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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 - Seite 42
von Euclides - 1853 - 147 Seiten
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1859
...line between the points of section, is equal to the square of half the line. 10. Divide a straight line into two parts, so that the rectangle contained...parts shall be equal to the square of the other part. JULIUS CAESAR. 1. Write a short account of the author of the play Julius Ceesar. 2. What ancient writer...
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## Examination papers used at the examinations for admission to the Royal ...

Sandhurst roy. military coll - 1859 - 1869 Seiten
...equal and parallel straight lines toward the same parts are themselves equal. 3. To divide a straight line into two parts so that the rectangle contained...and one of the parts shall be equal to the square on the other part. 4. In a circle the angle in a semicircle is a right angle. Voluntary Portion. 2....
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## Algebra for High Schools and Colleges: Containing a Systematic Exposition ...

James B. Dodd - 1859 - 306 Seiten
...gentlemen ? Ans. 12. 21. Divide the number 20 into two such parts, that the product of the whole number and one of the parts shall be equal to the square of the other. Ans. 10/ 5— 10, and 30 — 10.V5. 22. A laborer dug two trenches, one of which was 6 yards longer...
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## Key to Dodd's Algebra: Containing All the Problems, and the More Difficult ...

James William Dodd - 1859
...whence z— 12. 21 . Divide the number 20 into two such parts, that the product of the whole number and one of the parts shall be equal to the square of the other. Let x represent the less number ; then 20 — x represents the greater. We shall then have the Equation...
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## The examination papers as set for the preliminary literary examination of ...

...sides of it, the angle contained by these two sides is a right angle. 4. To divide a given straight line into two parts, so that the rectangle contained...and one of the parts shall be equal to the square on. the other part. 5. To describe a square that shall be equal to a given rectilineal figure. 6. The...
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## Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1860 - 361 Seiten
...PROPOSITION XI. PROBLEM. To divide a given straight line into two parts, so that the rectangle eontained by the whole and one of the parts, shall be equal to the square on the other part. Let AB be the given straight line. It is required to divide AB into two parts, so...
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## Elements of algebra

Philip Kelland - 1860
...together. Eequired their rates of running. 19. To divide a line 12 inches long into two such parts that the rectangle contained by the whole and one of the parts may be equal to the square of the other part. (Euclid, 2, 11). 20. To divide a given line (a) into...
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## Examination papers used at the examination of candidates for appointment to ...

War office - 1861
...MA 1. Any two sides of a triangle are together greater than the third. 2. To divide a given straight line into two parts so that the rectangle contained...and one of the parts shall be equal to the square on the other part. If the given line be a foot long, compute the lengths of the parts to the nearest...
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## The elements of algebra. [With] Answers

Robert Fowler - 1861
...7. 5. Divide a line а feet long into two parts, so that the rectangle contained by the whole line and one of the parts shall be equal to the square of the other part. Let x = the length of the greater part, in feet. . ' . a - x = „ less „ x2 = (a — 3¿) a . • ....
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## The First Six Books of the Elements of Euclid: And Propositions I-XXI of ...

Euclid, John Casey - 1885 - 312 Seiten
...together with four times the square on the line joining the points of bisection. 6. Divide a given line into two parts, so that the rectangle contained by the whole and one segment may be equal to any multiple of the square on the other segment. 7. If P be any point in the...
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