#### Mathematical English Usage - a Dictionary

##### by Jerzy Trzeciak

## before

The sum of the depths is at most two-thirds of what it was before.

Each tree is about two-thirds as deep as it was before.

The remainder of the estimation is largely as before with B replaced by C.

Most of the theorems presented here have never been published before.

Note that P comes before Q along the arc l.

We may require that the point P lie in one of the trees constructed before or during the ith stage of the induction.

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