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" Iff a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other... "
Arithmetic, algebra, differential and integral calculus, by W. Rutherford ... - Página 153
por Royal Military Academy, Woolwich - 1853
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An Elementary Treatise on Algebra, Theoretical and Practical ...

James Ryan, Robert Adrain - 1824 - 516 páginas
...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...
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An Introduction to Algebra: With Notes and Observations, Designed for the ...

John Bonnycastle - 1825 - 312 páginas
...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...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - 1825 - 372 páginas
...QED | ¿J J'rojjosiiion VIII. Theorem. If a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line, which is made...
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The Principles of Analytical Geometry: Designed for the Use of Students

Henry Parr Hamilton - 1826 - 326 páginas
...number of solutions. For example, if it be required to divide a given straight line into two such parts, that the rectangle contained by the whole line and...parts, shall be equal to the square of the other part; this problem is determinate. If on the other hand, it were proposed to find a point such, that the...
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - 1827 - 513 páginas
...straight line, 8cc. QED G PROP. VIII. THEOR. If a straight line he divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made...
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Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

John Playfair - 1829 - 186 páginas
...together equal to the square of the whole line. ..If a straight line be divided into any two parts, the rectangle contained by the whole line and one of the parts is equal to the rectangle contained by the two parts together with the square of the foresaid part....
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Library of Useful Knowledge: Geometry, plane, solid, and spherical [by ...

1835
...square of the whole une. PROP. 31. (Eue. ii. 3.) If a straight line be divided into any two parts, the rectangle contained by the whole line and one of the parts, shall be equal to the rectangle contained by the two parts, together with the square of the aforesaid part. Let the straight...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 513 páginas
...QED PROP. VIII. THEOR. JJ F E a 34. 1. If a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts; together with the square of t/ie other part, is equal to the square of the straight line which is made...
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The Element of Geometry

John Playfair - 1836 - 114 páginas
...straight line : it is required to divide it into two parts, so that the rectangle contained by the whole and one of the parts shall be equal to the square of the other part. Upon AB describe (16. 2.) the square ABDC; bisect (8. 1.) AC in E, and join BE ; produce CA to F, and...
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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

1836 - 472 páginas
...of the difference of the lines. VIII. If a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made...
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