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" AB be the given 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. "
Elements of geometry: consisting of the first four,and the sixth, books of ... - Page 53
by Euclides - 1842
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University of Durham

University of Durham - Education, Higher - 1851 - 222 pages
...twice the rectangle contained by the parts. 5. To divide a given straight line into two parts, such that the rectangle contained by the whole and one of the parts shall be equal to the square of the other part. 6. If two circles cut one another they cannot have the same...
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Scholarship examinations of 1846/47 (-1853/54).

Bengal council of educ - 1852 - 348 pages
...angle. Is this proposition included in any more general one ? (2.) To divide a given straight line 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. Can this be solved arithmetically ? if so, find approximately...
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The first two books of the Elements of Euclid, with additional figures ...

Euclides - 1852 - 152 pages
...PROP. X. PEOB. To bisect a (jiven 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 " upon it an equilateral triangle ABC, and bisect b the angle ACB by the straight...
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Five Years in an English University, Volume 2

Charles Astor Bristed - 1852 - 470 pages
...every triangle are equal to two right angles. 3. Divide a given straight line into two such parts, that the rectangle contained by the whole and one of the parts shall be equal to the square of the other part. 4. The angle at the centre of a circle is double of the angle...
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The Elements of Euclid, books i-vi; xi. 1-21; xii. 1,2; ed. by H.J. Hose, Book 1

Euclides - Geometry - 1853 - 334 pages
...two such parts, that the rectangle contained by the whole line and one of the parts shall be equal to the square of the other part. Let AB be the given...straight line. It is required to divide it into two such parts, that the rectangle contained by the whole line and one of the parts shall be equal to the...
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The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...PROPOSITION 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. i.) upon it an equilateral triangle ABC, and bisect (9. i.) the angle ACB...
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The first six books of the Elements of Euclid, with numerous exercises

Euclides - Geometry - 1853 - 178 pages
...X. — 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 (i. 1) upon ab an equilateral triangle abc, and bisect (i. 9) the angle acb by...
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The synoptical Euclid; being the first four books of Euclid's Elements of ...

Euclides - 1853 - 146 pages
...PROP. X. 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 (I. 1.) upon it an equilateral triangle ABC, and bisect (I. 9.) the angle ACB...
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Orr's Circle of the Sciences: Organic nature, vols. 1-3 (1854-1856)

William Somerville Orr - Science - 1854 - 534 pages
...the remarks at the end of this book. PROPOSITION XI.— PROBLEM. To divide a given straight line (AB) into two parts, so that the rectangle contained by the whole, and от of the parts, shall be equal to the square of the other part. From A draw AC perpendicular and...
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Elements of Geometry: Containing the First Six Books of Euclid with a ...

John Playfair - Geometry - 1855 - 334 pages
...rectangle contained by the whole, and one of the parts, may be equal to the square of the other part. I Let AB be the given straight line; it is required...contained by the whole, and one of the parts, shall be equal to the square of the other part. EF equal to EB, and upon AF describe A! _ |3T Upon AB describe...
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