word choice - "Of" and "For" Before "-ing"


What are the rules for choosing whether to use "of" or "for" before a word ending in "-ing?"


Example:



We propose a method of simplifying algebraic expressions.
We propose a method for simplifying algebraic expressions.



I have seen it written both ways, and would like to know which way is proper. Or is this a case where "it depends?"



Answer



The choice of preposition has less to do with the following gerund (-ing word; in your example, the word simplifying) than with the word method. It appears from the following NGram (corpus English, 1800 to 2008) that "method of" is much more commonly used than "method for." I think both are understandable, however, and both are used.


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