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" Which proves that the square of a number composed of tens and units contains, the square of the tens plus twice the product of the tens by the units, plus the square of the units. "
A Treatise on Algebra - Page 139
by Elias Loomis - 1873 - 360 pages
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Elements of Algebra

Silvestre François Lacroix - Algebra - 1818 - 422 pages
...tens plus the unite, or 2 a + b ; this multiplied by 7 or 6, reproduces 609 = 2 ab + 62, or double the product of the tens by the units, plus the square of the units. This being subtracted leaves no remainder, and the operation shows, that 47 is the square root of 2209....
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Elements of Geometry

Adrien Marie Legendre - Geometry - 1819 - 574 pages
...the tens plus the units, or 2 a + b ; this multiplied by 7 or b, reproduces 609 = 2a6 + 6s, or double the product of the tens by the units, plus the square of the units. This being subtracted leaves no remainder, and the operation •hows, that 47 is the square root of...
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A Theoretical and Practical Arithmetic: In which the Principles of that ...

Bézout - Arithmetic - 1825 - 258 pages
...add these products, and we have, for the square, the number 2916, which, as we see, is composed of the square of the tens, plus twice the product of...the tens by the units, plus the square of the units of the number 54. 134. What we have, observed being an immediate consequence of the rules of multiplication,...
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Elements of Algebra

William Smyth - Algebra - 1830 - 278 pages
...62=2209. Thus the square of a number, consisting of units and tens, is composed of three parts, viz. the square of the tens, plus twice the product of the tens multiplied by the units, plus the square of the units. Thus in 2209, the square of 47, we have The...
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The Youth's Assistant in Theorhetic [sic] and Practical Arithmetic: Designed ...

Zadock Thompson - Arithmetic - 1832 - 186 pages
...appears that the square of a number consisting of tens and units is made up of the square of the units, plus twice the product of the tens, by the units, plus the square of the tens. See this exhibited in figure F. As 10X 10=100, the square of the tens cau never make a part of...
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The Youth's Assistant in Theoretic and Practical Arithmetic: Designed for ...

Zadock Thompson - Arithmetic - 1832 - 186 pages
...appears that the square of a number consisting of tens and units is made up of the square of the units, plus twice the product of the tens, by the units, plus the square of the tens. See this exhibited in figure F. As 10X 10=100, the square of the tens can never make a part of...
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Elements of Algebra: Tr. from the French of M. Bourdon. Revised and Adapted ...

Charles Davies - Algebra - 1835 - 378 pages
...64 and (a+i)3= (64)3 Which proves that the square of a number composed of tens and units contains, the square of the tens plus twice the product of the tens by the units, plus the square of the units. 117. If now, we make the units 1, 2, 3, 4, &c., tens, by annexing to each figure a cipher, we shall...
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A New Introduction to the Science of Algebra ...

Silas Totten - Algebra - 1836 - 320 pages
...the units, we shall have, for the square of a + b, a3 + 2ab + b ; that is, the square of the tens, twice the product of the tens by the units, plus the square of the units. Let a = 8, and 6 = 5: then, since a represents the tens, and b the units, a + b becomes 80 + 5 = 85...
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Elements of Algebra

Algebra - 1838 - 372 pages
.... . aa+2a*+i3 =4096. Which proves that the square of a number composed of tens and units contains, the square of the tens plus twice the product of the tens by the units, plus the square of the units. 117. If now, we make the units 1, 2, 3, 4, &c., tens, by annexing to each figure a cipher, we shall...
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First Lessons in Algebra: Embracing the Elements of the Science

Charles Davies - Algebra - 1839 - 272 pages
...shall have a+b =64, and Which proves that the square of a number composed of tens and units, contains the square of the tens plus twice the product of the tens by the units, plus the square of the units. 94. If, now, we make the units 1,2, 3, 4, &c, tens, or units of the second order, by annexing to each...
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