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" IF a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts. "
The Elements of Euclid; viz. the first six books, together with the eleventh ... - Página 43
por Euclides - 1814
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Report of twenty-one years' experience of the Dick bequest for elevating the ...

Allan Menzies - 1854
...Euclid's general reasoning, and point out the part of your demonstration in which it is evaded. 3. If a straight line be divided into any two parts,...together with twice the rectangle contained by the parts. A modification of what you have here proved constitutes the rule for the extraction of the square root....
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Annual Report of the Normal, Model, and Common Schools in Upper Canada for ...

Upper Canada. Chief Superintendent of Schools - 1854
...required in the demonstrations of the 7th, 27th, 32nd and 48th prop, of the 1st book of Euclid. . 3. If a straight line be divided into any two parts,...the squares of the two parts, together with twice their rectangle. 4. If a straight line be divided into two equal and also into two unequal parts ;...
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Elements of geometry and mensuration

Thomas Lund - 1854 - 192 páginas
...to each, to which the equal sides are opposite, .-. / ACS = / BCD = a right angle. 44. PROP. XXII. If a straight line be divided into any two parts, the square of the whole line is equal to the sum of the squares of the two parts together with twice the rectangle* contained by the parts. QDEF....
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Orr's Circle of the Sciences: The mathematical sciences

William Somerville Orr - 1854
...THEOREM. If a straight line (AB) be divided into any two parts (А С, С В) the square of the wlak line is equal to the squares of the two parts, together with twice the rectangle contained by the parts : that is, А В1 = А С* + С Вг + twice А ОС В. * 46 I. Upon А В describe the square AE...
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Elements of Geometry, Plane and Spherical Trigonometry and Conic Sections

Horatio Nelson Robinson - 1854 - 335 páginas
...other demonstration than an explanation of exactly what is meant by the words of the text. THEOREM 33. If a straight line be divided into any two parts, the square of th« whole line is equal to the sum of the squares of the two parts, and twice the rectangle contained...
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1855
...one of the parts of the divided straight line, their rectangle becomes a square. PROP. IV. THEOREM. If a straight line be divided into any two parts,...the straig-ht line AB be divided into any two parts at С. square of AB is equal to the squares of A С and С B, together with twice the rectangle AС.СB....
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National Society's Monthly Paper

1855
...line drawn through the middle points of two sides of a triangle will be parallel to the third side' 5. If a straight line be divided into any two parts,...together with twice the rectangle contained by the parts. 6. In every triangle, the square of the side suhtending either of the acute angles is less than the...
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Minutes of the Committee of Council on Education

Great Britain. Committee on Education - 1855
...equal to a given triangle, and have one of its angles equal to a given rectilineal angle. Section 2. 1. If a straight line be divided into any two parts,...together with twice the rectangle contained by the two parts. 2. If a straight line be divided into two equal and also into two unequal parts ; the squares...
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The Popular Educator, Volumen6

1855
...than in ordinary language. The proposition, (Euclid 4, 2,) that when a straight line is divided into two parts, the square of the whole line is equal to...squares of the two parts, together with twice the product of the parts, is demonstrated, by squaring a binomial. Let the side of a square be represented...
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Elements of Geometry: Containing the First Six Books of Euclid with a ...

John Playfair - 1855 - 318 páginas
...therefore, multiplying both members of this equality by c, we shall have oc^ic+c 2 . PROP. IV. THEOR. If a straight line be divided into any two parts, the square of the whole line ts equal to the squares of the two parts, together with twicetke rectangle contained by tin- parts....
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