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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.
Euclid's Elements [book 1-6] with corrections, by J.R. Young - Page 70
by Euclides - 1838

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

Euclid, Robert Simson - Geometry - 1821 - 514 pages
...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 the whole and dne of the parts shall be equal to the square of the other part. Upon AB describe (46. 1.) the square...

## 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...

## A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - Mathematics - 1825 - 1046 pages
...are double of the squares of AC, CD. Wherefore, if a straight line, &c. QED Proposition Xf. Problem. To divide a given straight line into two parts, so...by the whole, and one of the parts, shall be equal 'o the square of the other part. Let AB be the given straight line ; it is required to divide it into...

## An Introduction to Algebra: With Notes and Observations, Designed for the ...

John Bonnycastle - Algebra - 1825 - 336 pages
...is required to divide a line, of 20 inches in length, into two such parts that the rectangle of (he whole and one of the parts shall be equal to the square of the other. Ans. 10^5-10, and 30—10^/5 6. It is required to divide the number 60 into two such parts that their...

## A Supplement to the Elements of Euclid

Daniel Cresswell - Euclid's Elements - 1825 - 616 pages
...produced, shall be to the square of the part produced, in a given ratio. VIII. PR. To divide a given finite straight line into two parts, so that the rectangle, contained by the whole line, and the difference of those two parts, shall be in a given ratio to the square of the less of...

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

Euclid, John Playfair - Euclid's Elements - 1826 - 326 pages
...DG=DB: Therefore, AD3-fDBi)==2AC»-|r'2CD>3< Wherefore, if a straight line, &e. QBD H B PROP, XI. PROB. To divide a given straight line into two parts, so that the reetangle eontained 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 ...

Robert Simson - Trigonometry - 1827 - 546 pages
...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 ABDC; bisect* AC in E, ahd join BE : produce CA to F, and make* EF equal...