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Bøker Bok 3140 av 194If a straight line be divided into two equal parts, and also into two unequal parts;...
" 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. "
Elements of Geometry: Containing the First Six Books of Euclid : with a ... - Side 56
av John Playfair - 1832 - 333 sider
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Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842
...a square are likewise squares. PROP. V. THEOR. IF a straight line be divided into two equal parts, and also into two unequal parts, the rectangle contained...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 ..., Volum 1

1844
...parallelogram shall be double of the triangle. 6. If a straight line be divided into two equal parts, and also into two unequal parts ; the rectangle contained...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 ...

James Thomson - 1845 - 358 sider
...the square of one of them. PROP. V. THEOR. — If a straight line be divided into two equal parts, and also into two unequal parts ; the rectangle contained...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 CD, is...
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Robert Potts - 1845
...double of the square of half the line, and of the square of the line between the points of section. Let the straight line AB be divided into two equal...the point C, and into two unequal parts in the point J). Then the squares of AD, DB together, shall be double of the squares of AC, CD. CD B From the point...
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A system of practical mathematics; being no.xvi. of a new series of school-books

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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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...into two unequal parts in the point D ; the rectangle AD.DB, together with the square of CD, is equal to the square of CB, or AD.DB+CD2= _CB2. Upon CB describe...
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The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846
...of a square are likewise squares. PROP. V. THEOR. If a straight Kne be divided into two equal parts, and also into two unequal parts, the rectangle contained...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 at the point D : the...
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The Elements of Geometry, Symbolically Arranged

1846
...(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 unequal parts, the rectangle contained...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

1846
...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 unequal parts, the rectangle contained...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 definitions, postulates, axioms, and enunciations of the propositions of ...

Euclides - 1848
...square are likewise squares. PROP. V. THEOREM. If a straight line be divided into two equal parts, and also into two unequal parts ; the rectangle contained...section, is equal to the square of half the line. EUCLID S ELEMENTS. PROP. VI. THEOREM. If a straight line be bisected, and produced to any point ; the...
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