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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 - Σελίδα 42
των Euclides - 1853 - 147 σελίδες
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Euclid Revised: Containing the Essentials of the Elements of Plane Geometry ...

Euclid - 1890 - 400 σελίδες
...+ 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. On AB describe the...

Mathematical Papers for Admission Into the Royal Military College for the ...

Eldred John Brooksmith, Robert Moir Milne - 1890 - 132 σελίδες
...approximately the thickness of the shell. II.— EUCLID AND TRIGONOMETRY. 1. 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 on the other part. 2. Describe a square that...

Annual Report of the Chief Superintendent of Education

1891
...be equal to a given triangle, and have one of its angles equal to a given angle. 4. Divide a given line into two parts, so that the rectangle contained by the whole and one of the parts shall lie equal to the square of the other part. 5. Find a line the square of which shall be equal to the...

Plane and Solid Geometry

Seth Thayer Stewart - 1891 - 406 σελίδες
...their squares may equal a given square, and their rectangle, a given rectangle. 19. Divide a straight line into two parts, so that the rectangle contained by the whole and one of the parts may equal the square of a line given less than the line to be divided. 20. Divide a given line into...

The Educational Record of the Province of Quebec: The Medium ..., Τόμος 11

1891
...that part together with the square on the other part. Prove this proposition. 8. Divide a straight line into two parts so that the rectangle contained by the whole and one of the parts may be equal to the square on the other part. 9. If a straight line be divided into any two parts,...

Rider Papers on Euclid: Books i and Ii, Graduated and Arranged in Order of ...

Rupert Deakin - 1891 - 79 σελίδες
...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 a perpendicular...

A Higher Algebra

George Albert Wentworth - 1891 - 521 σελίδες
...area of which would be doubled by increasing its radius by 1 inch. 14. Divide a line 20 inches long into two parts so that the rectangle contained by the whole and one part may be equal to the square on the other part. 16. A can do some work in 9 hours less time than...

The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1892 - 518 σελίδες
...on half their sum and on half their difference. 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 straight line. It is required...

A Text-book of Geometrical Deductions: Book I [-II] Corresponding ..., Βιβλίο 2

James Andrew Blaikie, William Thomson - 1892
...line bisected, and on the line made up of the half and the part produced. 11. To divide a straight line into two parts so that the rectangle contained by the whole line and one part shall be equal to the square on the other part. 12. In an obtuse-angled triangle,...

The First Book of Euclid's Elements: Arranged for Beginners

Euclid, John Bascombe Lock - 1892 - 167 σελίδες
...drawn, etc. QEF Example. Divide a given straight line into any given number (say five) of equal parts. Let AB be the given straight line ; it is required to divide AB into five equal parts. Construction. From A draw a line AC making an angle of about half a right...




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