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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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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1846 - 317 páginas
...(2a+i)2+J2=2o2+2(a+4)2, and the proposition is evident from this algebraical equality. PROP. XI. PROB. To divide a given straight line into two parts, so...rectangle contained by the whole, and one of the parts, may be equal to the square of the other part. Let AB be the given straight line ; it is required to...
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An Elementary Course of Mathematics: Designed Principally for Students of ...

Harvey Goodwin - 1846 - 468 páginas
...(l + n) ' ma ' na n (a> + mx) = Ex. 5. Divide the quantity a into two parts such that the product of the whole and one of the parts shall be equal to the square of the other part. Let a? = one part ; .-. a- n' = the other; .-. by the question, ax = (a — at): =...
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The English Journal of Education, Volumen1

1847
...angle contained by these two sides is a light angle. SECTION Il. — 1. To divide a straight line, so that the rectangle contained by the whole and one of the parts shall be equal to the square of the other part. 2. In every triangle the square of the side subtending either of the acute angles is...
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Minutes of the Committee of Council on Education, Volumen1

Great Britain. Committee on Education - 1847
...the angle contained by these two sides is a right angle. SECTION II. 1. To divide a straight line, so that the rectangle contained by the whole and one of the parts shall be equal to the square of the other part. 2. In every triangle the square of the side subtending either of the acute angles is...
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The definitions, postulates, axioms, and enunciations of the propositions of ...

Euclides - 1848
...the line bisected, and of the square of the line made up of the half and the part produced. PROP. XI. PROBLEM. To divide a given straight line into two...one of the parts, shall be equal to the square of the other part. PROP. XII. THEOREM. In obtuse-angled triangles, if a perpendicular be drawn from either...
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Solutions to the questions of the general examination at Easter, 1848 ...

J. Goodall, W. Hammond - 1848
...line intercepted without the triangle between the perpendicular and the obtuse angle. Section 4. 1. Divide a given straight line into two parts, so that...and one of the parts shall be equal to the square of the other part. 2. Describe a square that shall be double a given triangle. 3. Prove that the diagonals...
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Register

University of Cambridge - 1849
...upon the necessary homogeneity of algebraical equations, or any demonstration other than Euclid's ? 3. Divide a given straight line into two parts, so that...and one of the parts shall be equal to the square of the other part. Shew that in Euclid's figure four other lines, beside the given line, are divided in...
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The first three books of Euclid's Elements of geometry, with theorems and ...

Euclides, Thomas Tate - 1849 - 108 páginas
...squares of AC, CD: Wherefore, if a straight line, &c. QED Again, because EG F is EF PROP. XI. PROB. To divide a given straight line into two parts, so...contained by the whole, and one of the parts, shall Tie equal to the square of the other part. Let AB be the given straight line; it is required to divide...
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Minutes of the Committee of Council on Education, with Appendices, Volumen2

Great Britain. Committee on Education - 1850
...between the same parallels, are equal to one another. 3. Solve Euc. II. 11. To divide a given finite straight line into two parts, so that the rectangle contained by the whole and one of the parts may be equal to the squire of the other part. 4. Prove Euc. III. 22. The opposite angles of any quadrilateral...
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Reports on Elementary schools

Her MAjesty' Inspectors of schools - 1850
...figures, and duplicate ratio. 3. Solve Euc. II. 11. To divide a given finite straight line into two part*, so that the rectangle contained by the whole and one of the parts may be equal to the square of the other jjart. '2. Prove Kuc. 1. 36. Parallelograms upon equal bases,...
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