# Projectively Sentence Examples

The linear transformation replaces points on lines through the origin by corresponding points on **projectively** corresponding lines through the origin; it therefore replaces a pencil of lines by another pencil, which corresponds **projectively**, and harmonic and other properties of pencils which are unaltered by linear transformation we may expect to find indicated in the invariant system.

Or, instead of looking upon a linear substitution as replacing a pencil of lines by a **projectively** corresponding pencil retaining the same axes of co-ordinates, we may look upon the substitution as changing the axes of co-ordinates retaining the same pencil.

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