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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. "
The Principles of Analytical Geometry: Designed for the Use of Students - Pągina 7
per Henry Parr Hamilton - 1826 - 326 pągines
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Scholarship examinations of 1846/47 (-1853/54).

Bengal council of educ - 1852 - 348 pągines
...? (2.) 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. Can this be solved arithmetically ? if so, find approximately into how many parts the given line must...
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Five Years in an English University, Volum 2

Charles Astor Bristed - 1852 - 470 pągines
...angles. 3. Divide a given straight line into two such parts, that the rectangle contained by the whole and one of the 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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The Elements of Euclid, books i-vi; xi. 1-21; xii. 1,2; ed. by H.J ..., Llibre 1

Euclides - 1853 - 334 pągines
...the squares of AD, DB are double of the squares of AC, CD. Which was to be proved. PEOP. XI. PEOB. To divide a given straight line into two such parts,...parts shall be equal to the square of the other part. Let AB be the given straight line. It is required to divide it into two such parts, that the rectangle...
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Arithmetic, algebra, differential and integral calculus, by W. Rutherford ...

Royal Military Academy, Woolwich - 1853 - 474 pągines
...the question in its literal meaning. 2. To divide a line of 20 inches in length into two parts such that the rectangle contained by the whole line and...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...
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The first six books of the Elements of Euclid, with numerous exercises

Euclides - 1853 - 178 pągines
...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. 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 geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich - 1853 - 400 pągines
...PROB. 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. 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 synoptical Euclid; being the first four books of Euclid's Elements of ...

Euclides - 1853 - 146 pągines
...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. 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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Solutions of the Problems and Riders Proposed in the Senate-house ...

William Walton, Charles Frederick Mackenzie - 1854 - 266 pągines
...parallelograms is equal to twice the triangle BSD. 2. Divide a given straight line into two parts so that the rectangle contained by the whole line and...parts shall be equal to the square of the other part. Produce a given straight line to a point such that the rectangle contained by the whole line thus produced...
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Solutions of the problems and riders proposed in the Senate-house ...

Cambridge univ, exam. papers - 1854 - 282 pągines
...parallelograms is equal to twice the triangle BKD. 2. Divide a given straight line into two parts so that the rectangle contained by the whole line and...parts shall be equal to the square of the other part. Produce a given straight line to a point such that the rectangle contained by the whole line thus produced...
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Orr's Circle of the Sciences: Organic nature, vols. 1-3 (1854-1856)

William Somerville Orr - 1854 - 534 pągines
...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 equal to AB;* bisect AC in E,t and draw BE. Prolong С A to F, making...
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