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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. "
The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... - Pągina 54
per Robert Simson - 1762 - 466 pągines
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The Principles of the Solution of the Senate-house 'riders,' Exemplified by ...

Francis James Jameson - 1851 - 144 pągines
...4BC2 + AB2 + AC2, = 4BC2 + BC2, - 5BC8. 1849. (A). 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. (ii. 11.) (B). Shew that in Euclid's figure, four other...
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Papers for the schoolmaster, Volums 1-6

582 pągines
...Book 1 and state what ease is omitted. SECTION IT. 1. 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. 2. If a straight line be divided into any two parts,...
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University of Durham

University of Durham - 1851 - 222 pągines
...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...
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A Collection of Problems and Examples Adapted to the "Elementary Course of ...

Harvey Goodwin - 1851 - 196 pągines
...equations, or any demonstration other than Euclid's ? 3. 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. Shew that in Euclid's figure four other lines, beside...
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The first two books of the Elements of Euclid, with additional figures ...

Euclides - 1852 - 152 pągines
...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 the whole, and one of the parts, shall be equal to the square of the other part. Upon AB describe* the square ABDC; • x hi. i. bisect*...
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Scholarship examinations of 1846/47 (-1853/54).

Bengal council of educ - 1852 - 348 pągines
...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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Five Years in an English University, Volum 2

Charles Astor Bristed - 1852 - 470 pągines
...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...
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The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich - 1853 - 400 pągines
...a straight line, etc. QED PROPOSITION XI. PROB. 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. Upon AB describe (46. i.) the square ABDC ; bisect...
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The synoptical Euclid; being the first four books of Euclid's Elements of ...

Euclides - 1853 - 146 pągines
...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 the whole and one of the parts, shall be equal to the square of the other part. Upon AB describe (1. 46.) the square ABDC ; bisect...
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The first six books of the Elements of Euclid, with numerous exercises

Euclides - 1853 - 178 pągines
...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 the whole and one of the parts shall be equal to the square of the other part. Upon ab describe (i. 46) the square abdС; bisect (i....
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