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" ... 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. "
Elements of Geometry - Page 122
by Adrien Marie Legendre - 1825 - 224 pages
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The Popular Educator, Volumes 5-6; Volume 14

Geography - 1867 - 878 pages
...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 unknown quantity, and add it to both tides of the equation. It will be observed that there is nothing peculiar in the...
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The British Encyclopedia, Or Dictionary of Arts and Sciences ..., Volume 1

William Nicholson - Natural history - 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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Elements of Algebra

Silvestre François Lacroix - Algebra - 1818 - 430 pages
...when those of y would be so, they become therefore imaginary in the case under consideration, when q exceeds ^—. It will be perceived then from what...and greater than the square of half the coefficient ofthefirst power of the unknown quantity, thisequation can have only imaginary roots. 115. The expressions...
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American Edition of the British Encyclopedia: Or, Dictionary of ..., Volume 1

William Nicholson - Arts - 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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An Introduction to Algebra: Being the First Part of a Course of Mathematics ...

Jeremiah Day - Algebra - 1820 - 332 pages
...derived the following rule : 305. To COMPLETE THE SQUARE, in an affected quadratic equation ; TAKE THE SQUARE OF HALF THE CO-EFFICIENT OF THE FIRST POWER OF THE UNKNOWN QUANTITY, AND ADD IT TO. BOTH SIDES OF THE EQUATION. Before completing the square, the known and unknown quantities...
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The North American Review, Volume 13

North American review and miscellaneous journal - 1821 - 526 pages
...of the question, the necessity of the roots being imaginary in an equation, of which the known term is negative in the second member, and greater than...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 Algebra

Silvestre François Lacroix - Algebra - 1825 - 276 pages
...would be so, they become therefore imaginary in the case under consideration, when q exceeds—. \ 4 It will be perceived then from what has been said,...quantity, this equation can have only imaginary roots. 1 1 5. The expressions and, in general, those, which involve the square root of a negative quantity,...
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Elements of Algebra

Silvestre François Lacroix - Algebra - 1825 - 276 pages
...when those of y would be so, they become therefore imaginary in the case under consideration, when q exceeds — . It will be perceived then from what has been said, how, and for what reason, tahen the known term of an equation of the second degree is negative in the second member, and greater...
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An Introduction to Algebra: Being the First Part of a Course of Mathematics ...

Jeremiah Day - Algebra - 1827 - 332 pages
...is derived the following rule: 305. To COMPLETE THE SQUARE, in an affected quadratic equation ; TAKE THE SQUARE OF HALF THE CO-EFFICIENT OF THE FIRST POWER OF THE UNKNOWN QUANTITY, AND ADD IT TO BOTH SIDES OF THE EQUATION. Before completing the square, the known and unknown quantities...
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Elements of Algebra, Volume 1

Silvestre François Lacroix - Algebra - 1831 - 298 pages
...would be so, they become therfore imaginary in the case under consideration, p2 when q exceeds j-. It will be perceived then from what has been said,...greater than the square of half the coefficient of the jirst power of the unknown quantity, this equation can have only imaginary roots. 115. The expressions...
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