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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
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Algebra for High Schools and Colleges: Containing a Systematic Exposition ...

James B. Dodd - Algebra - 1859 - 368 pages
...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 - 188 pages
...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 ...

Royal college of surgeons of England - 1860 - 336 pages
...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 by...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 - Geometry, Plane - 1860 - 380 pages
...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 - 308 pages
...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 - 260 pages
...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 by...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 - 426 pages
...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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Examination papers used at the examinations for direct commissions [&c.].

War office - 1861 - 714 pages
...angles. Enunciate the propositions required in the proof. 3. To divide a straight line into two parte so that the rectangle contained by the whole and one of the parts may be equal to the square on the other part. 4. If a straight line touch a circle and from the point...
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The school Euclid: comprising the first four books, by A.K. Isbister

Euclides - 1862 - 172 pages
...straight line, &c. QED PROP. XI.— PROBLEM. To divide a given straight line into two parts, so that tlie rectangle contained by the whole and one of the parts shall be equal to the square of the other part. (References— Prop. i. 3, 10, 46, 47 ; Ii. 6.) Let AB be the given straight line. It is required to...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1883 - 428 pages
...10. PROBLEM. 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 on it an equilateral triangle ABC, [I. 1. and bisect the angle ACB by the straight...
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