An introduction to mathematics, by A. N. Whitehead.

108 INTRODUCTION TO MATHEMATICS
The general rule for the geometrical representation of multiplication can now be
enunciated thus:
R? F.
Theo of
Fig. 12.
The product of the two vectors OP and
OQ is a vector OR, whose length is the product of the lengths of OP and OQ and whose
direction OR is such that the angle ROX is
equal to the sum of the angles POX and QOX.
Hence we can conceive the vector OP as
making the vector OQ rotate through an
angle POX (i.e. the angle ROQ=the angle
POX), or the vector OQ as making the vector
OP rotate through the angle QOX (i.e. the
angle ROP =the angle QOX).
We do not prove this general law, as we