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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; viz. the first six books, together with the eleventh ... - Page 3-16
by Euclides - 1814
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - 1883 - 376 pages
...XI. PROBLEM. To divide a given straight line into tiro jiarts, so that the rectangle contained by ike whole and one of the parts shall be equal to the square on the ether part. & _ JJ 1C f Let AB be the given st. line. On AB descr. the sq. ADCB. Bisect AD in...
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The Civil service year book and official calendar

1884 - 266 pages
...bisected at right angles by the straight line joining their centres. 3. Divide a given straight line into two parts so that the rectangle contained by...parts shall be equal to the square of the other part. 4. The angles in the same segment of a circle are equal to one another. 5. If the diameter of a circle...
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Yale Examination Papers

F. B. Stevens - Examinations - 1884 - 202 pages
...towards the same parts, are also themselves equal and parallel. 2. 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 on the other part. (LEGENDRE.) 1. In an isosceles triangle the angles opposite...
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Cambridge University Examination Papers

University of Cambridge - 1884 - 624 pages
...each of the parte are together equal to the square on the whole line. 5. 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 on the other part. Prove that the rectangle contained by the two parts is...
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Stewart's specific subjects. Euclid. [1st] (-3rd stage). [With 2 issues of ...

Stewart W. and co - 1884 - 272 pages
...line AF. X. — To Used a given finite straight line, that is, divide it into two equal parts. Let AB be the given straight line; it is required to divide it into two equal parts. Describe on it an equilateral triangle ABC, and bisect the angle ACB by the straight line...
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The Elements of Euclid, books i. to vi., with deductions, appendices and ...

Euclides - 1884 - 434 pages
...PROBLEM. To divide a given straight line internally and externally* in medial section. ir i; G' H Let AB be the given straight line : it is required to divide it in medial section. The second part of this proposition is not given by Euclid. L' G' — D (1) Internally...
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The Elements of Plane Geometry ...

Association for the improvement of geometrical teaching - Geometry, Modern - 1884 - 150 pages
...contained by the given line and one of the segments may be equal to the square on the other segment. Let AB be the given straight line : it is required to divide it internally and externally so that the rectangle contained by AB and one segment may be equal to the...
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Annual Report of the Chief Superintendent of Education

1885 - 608 pages
...line and of the square on the line between the points of section. 4. To divide a given straight line into two parts, so that the rectangle contained by...and one of the parts shall be equal to the square on the other part. •">. Prove that the sum of the squares on any two sides of a triangle is equal...
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The Elements of Geometry

George Bruce Halsted - Geometry - 1885 - 389 pages
...rectangle BA,AF + AG2 = GF* = GH2 = AH2 + A(?, by 243 ; 112 PROBLEM II. 313. To divide a given sect into two parts so that the rectangle contained by...and one of the parts shall be equal to the square on the other part. Jf X GIVEN, the sect AB. REQUIRED, to find a point C such that rectangle AB,BC =...
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The Practical Teacher, Volume 4

Education - 1885 - 630 pages
...parts of BC. Let A=e, andBC = , and BU, I,E ~K. = x г. Then ab= 3. 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 on the other part. Prop, il, Bk. II. Algebra. Anxvtr two Questions. 1. What...
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