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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 first six books of the Elements of Euclid, with numerous exercises - Seite 42
von Euclides - 1853 - 147 Seiten
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A collection of examples in pure and mixed mathematics, with hints and ...

Alfred Wrigley - 1845
...diameter drawn from one of these points. (Euclid, iii. 18. Cape, ii. 38.) 59. 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 a given line, which is less than the line to be divided. (Euclid, iii....
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The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846
...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 the square ACDB ; bisect AC in E, and join BE ; produce CA to F, and make EF equal...
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An Elementary Course of Mathematics: Designed Principally for Students of ...

Harvey Goodwin - 1846 - 468 Seiten
...(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): = o2 - Zax + a?2, x- -...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - 1846 - 317 Seiten
...the proposition is evident from this algebraical equality. PROP. XI. PROB. 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. Let AB be the given straight line ; it is required to...
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The English Journal of Education, Band 1

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...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 less than the...
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Minutes of the Committee of Council on Education, Band 1

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

John Playfair - 1847 - 317 Seiten
...PROP. X. PROB. To bisect a given finite straight line, that is, to divide it into two equal parts. Let AB be the given straight line ; it is required to divide if into two equal parts. Describe (1. 1.) upon it an equilateral triangle ABC, and bisect (9. 1.) the...
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The definitions, postulates, axioms, and enunciations of the propositions of ...

Euclides - 1848
...of the line made up of the half and the part produced. PROP. XI. PROBLEM. To divide a given straight line into two parts, so that the rectangle contained...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 of the acute...
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Solutions to the questions of the general examination at Easter, 1848 ...

J. Goodall, W. Hammond - 1848
...the triangle between the perpendicular and the obtuse angle. Section 4. 1. Divide a given straight line into two parts, so that the rectangle contained...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 of a parallelogram...
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Register

University of Cambridge - 1849
...homogeneity of algebraical equations, or any demonstration other than Euclid's ? 3. Divide a given straight line into two parts, so that the rectangle contained...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 the required manner....
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