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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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Five Years in an English University, Volume 2

Charles Astor Bristed - 1852
...every triangle are equal to two right angles. 3. Divide a given straight line into two such parts, that the rectangle contained by the whole and one...parts shall be equal to the square of the other part. 4. The angle at the centre of a circle is double of the angle at the circumference, upon the same base,...
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General Report on Public Instruction in the Bengal Presidency

Education - 1852
...which contain the right angle. Is this proposition included in any more general one ? 2. To divide a given straight line into two parts, so that the rectangle contained hy the whole and one of the parts, shall be equal to the square of the other part. Can this be solved...
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The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich - Mathematics - 1853
...double of the squares of AC, CD. Wherefore, if a straight line, etc. QED PROPOSITION XI. PROB. To divide a given straight line into two parts, so that the...parts, shall be equal to the square of the other part. Upon AB describe (46. i.) the square ABDC ; bisect (10. i.) AC in E, and join BE ; produce CA to F,...
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The first six books of the Elements of Euclid, with numerous exercises

Euclides - Geometry - 1853 - 147 pages
...equal to the square of the other part. LET ab be the given straight line ; it is required to divide it into two parts, so that the rectangle contained by...parts shall be equal to the square of the other part. Upon ab describe (i. 46) the square abdС; bisect (i. 10) a С in e, and join be, produce С a to f,...
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The synoptical Euclid; being the first four books of Euclid's Elements of ...

Euclides - 1853
...equal to the square of the other part. Let AB be the given straight line ; it is required to divide it into two parts, so that the rectangle contained by...parts, shall be equal to the square of the other part. Upon AB describe (1. 46.) the square ABDC ; bisect (I. 10.) AC in E, and join BE; produce CA to F,...
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Arithmetic, algebra, differential and integral calculus, by W. Rutherford ...

Royal Military Academy, Woolwich - Mathematics - 1853
...divide a line of 20 inches in length into two parts such that the rectangle contained by the whole line and one of the parts shall be equal to the square of the other part. Let x = the greater part ; then 20 — x = the less part, and hence by the question we have x8 = 20 (20...
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The Elements of Euclid. Books I.-VI.; XI. 1-21 XII. 1-2. A New Text ..., Book 1

Euclides - Geometry - 1853
...line. It is required to divide it into two such parts, that the rectangle contained by the whole line and one of the parts shall be equal to the square of the other part. On AB describe (i. 46) the square ACDB ; and supposing A to be that extremity of AB adjacent to which...
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Solutions of the problems and riders proposed in the Senate-house ...

Cambridge univ, exam. papers - 1854
...therefore the difference of the parallelograms GF, EH is equal to twice the triangle KBD. 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 ...

William Walton, Charles Frederick Mackenzie - Mathematics - 1854 - 225 pages
...therefore the difference of the parallelograms GF, EH is equal to twice the triangle KBD. 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: The mathematical sciences

William Somerville Orr - Science - 1854
...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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