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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, shall be equal to the square of the other part. "
A companion to Euclid: being a help to the understanding and remembering of ... - Página 45
por Euclides - 1837 - 88 páginas
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THE PRINCIPLES OF THE SOLUTION OF SENATE-HOUSE 'RIDERS'

FRANCIS J. JAMESON - 1851
.../. 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 line,...
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A Collection of Problems and Examples Adapted to the "Elementary Course of ...

Harvey Goodwin - 1851 - 173 páginas
...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 in...
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Papers for the schoolmaster, Volúmenes1-6

...every respect." Enumerate tlie cases proved in Book 1 and state what ease is omitted. SECTION IT. 1. Divide a given straight line into two parts, so that...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, the square of the whole line is...
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University of Durham

University of Durham - 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 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
...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...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, so...
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Scholarship examinations of 1846/47 (-1853/54).

Bengal council of educ - 1852
...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...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 the...
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Five Years in an English University, Volumen2

Charles Astor Bristed - 1852
...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

1852
...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
...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...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, so...
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The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich - 1853
...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...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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