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" If a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided... "
The figures of Euclid with the enunciations, as printed in Euclid's Elements ... - Page 26
by Euclides - 1840
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1844 - 338 pages
...then, AD=2a+6, and CD=a+6. Now by multiplication, PROP. VII. THEOR. If a straight line be divided into two parts, the squares of the whole line, and of one...equal to twice the rectangle contained by the whole and that part, together with the square of the other part. two parts in the point C ; the squares of...
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The elements of algebra

James Wood - Algebra - 1845 - 442 pages
...following Examples will sufficiently illustrate the preceding Theory, for our present purpose: — Ex. !.. If a straight line be divided into any two parts,...equal to twice the rectangle contained by the whole and that part, together with the square of the other part. (EUCLID, Book n. Prop. 7-) Let a and b represent...
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Report of the Committee of Council on Education (England and Wales ..., Volume 2

Great Britain. Council on Education - 1845 - 696 pages
...described upon the other two sides of it, the angle contained by these two sides is a right angle. 61. If a straight line be divided into any two parts,...equal to twice the rectangle contained by the whole and that part, together with the square of the other part. 62. To divide a given straight line into...
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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1845 - 382 pages
...with the square of CB, is equal to the square of CD : which was to be proved. PROP. VII. THEOB. — If a straight line be divided into any two parts,...equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into...
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Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - Geometry - 1845 - 218 pages
...line, &c. QED PROPOSITION VII. THEOR. — If a straight line be divided into any two parts, the iquares of the whole line, and of one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into...
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The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846 - 292 pages
...together with the square of CB, is equal to the square of CD. Wherefore, If a straight line %c. QED PROP. VII. THEOR. If a straight line be divided into...equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into...
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The Elements of Geometry, Symbolically Arranged

Great Britain. Admiralty - Geometry - 1846 - 128 pages
...b, the proposition algebraically expressed is (2a+b)b+a i =(a+b) s . PROP. XLVI. THEOR. 7 . 2 Eu . If a straight line be divided into any two parts,...equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the str. line AB be divided into any...
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The Elements of Geometry, Symbolically Arranged

Great Britain. Admiralty - Geometry - 1846 - 128 pages
...produced b, the proposition algebraically expressed is (2a+b)b+a8=(a+b)8. PROP. XLVI. THEOR. 7 . 2 Eu . If a straight line be divided into any two parts,...equal to twice the rectangle contained by the whole and that part, together with the square of the other part. Let the str. line AB be divided into any...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - Euclid's Elements - 1846 - 334 pages
...equality, we shall have, .-. i(2a+6)+o2=(a+i)2. PROP. VII. THEOR. •• If a straight line be divided into two parts, the squares of the whole line, and of one...equal to twice the rectangle contained by the whole and that part, together with the square of the other part. L et the straight line AB be divided into...
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The definitions, postulates, axioms, and enunciations of the propositions of ...

Euclides - 1848 - 52 pages
...square of the straight line which is made up of the half and the part produced. PROP. VII. THEOREM. If a straight line be divided into any two parts,...equal to twice the rectangle contained by the whole and that part, together with the square of the other part. PROP. VIII. THEOREM. If a straight line...
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