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 Bøker Bok 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 ... - Side 64
av Robert Simson - 1806 - 518 sider
Uten tilgangsbegrensning - Om denne boken ## A collection of examples in pure and mixed mathematics, with hints and ...

Alfred Wrigley - 1845
...contact, and the 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....
Uten tilgangsbegrensning - Om denne boken ## The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1845 - 352 sider
...the first and third partu of whioh are, by the same curolla'y, tli» 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...
Uten tilgangsbegrensning - Om denne boken ## 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...
Uten tilgangsbegrensning - Om denne boken ## Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1846 - 317 sider
...(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 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...
Uten tilgangsbegrensning - Om denne boken ## An Elementary Course of Mathematics: Designed Principally for Students of ...

Harvey Goodwin - 1846 - 468 sider
...(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- -...
Uten tilgangsbegrensning - Om denne boken ## Minutes of the Committee of Council on Education, Volum 1

...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...
Uten tilgangsbegrensning - Om denne boken ## The English Journal of Education, Volum 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...
Uten tilgangsbegrensning - Om denne boken ## The definitions, postulates, axioms, and enunciations of the propositions of ...

Euclides - 1848
...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 parts, so that 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 of the acute...
Uten tilgangsbegrensning - Om denne boken ## Solutions to the questions of the general examination at Easter, 1848 ...

J. Goodall, W. Hammond - 1848
...intercepted without the triangle between the perpendicular and the obtuse angle. Section 4. 1. Divide a given straight line into two parts, so that 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 of a parallelogram...
Uten tilgangsbegrensning - Om denne boken ## Register

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