By H. F. Baker

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**Additional resources for An Introduction To The Theory Of Multiply Periodic Functions**

**Example text**

T be homogeneous coordinates, and P =t Q = xQ + yQ + zQ + P = 0, the equation varying parameters six common points, x, y, z, 4 represents a system of quadric surfaces having ,/*-{/* /l P= intersected will 3 namely those where the cubic space curve by the quadric of the cubic curve in which 6 is 2 l for be a cone of vertex (f , rj, 4 is ; these are T/* (0, 0, 0, 1) one of the roots of f(6) and the five points Q = 0. The quadric Q T) if the four equations dQ/dj; = 0, SQ/drj = 0, 40 Geometrical note.

Ft>21<2> **) 6 4 we are real, PI, Pi, 1\, ^2 \ tn t /e = have, since T, w) (a)', W/ /&J \ t,,t = &)o> ') (a>'w W = (**

2 regard to M, and 2 ; the The quadruply periodic 38 as we [CHAP. y) = 4\ , (3fl5, Thus we have and these, together with the fact that a;,, x^ are the roots of the equation give the solution of the inversion problem expressed by the equations U It can two places X>, 1, -). U] *t, O, ^ Ui> ^Jr,. , (M), fm (u), that these functions are in the ratios of the minors of the elements of any row of this vanishing ART. 11] or Abelian Functions. ,,, p-mpwi, are all rational integral polynomials of the third degree in jfe, pa p,, in particular , >-,- - X, - \ 3 ; ,2 - x^-"-[F(x ara l ) 2y,y2], or 4p u thus it is easy the minor of the element X in the first row one-quarter and column of the determinant above thus we have, for arbitrary values of at once found to be is to see that j^ (a:, , ; is ; X AX, 2(2),, -2p 2^ 2 - 20,,, i 2 ls ^ 0^ ?