A single, direct, and self-contained demonstration is given of the important self-indexing characteristic of the gnomonic projection. The demonstration is given first for two dimensions, then generalized to three dimensions. The self-indexing characteristic of the projection is limited to the case in which one of the lattice lines chosen as a crystallographic axis is set normal to the plane of projection. The implied lattice significance of changing the origin, length, and positive sense of units is given; these correspond with changing the direction, length and positive sense of the a axis of the lattice, c remaining fixed. Transformation of indices from one plane of projection to another is discussed. This can be resolved into a change of direction of the lattice a axis plus a change of projection from normal to the c axis to normal to the new a axis. The latter transformation requires an index to be replaced by its negative reciprocal. Goldschmidt's transformation:
is then analysed, and shown to be compounded from the above fundamental transformations.
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