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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: The Errors, by which Theon, Or Others, Have Long Ago ... - Page 60
by Robert Simson - 1806 - 518 pages
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The first three books of Euclid's Elements of geometry, with theorems and ...

Euclid, Thomas Tate - 1849 - 108 pages
...AC, CD: Wherefore, if a straight line, &c. QED Again, because EG F is EF PROP. XI. PROB. To divide a given straight line into two parts, so that the...contained by the whole, and one of the parts, shall Tie equal to the square of the other part. Let AB be the given straight line; it is required to divide...
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Minutes of the Committee of Council on Education, with Appendices, Volume 2

Great Britain. Committee on Education - 1850
...between the same parallels, are equal to one another. 3. Solve Euc. II. 11. To divide a given finite straight line into two parts, so that the rectangle contained by the whole and one of the parts may be equal to the squire of the other part. 4. Prove Euc. III. 22. The opposite angles of any quadrilateral...
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An elementary course of practical mathematics, Part 2

James Elliot - 1850
...the half of its square by ? 3. Divide 100 into two such parts, that the product of the whole by one of the parts shall be equal to the square of the other part. 4. A horse-dealer bought a number of young horses at a fair, all at the same price, for the sum of...
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Reports on Elementary schools

Her MAjesty' Inspectors of schools - 1850
...figures, and duplicate ratio. 3. Solve Euc. II. 11. To divide a given finite straight line into two part*, so that the rectangle contained by the whole and one of the parts may be equal to the square of the other jjart. '2. Prove Kuc. 1. 36. Parallelograms upon equal bases,...
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A Collection of Problems and Examples Adapted to the "Elementary Course of ...

Harvey Goodwin - Mathematics - 1851 - 173 pages
...necessary homogeneity of algebraical equations, or any demonstration other than Euclid's ? 3. Divide a given straight line into two parts, so that the...parts shall be equal to the square of the other part. Shew that in Euclid's figure four other lines, beside the given line, are divided in the required manner....
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THE PRINCIPLES OF THE SOLUTION OF SENATE-HOUSE 'RIDERS'

FRANCIS J. JAMESON - 1851
...(BE2 + CF2) = 4 (ABa + AC2) + 4AE2 + 4AF2, = 4BC2 + AB2 + AC2, = 4BC2 + BC2, - 5BC8. 1849. (A). Divide a given straight line into two parts, so that the...parts shall be equal to the square of the other part. (ii. 11.) (B). Shew that in Euclid's figure, four other lines, beside the given line, are divided in...
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University of Durham

University of Durham - Education, Higher - 1851
...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...parts shall be equal to the square of the other part. 6. If two circles cut one another they cannot have the same centre. 7. Equal straight lines in a circle...
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BONNYCASTLE'S INTRODUCTION TO ALGEBRA; CONTAINING THE INDETERMINATE AND ...

JAMES RYAN - 1851
...to divide a line y of 20 inches in length, into two such parts that the rectangle of the whole arid one of the parts shall be equal to the square of the other. Ans. 10^/5 — 10, and 30— 10 ^5. 5. It is required to divide the number 60 into two such parts,...
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Scholarship examinations of 1846/47 (-1853/54).

Bengal council of educ - 1852
...which contain the right angle. Is this proposition included in any more general one ? (2.) To divide a given straight line into two parts, so that the...parts, shall be equal to the square of the other part. Can this be solved arithmetically ? if so, find approximately into how many parts the given line must...
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The First Two Books of the Elements of Euclid ... with Additional Figures ...

Euclides - 1852
...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; • x hi. i. bisect* AC in E, " x . i. and join BE; produce CA to...
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