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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 English Journal of Education - Page 272
1851
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Ars Quatuor Coronatorum: Being the Transactions of the Quatuor ..., Volume 3

1840
...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 - 351 pages
...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...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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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1842 - 317 pages
...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...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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Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842
...manifest that the parallelograms about the diameter of a square are likewise squares. PROP. V. THEOR. IF a straight line be divided into two equal parts,...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 ..., Volumes 1-2

1844
...the same base, and between the same parallels, the parallelogram shall be double of the triangle. 6. If a straight line be divided into two equal parts,...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 - 352 pages
...being 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,...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
...that 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

Scottish school-book assoc - 1845
...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
...b, 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,...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
...be 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,...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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