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" In the same manner, it may be proved, that the last term of the square of any binomial quantity, is equal to the square of half the co-elficient of the root of the first term. "
An Introduction to Algebra: Being the First Part of a Course of Mathematics ... - Página 137
por Jeremiah Day - 1827 - 332 páginas
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The Popular Educator, Volúmenes5-6;Volumen14

1867
...term of the square of any binomial quantity is equal to the square of half the co-efficient of tho root of the first term. From this principle is derived the following METHOD FOB COMPLETING THE SQUARE. Take the square of half the co-efficient of the first power of the...
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The British Encyclopedia, Or Dictionary of Arts and Sciences ..., Volumen1

William Nicholson - 1809
...all the terms, that the equation may be reduced to this farm, x* ^ px = i J. Then add to both sides the square of half the co-efficient of the first power of the unkwown quantity, by which means the first side of the equation is made a complete square, and the...
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An Introduction to Algebra: Being the First Part of a Course of Mathematics ...

Jeremiah Day - 1814 - 303 páginas
...the last termof the square of any binomial quantity, is equal to th& square of half the co-efficient of the root of the first term. From this principle,...square of half the co-efficient of the first power if the unknown quantity, and add it to both sides of the equation. Before completing the square, the...
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American Edition of the British Encyclopedia: Or, Dictionary of ..., Volumen1

William Nicholson - 1819
...all the terms, that the equation may be reduced to this form, x' ±px = ± g. Then add to both sides the square of half the co-efficient of the first power of the unknown quantity, by which means the first side 6f the equation is made a complete square, and the other consists of...
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The North American Review, Volumen13

1821
...imaginary in an equation, of which the known term is negative in the second member, and greater than the square of half the coefficient of the first power of the unknown quantity, he gives a striking specimen of his way of investigating ' analytical facts,' and displaying the spirit...
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Elements of Geometry

Adrien Marie Legendre - 1825 - 224 páginas
...the known term of an equation of the second degree is negative in the second member, and greater than the square of half the coefficient of the first power of the unknown quantity, this equation can have only imaginary roots. 115. The expressions > V'"^, a + \s~-bi and, in general,...
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Elements of Algebra

Silvestre François Lacroix - 1825 - 276 páginas
...the known term of an equation of the second degree is negative in the second member, and greater than the square of half the coefficient, of the first power of the unknown quantity, this equation can have only imaginary roots. 1 1 5. The expressions v/"^6, a + <S~—i>, and, in general,...
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An Introduction to Algebra: Being the First Part of a Course of Mathematics ...

Jeremiah Day - 1831 - 332 páginas
...the last term of the square of any binomial quantity, is equal to the square of half the co-efficient of the root of the first term. From this principle is derived the following rale: 305. To COMPLETE THE SQUARE in an affected quadratic equation: TAKE THE SQUARE OF HALF THE CO-EFFICIENT...
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An Introduction to Algebra: Being the First Part of a Course of Mathematics ...

Jeremiah Day - 1832 - 332 páginas
...the last term of the square of any binomial quantity, is equal to the square of half the co-efficient of the root of the first term. From this principle...equation: TAKE THE SQUARE OF HALF THE CO-EFFICIENT OP THE FIRST POWER OF THE UNKNOWN QUANTITY, AND ADD IT TO BOTH SIDES OF THE EQUATION. Before completing...
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An Introduction to Algebra: Being the First Part of a Course of Mathematics ...

Jeremiah Day - 1832 - 332 páginas
...the last term of the square of any binomial quantity, is equal to the square of half the co-efficient of the root of the first term. From this principle is derived the following rule : J 305. To COMPLETE THE SQUARE in an affected quadratic equation : TAKE THE SQUARE OF HALF THE CO-EFFICIENT...
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