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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 Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1834
...PROBLEM. — To divide a given straight line into two parts, to that the rectangle contained by the wholc 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, so...
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## The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 513 páginas
...AD, DB are double the squares of AC, CD. Wherefore, " if a straight line," &c. QED PROP. 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. Let AB be the given straight line; it is required to divide it into two parts, so that...
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## The Elements of Euclid: viz. the first six books, together with the eleventh ...

Robert Simson - 1835 - 513 páginas
...CD. Wherefore, " if a straiglit line," &.c. QED PROP. XI. PROB. To divide a given straight line info two parts, so that the rectangle contained by the...one of the parts, shall be equal to the square of the other part. Let AB be the given straight Hue; it is required to divide it into two part", so that...
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## The Element of Geometry

John Playfair - 1836 - 114 páginas
...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...and one of the parts shall be equal to the square of the other part. Upon AB describe (16. 2.) the square ABDC; bisect (8. 1.) AC in E, and join BE ; produce...
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## The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1837 - 390 páginas
...HB, AD are equal. Then c B (II. 9.) HB2 + BD*, or AD2 + BD2= 5-a ' — 2CD2+2AC2.* PROP. XI. PROB. To divide a given straight line into two parts, so...rectangle contained by the whole and one of the parts, may be equal to the square of the other part. Let AB be the given straight line ; it is required to...
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## Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838
...AD, DB are double of the squares of AC, CD. Wherefore, if a straight line, &c. QED PROP. XI. PROS. 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 that...
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## An Elementary Treatise on Algebra, in Theory and Practice: With Attempts to ...

John D. Williams - 1840 - 605 páginas
...required to divide a line of 20 inches in length, into two such parts that the rectangle of the whple and one- of the parts shall be equal to the square of the other. Let one part — x ; then the other will be 20 — x. And by the question 20(20 — х)=з?,...
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## The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - 1841 - 351 páginas
...AD, DB are double of the squares of AC, CD. Wherefore, if a straight line, &c. QED PROP. XI. PROB. 1 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 that...
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## Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842
...are equivalent to double the squares of AC, CD. If therefore a straight line, &c. QED PROP. XI. PROB. To divide a given straight line into two parts, so...contained by the whole, and one of the parts, shall be equivalent to the square of the other part. Let AB be the given straight line : it is required to divide...
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## Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1842 - 317 páginas
...(2a-f*)2+*2=2a2+2(a+i)2, and the proposition is evident from this algebraical equality. PROP. XI. PROB. To divide a given straight line into two parts, so...rectangle contained by the whole, and one of the parts, may be equal to the square of the other part. Let AB be the given straight line ; it is required to...
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