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If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.
The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... - Side 53
av Euclid, Robert Simson - 1821 - 516 sider
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## The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1845 - 352 sider
...bisected, the rectangle of the parts is equal to the square of one of them. PROP. V. THEOR. — If a straight line be divided into two equal parts, and...section, is equal to the square of half the line. Let the straight line AB be bisected in C, and divided unequally in D : the rectangle AD.DB, together...
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## Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845
...the parallelograms about the diameter of a square are likewise squares. PROPOSITION V. THEOREM. If a straight line be divided into two equal parts, and also into Iwo unequal parts ; the rectangle contained by the unequal parts, together with the square of the line...
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## A system of practical mathematics; being no.xvi. of a new series of school-books

...be bisected in C, and divided unequally in D, 1 the rectangle AD-DB. together with the square on CD, the line between the points of section is equal to the square on (AC or CB) half the line. For AB2=AD-' + DB-+2AD-DB, (Prop. 37), but AB"=4AC2, (Prop. 37, Cor. 2),...
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## The Elements of Geometry, Symbolically Arranged

...a and b, the proposition algebraically expressed is (a+by=a8+2ab+b8. PROP. XLIV. THEOR. 5. 2 Eu. If a straight line be divided into two equal parts, and...points of section, is equal to the square of half the whole line. Let the str. line AB be divided into two equal parts at the pt. C, and into two unequal...
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## The Elements of Geometry, Symbolically Arranged

...the proposition algebraically expressed is (a+b)*—a*-\-2ab + b*. PROP. XLIV. THEOR. 5 . 2 EU. If a straight line be divided into two equal parts, and...points of section, is equal to the square of half the whole line. Let the str. line AB be divided into two equal parts at the pt. C, and into two unequal...
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## The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846
...parallelograms about the diameter of a square are likewise squares. PROP. V. THEOR. If a straight Kne be divided into two equal parts, and also into two...section, is equal to the square of half the line. Let the straight line ATI be divided into two equal parts at the point C, and into two unequal parts...
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## Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1846 - 317 sider
...PROP. V. THEOR. If a straight line le dividedinto two equal parts, and also into two unequalparts ; the rectangle contained by the unequal parts, together...section, is equal to the square of half the line. Let the straight line AB be divided into two equal parts in the point C, and into two unequal parts...
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## The Mechanics' Magazine, Museum, Register, Journal, and Gazette, Volum 44

1846
...dependent on the 5th Proposition of the 2nd Book of Euclid's Elements, where it is demonstrated, that if a line be divided into two equal parts, and also into two unequal parts, the square of half the line is greater than the rectangle of the two unequal parts. Almost the whole of...
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## Iron: An Illustrated Weekly Journal for Iron and Steel ..., Volum 44

Perry Fairfax Nursey - 1846
...dependent on the 5th Proposition of the 2nd Book of Euclid's Elements, where it is demonstrated, that if a line be divided into two equal parts, and also into two unequal parts, the square of half the line is greater than the rectangle of the two unequal parts. Almost the whole of...
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## Arithmetic, in Two Parts

Frederic A. Adams - 1846 - 212 sider
...what are the numbers ? The theorem on which the solution of this question depends is this, If a number be divided into two equal parts, and also into two unequal parts, the product of the two equal parts, that is, the square of half the number, will equal the product of the...
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