ISBN: 1230100261

[EAN: 9781230100265], Neubuch, [PU: RareBooksClub.com], ROYAL SOCIETY OF EDINBURGH,SUBJECTS, This item is printed on demand. Paperback. 48 pages. Dimensions: 9.7in. x 7.4in. x 0.1in.This … More...

[EAN: 9781230100265], Neubuch, [PU: RareBooksClub.com], ROYAL SOCIETY OF EDINBURGH,SUBJECTS, This item is printed on demand. Paperback. 48 pages. Dimensions: 9.7in. x 7.4in. x 0.1in.This historic book may have numerous typos and missing text. Purchasers can usually download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1897 edition. Excerpt: . . . bz! cxp--pi Q (29). When the Equation (15) has an Envelope Singular Solution its Integral is a Family of Algebraic Curves (Parabola: ). If we put x2, vs dyjd, (29) becomes ay(b2cmAvjz)i0 If we solve for rs and put y t, we get The general existence of the cusp-locus of the integral family of a differential equation of the first order was indicated as early as 1851 by De Morgan Gamb. Phil. Trans. , vol. ix. pt. 2, p. 113). The earliest absolutely explicit statement of the theorem seems to have been made by Darbodx (GvnvpUs Eendus, t. lxx. p. 1331; also t. lxxi. p. 267, 1870). In an extremely interesting paper in the Bulletin des Sciences Mathematiques, and c, t. iv. , 1873, p. 158, Darboux establishes most of the propositions above given. It is surprising that Darbodxs work does not seem to have attracted the notice of Cayley. Reference may also be made to Clebsch, Mathematische Annalen, Bd. vi. p. 211, 1873; and to Clebschs theory of Connexes, Vorlesungen vher Geometric, Bd. i. p. 1014 el seqq. We have thought it worth while to deduce these results throughout by the approximative method first employed by Briot and Bouquet, because this method is a general one, applicable to the discrimination of special cases, such as arise when an envelope is also a cusp-locus or a tac-locus, and c; and because this method is little used by English mathematicians. Now, by (12), since (15) has a singular solution we must have acc--4bQ. or (f)V-XX-M)A (36), where u T Jc--46-4aya. Since 0, it is obvious that the necessary and sufficient condition that (3G) be algebraic is that fi be a perfect square, that is, that ( 2c)2--166 be a perfect square. It is assumed, of course, that a, b, . . . This item ships from La Vergne,TN.<

2013, ISBN: 9781230100265

Rarebooksclub.com, Taschenbuch, 48 Seiten, Publiziert: 2013-09-13T00:00:01Z, Produktgruppe: Buch, 0.23 kg, Kategorien, Bücher, Rarebooksclub.com, 2013