This definition is a form of the modern theorem that if r is a double root of ƒ(x) = 0, then r is a root of ƒ '(x) = 0.
2. If for x = a the polynomial
takes on a relative maximum or minimumvalue, then a is a root of the equation
This definition is a modification of Fermat's theorem in the form that if ƒ(a) is a relative maximum or minimum value of a polynomial ƒ(x), then ƒ '(a) = 0, where ƒ ' is the derivative of ƒ.
Hudde was working with Frans van Schooten on a Latin edition of La Géométrie of René Descartes. In the 1659 edition of the translation, Hudde contributed two letters: "Epistola prima de Redvctione Ǣqvationvm" (pages 406 to 506), and "Epistola secvnda de Maximus et Minimus" (pages 507 to 16). These letters may be read by the Internet Archive link below.
hudde, rules, mathematics, properties, polynomial, roots, described, johann, hudde, double, root, polynomial, equation, displaystyle, cdots, displaystyle, dots, numbers, arithmetic, progression, then, also, root, displaystyle, cdots, this, definition, form, mo. In mathematics Hudde s rules are two properties of polynomial roots described by Johann Hudde 1 If r is a double root of the polynomial equation a 0 x n a 1 x n 1 a n 1 x a n 0 displaystyle a 0 x n a 1 x n 1 cdots a n 1 x a n 0 dd and if b 0 b 1 b n 1 b n displaystyle b 0 b 1 dots b n 1 b n are numbers in arithmetic progression then r is also a root ofa 0 b 0 x n a 1 b 1 x n 1 a n 1 b n 1 x a n b n 0 displaystyle a 0 b 0 x n a 1 b 1 x n 1 cdots a n 1 b n 1 x a n b n 0 dd This definition is a form of the modern theorem that if r is a double root of ƒ x 0 then r is a root of ƒ x 0 2 If for x a the polynomial a 0 x n a 1 x n 1 a n 1 x a n displaystyle a 0 x n a 1 x n 1 cdots a n 1 x a n dd takes on a relative maximum or minimum value then a is a root of the equationn a 0 x n n 1 a 1 x n 1 2 a n 2 x 2 a n 1 x 0 displaystyle na 0 x n n 1 a 1 x n 1 cdots 2a n 2 x 2 a n 1 x 0 dd This definition is a modification of Fermat s theorem in the form that if ƒ a is a relative maximum or minimum value of a polynomial ƒ x then ƒ a 0 where ƒ is the derivative of ƒ Hudde was working with Frans van Schooten on a Latin edition of La Geometrie of Rene Descartes In the 1659 edition of the translation Hudde contributed two letters Epistola prima de Redvctione Ǣqvationvm pages 406 to 506 and Epistola secvnda de Maximus et Minimus pages 507 to 16 These letters may be read by the Internet Archive link below References EditCarl B Boyer 1991 A History of Mathematics 2nd edition page 373 John Wiley amp Sons Robert Raymond Buss 1979 Newton s use of Hudde s Rule in his Development of the Calculus Ph D Thesis Saint Louis University ProQuest 302919262 Rene Descartes 1659 La Geometria 2nd edition via Internet Archive Kirsti Pedersen 1980 5 Descartes s method of determining the normal and Hudde s rule chapter 2 Techniques of the calculus 1630 1660 pages 16 19 in From the Calculus to Set Theory edited by Ivor Grattan Guinness Duckworth Overlook ISBN 0 7156 1295 6 Retrieved from https en wikipedia org w index php title Hudde 27s rules amp oldid 955972114, wikipedia, wiki, book, books, library,
