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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, shall be equal to the square of the other part. "
A companion to Euclid: being a help to the understanding and remembering of ... - Página 45
por Euclides - 1837 - 88 páginas
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The first six books of the Elements of Euclid, with numerous exercises

Euclides - 1853 - 147 páginas
...С d. Wherefore, if a straight line, &c. QED PROPOSITION XI. — PROBLEM. To divide a given straigM line into two parts, so that the rectangle contained...and one of the 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 parts, so...
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The Elements of Euclid, books i-vi; xi. 1-21; xii. 1,2; ed. by H.J ..., Libro 1

Euclides - 1853
...To divide a given straight line 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. Let AB be the given straight line. It is required to divide it into two such parts,...
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Arithmetic, algebra, differential and integral calculus, by W. Rutherford ...

Royal Military Academy, Woolwich - 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...
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Solutions of the problems and riders proposed in the Senate-house ...

Cambridge univ, exam. papers - 1854
...BD the other diameter, the difference of the 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 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 - 1854 - 225 páginas
...BD the other diameter, the difference of the 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 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 - 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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Liber Cantabrigiensis, an account of the aids afforded to poor students, the ...

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

Great Britain. Committee on Education - 1855
...upon the other 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...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 equal. 2. If from a point...
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Elements of Geometry: Containing the First Six Books of Euclid with a ...

John Playfair - 1855 - 318 páginas
..., 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
...the square of 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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