The axioms of descriptive geometry, by A.N. Whitehead.

60 GENERAL FORM FOR INFINITESIMAL ROTATIONS

[CH. VI

Hence remembering that wc, o2, (3 are arbitrary parameters, we find
that any infinitesimal rotation round an axis through the origin can be
expressed in the form
dx dy dz
7t= - _ Y + 7.A - = - W2 +, -..y(6).
dt=-y+o2z, dt ' " dt o (6).
The latent line of the rotation is given by
x/W1 = yl/2 = zl/.
Thus this form gives one and only one infinitesimal rotation round any
line through the origin. Hence the form (6) can include no infinitesimal transformation other than those of the congruence group under
consideration.
A tetrahedron formed by three mutually perpendicular axes, with
the common latent plane of the three rotations round the axes for its
fourth plane, and with the unit points of its axes chosen so as to produce
equations (6), will be called a normal reference tetrahedron.
When the congruence group is given, the normal reference tetrahedrons are determinate, though infinite in number. But a congruence
group can be found so that any given tetrahedron is a normal reference
tetrahedron.