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" AB into two parts, so that the rectangle contained by the whole line and one of the parts, shall be equal to the square on the other part. "
A Text-book of Euclid's Elements for the Use of Schools, Books I.-IV. - Página 162
por Henry Sinclair Hall, Frederick Haller Stevens - 1900 - 304 páginas
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Euclid Revised: Containing the Essentials of the Elements of Plane Geometry ...

Euclid - 1890 - 400 páginas
...each side, we get sq. on AX + sq. on BX = 2 (sq. on AM + sq. on MX). 95 Proposition 11. PROBLEM — To divide a given straight line into two parts so that the rectangle contained by the whole and one part may be equal to the square on the other part. Let AB be the given st. line....
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Report of the Secretary for Public Instruction ...

Queensland. Department of Public Instruction - 1890
...triangle. 4. Explain clearly the construction only, necessary in each of the following problems: — (a) 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 on the other part. (6) To describe a square...
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Mathematical Papers for Admission Into the Royal Military College for the ...

Eldred John Brooksmith, Robert Moir Milne - 1890 - 132 páginas
...employed, but the method of proof must be geometrical. Great importance will be attached to accuracy I\ i. Divide a given straight line into two parts, so that the rectangle contained by the whole line and one of the parts may be equal to the square on the other part. If the straight line...
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The Harpur Euclid: An Edition of Euclid's Elements

Edward Mann Langley, W. Seys Phillips - 1890 - 515 páginas
...of the complements, show that the complement is equal to half the other parallelogram. Ex. 652. — Divide a given straight line into two parts so that the rectangle contained by the whole and one part may be equal to the rectangle contained by the other part and a given finite...
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Rider Papers on Euclid: Books i and Ii, Graduated and Arranged in Order of ...

Rupert Deakin - 1891 - 79 páginas
...square on half the line and of the square on the line made up of the half and the part produced. 11. To divide a given straight line into two parts, so that the rectangle contained by the whole and one part shall be equal to the square on the other. 12. In obtuse-angled triangles, if...
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Examinations Papers

1891
...the squares on half the line bisected and on the line made up of the half and the part produced. 6. Divide a given straight line into two parts so that the rectangle contained bv the whole and one of the parts may be equal to the square on the other part. 7. If a diameter of...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1892 - 518 páginas
...as centre any circle is described, and P is any point upon this circle : shew that PA2 + PB2+ PC2 + PD2 is constant, being equal to 36. The squares on...39. Given a square and one side of a rectangle which is equal to the square, find the other side. 40. Produce a given straight line so that the rectangle...
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A Text-book of Geometrical Deductions: Book I [-II] Corresponding ..., Libro 2

James Andrew Blaikie, William Thomson - 1892
...to the line. CHAPTER II. PROBLEMS. § 39. Problems which follow directly from known propositions. 1. Divide a given straight line into two parts so that the rectangle contained by the parts shall be equal to a given square. This is a converse problem to Euc. II. 14, and the following...
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Euclid's Elements of Geometry, Libros 1-6

Henry Martyn Taylor - 1893 - 504 páginas
...square on UK are equal to the square on BD and three times the square on AD. 156 PROPOSITION 11. To divide a, given straight line into two parts, so that the rectangle contained by the whole and one part may be equal to the square on the other part*. Let AB be the given straight...
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Annual Report of the Department of Education

New Brunswick. Board of Education, New Brunswick. Department of Education - 1893
...of squares on one pair of opposite sides is equal to the sum of squares on the other pair. 4. (a) To divide a given straight line into two parts so that the rectangle contained by the whole and one part shall be equal to the square on the other part, (b) Show that when a line is...
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