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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. "
Elements of geometry, based on Euclid, books i-iii - Page 71
by Edward Atkins - 1876 - 119 pages
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A Collection of Problems and Examples Adapted to the "Elementary Course of ...

Harvey Goodwin - Mathematics - 1851 - 196 pages
...upon the necessary homogeneity of algebraical equations, or any demonstration other than Euclid's ? 3. Divide a given straight line into two parts, so that...and one of 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...
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The Principles of the Solution of the Senate-house 'riders,' Exemplified by ...

Francis James Jameson - Mathematics - 1851 - 144 pages
.../. 4 (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...and one of 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...
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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 centre. 7. Equal straight...
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The first two books of the Elements of Euclid, with additional figures ...

Euclides - 1852 - 152 pages
...and part produced (25). These two Propositions may be omitted at the first reading.] PEOP. XL PROB. To divide a given straight line into two parts, so...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 parts,...
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Scholarship examinations of 1846/47 (-1853/54).

Bengal council of educ - 1852 - 348 pages
...two sides 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...and one of 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...
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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 at the circumference,...
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General Report on Public Instruction in the Bengal Presidency

Education - 1852 - 478 pages
...two sides 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 rectangle contained hy the whole and one of the parts, shall be equal to the square of the other part. Can this be solved...
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The synoptical Euclid; being the first four books of Euclid's Elements of ...

Euclides - 1853 - 146 pages
...of AD, DB, are double of the squares of AC, CD. Wherefore, if a straight line, &c. QED PROP. XI. — PROBLEM. To divide a given straight line into two...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 parts,...
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The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...are double of the squares of AC, CD. Wherefore, if a straight line, etc. QED PROPOSITION XI. PROB. To divide a given straight line into two parts, so...and one of the parts, shall be equal to the square of the other part. Upon AB describe (46. i.) the square ABDC ; bisect (10. i.) AC in E, and join BE...
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The first six books of the Elements of Euclid, with numerous exercises

Euclides - Geometry - 1853 - 176 pages
...С d. Wherefore, if a straight line, &c. QED PROPOSITION XI. — PROBLEM. To divide a given straigM line into two parts, so that the rectangle contained...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 parts,...
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