System-of-equations meaning

= wj, aa 1 aa 2 a a 3 the complete system of equations satisfied by an invariant.

This system of equations must involve the three conditions of equilibrium of the extraneous forces which are already identically satisfied, by hypothesis; there remain therefore 2n ~ independent relations to determine the 2n3 unknown stresses.

arid if this be denoted by o~1~ we have a second system of equations similar to (23).

If, however, the point (x', y', z') is situate on the curve u'=o, then one point of the system of points in question is situate on the curve u = o, that is, to a given point of the curve u' = o there corresponds a single point of the curve u =o; and hence also this point must be given by a system of equations such as x: y : z =X': Y': Z'.

It will be observed that the equations x': y' :z = X: Y: Z before mentioned do not of themselves lead to the other system of equations x: y : z= X': Y': Z', and thus that the theory does not in anywise establish a (r, I) correspondence between the points (x, y, z) and (x', y', z) of two planes or of the same plane; this is the correspondence of Cremona's theory.