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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 Elements of Euclid; viz. the first six books, together with the eleventh ... - Page 3-16
by Euclides - 1814

## Geometrical Problems Deducible from the First Six Books of Euclid, Arranged ...

Miles Bland - Euclid's Elements - 1819 - 442 pages
...equal to a given square, and their rectangle equal to a given rectangle. 9. To 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 of a given line, which is less than the line to be divided. 10. To divide...

## Geometrical Problems Deducible from the First Six Books of Euclid, Arranged ...

Miles Bland - Euclid's Elements - 1819 - 444 pages
...DB are equal to the square of AB, ie to the given square. (9.) To divide a straight line into ttvo 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. L,etAB be the...

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

John Playfair - Circle-squaring - 1819 - 350 pages
...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 it into two equal parts. Describe (1. 1.) upon it an equilateral triangle ABC, and bisect (9. 1.) the angle ACB...

## Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 354 pages
...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 it into two equal parts. Describe (1. 1.) upon it an equilateral triangle ABC, and bisect (9. 1.) the angle ACB...

## A Supplement to the Elements of Euclid

Daniel Cresswell - Geometry - 1819 - 446 pages
...> the L HAG ; and so on. . PROP. XXXIII. 47. PROBLEM. To trisect av given finite straight line. Let AB be the given straight line: It is required to divide it into three equal parts. Upon AB describe (E. 1.1.) the equilateral A CAB ; bisect (E. 9. 1.) the two equal...

## A Supplement to the Elements of Euclid

Daniel Cresswell - Geometry - 1819 - 486 pages
...manifest from this proposition, and from E. 1O. 4., that if the semi-diameter of a circle be divided into two parts, so that the rectangle contained by the whole and the lesser part may be equal to the square of the greater part, the greater segment shall be equal...

## An Elementary Treatise on Algebra: Theoretical and Practical

James Ryan - Algebra - 1824 - 550 pages
...sought. Ans. 1 1 , or 3] . Prob. 22. It is required to divide 20 into two such parts, that the product of the whole and one of the parts, shall be equal to the square of the other. Ans. lOv/5— 10, and 30— lOy/5. Prob. 23. A labourer dug two trenches, one of which was 6 yards...

## An Elementary Treatise on Algebra: Theoretical and Practical

James Ryan, Robert Adrain - Algebra - 1824 - 542 pages
...sought. Ans. II, or 3], Prob. 22. It is required to divide 20 into two such parts, that the product of the whole and one of the parts, shall be equal to the square of the other. Ans. lOv/5 — 10, and 30— 10^/5, Prob. 23. A labourer dug two trenches, one of which was 6 yards...