civil service examinations [by H. White]. By H. White

Henry White - 1856 - 178 pages
...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
...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 contained by the whole and one of the parts shall be equal to the square of the other part. Give the full construction. 4. Define a decimal fraction. Prove...
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The elements of algebra

Archibald Montgomerie - Algebra - 1857 - 118 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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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1858 - 256 pages
...line into two parts, such that ihe greater part may be a mean proportional between the whole line and the other part. Let AB be the given straight line ; it is required to divide it into two parts at the point F, such that AB : AF : : AF : FB. At the extremity of the line AB, erect the perpendicular...
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Gradations in Euclid : books i. and ii., with an explanatory preface [&c ...

Euclides - 1858 - 248 pages
...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 by the whole and one of the parts shall be equal to the square of the other part. SOL. — 46. I. To describe a square on a given line. 10. I....
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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 by the whole and one of the 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....
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