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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, the parts read in the University of Cambridge [book ... - Página 62
por Euclides - 1846
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## Ars Quatuor Coronatorum: Being the Transactions of the Quatuor ..., Volumen3

1840 - 288 páginas
...fancies about numbers. All even numbers (except the duad — two — which is simply two unities) may be divided into two equal parts, and also into two unequal parts But the ODD number is only divisible into uneven parts, &c. The Antients also remarked the monad to...
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## The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - 1841 - 378 páginas
...parallelograms about the diameter of a square are likewise squares. PROP. V. THEOR. If a straight fine be divided into two equal parts, and also into two...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 at the point D; the rectangle...
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## Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1842 - 332 páginas
...which this line is divided be denoted by a and b; then, (a-\-b)2 PROP. V. THEOR. If a straight line lie divided into two equal parts, and also into two unequal...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 in the point D ; the...
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## Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842 - 316 páginas
...parallelograms about the diameter of a square are likewise squares. PROP. V. THEOR. IF a straight line be divided into two equal parts, and also into two...square of the line between the points of section, is equivalent to the square of half the line. Let the straight line AB be divided into two equal parts...
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## The British Annals of Education for ...: Being The Scholastic ..., Volúmenes1-2

1844 - 688 páginas
...between the same parallels, the parallelogram shall be double of the triangle. 6. If a straight line be divided into two equal parts, and also into two...section, is equal to the square of half the line. 7. In obtuse angled-triangles, if a perpendicular be drawn from either of the acute angles to the opposite...
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## The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1845 - 382 páginas
...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 also into two...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 with the square of...
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## Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845 - 546 páginas
...= a2 — ma, to each of these equals add m* ; .-. (a + m) (a — m) + m' = a'. That is, if a number be divided into two equal parts, and also into two unequal parts, the product of the unequal parts and the square of half their difference, is equal to the square of half...
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## A system of practical mathematics; being no.xvi. of a new series of school-books

Scottish school-book assoc - 1845 - 444 páginas
...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

Great Britain. Admiralty - 1846 - 128 páginas
...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 also into two...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

Great Britain. Admiralty - 1846 - 128 páginas
...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 also into two...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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