Search Images Maps Play YouTube News Gmail Drive More »
Sign in
Books Books
" ... preceding equation is only of the fourth power or degree ; but it is manifest that the above remark applies to equations of higher or lower dimensions : viz. that in general an equation of any degree whatever has as many roots as there are units in... "
A Course of Mathematics for the Use of Academies, as Well as Private Tuition - Page 258
by Charles Hutton - 1822
Full view - About this book

The Elements of Mathematical Analysis, Abridged: For the Use of Students ...

Nicolas Vilant - 1798 - 196 pages
...all degrees to be produced by a multiplication of binomial factors. Every affefted equation will have as many roots as there are units in the exponent of the higheft power of the variable quantity ; and, if the terms of the equation are alternately affirmative...
Full view - About this book

A Course of Mathematics: For the Use of Academies as Well as ..., Volume 2

Charles Hutton - 1812 - 624 pages
...instead of x+ the aggregate of the terms of the equation vanishes by the opposition of the signs + and — . The preceding equation is only of the fourth...exponent of the highest power of the unknown quantity, und that each root has the properly of rendering, by its substitution in place of the unknown quantity,...
Full view - About this book

Encyclopaedia Britannica; Or A Dictionary of Arts, Sciences, and ..., Volume 13

1823 - 876 pages
...degree may be considered as proekiced by the multiplication of аз many simple equations ns there arc units in the exponent of the highest power of the unknown quantity. From this he deduced the relation which exists bctw en the roots of an equation, and the coefficients...
Full view - About this book

A Course of Mathematics for the Use of Academies: As Well as ..., Volume 2

Charles Hutton - 1826 - 682 pages
...instead of r, the aggregate of the terms of the equation vanishes by the opposition of the signs + and — . The preceding equation is only of the fourth...of the highest power of the unknown quantity, and thnt each root h;is the property of rendering, by its substitution in place of the unknown quantity,...
Full view - About this book

A Course of Mathematics: For the Use of Academies as Well as ..., Volume 2

Charles Hutton - 1831 - 662 pages
...aggregate of the terms of the equation vanishes, by the opposition of the signs + and — . ' 1 he preceding equation is only of the fourth power or...quantity, the aggregate of all the terms of the equation equul to nothing. It must be observed that we cannot have all at once x = a, x = b, x = c, &c. for...
Full view - About this book

A Course of Mathematics: For the Use of Academies as Well as ..., Volume 2

Charles Hutton - 1831 - 656 pages
...is only of the fourth power or degree ; but it is manifest that the above remark applies i<equations of higher or lower dimensions : viz. that in general...rendering, by its substitution in place of the unknown quantify, the aggregate of all Ihe terms of the equation equal to nothing. It must be observed that...
Full view - About this book

Elements of Algebra: Tr. from the French of M. Bourdon. Revised and Adapted ...

Charles Davies - 1835 - 378 pages
...law should be remembered. Second Property. 264. Every equation involving but one unknown quantity, has as many roots as there are units in the exponent of its degree, and no more. Let the proposed equation be if+Par-i+Q«" 3+ • • . +Tx+\J=0. Since every...
Full view - About this book

Elements of Algebra

1838 - 372 pages
...law should be remembered. Second Property. 281. Every equation involving but one unknown quantity, has as many roots as there are units in the exponent of its degree, and no more. Let the proposed equation be xn+Pxm~l+Q.xm-2+ . . . +Ta;+U=0. Since every...
Full view - About this book

The Analysis and Solution of Cubic and Biquadratic Equations: Forming a ...

John Radford Young - 1842 - 276 pages
...all arranged on one side, the polynomial we thus get is composed of as many simple binomial factors as there are units in the exponent of the highest power of the unknown quantity. The discovery of these factors would he the discovery of the roots of the equation, since these are...
Full view - About this book

An Elementary Treatise on Algebra: Designed to Facilitate the Comprehension ...

Ormsby MacKnight Mitchel - 1845 - 308 pages
...on of the divisors of all degrees. 234. As an exemplification of the principle, that every equation has as many roots as there are units in the exponent of the highest power of the unknown quantity, we propose to examine the equation xm—! =0. Let us commence by making m=2, and we have x2 — 1=0By...
Full view - About this book




  1. My library
  2. Help
  3. Advanced Book Search
  4. Download EPUB
  5. Download PDF