Difference between Approximate and Proximate?

Solution 1:

Both proximate and approximate come from the latin proximāre, which means close or near. Both proximate and approximate indicate being near or close to something, but approximate is usually used to indicate being within a certain range of a goal, while proximate usually means physically close. When talking about measurements, you'd say that a sharp stick is approximately three inches long, meaning its length is near to, but not exactly, three inches.

If you said the stick was proximate to my eye, that would mean the stick is physically close to my eye.

Both are usually adjectives, but can also be verbs. However approximate as a verb is much more common than proximate.

The prefix ap comes from the latin ad, meaning to, so approximate could be said to mean to come close to

http://www.oed.com/search?searchType=dictionary&q=proximate

Solution 2:

Both words can mean close by in position, quality, and accuracy.

The OED's examples for "proximate" illustrate its sense of closeness in the meaning of words, geographical position, and strength of commercial relationships. The substitution of "approximate" would be apt in these examples, given its definition "Very near, in position or in character."

From History of the Berwickshire Naturalists' Club, Volume 1 (which is quoted in part as an example from the OED) describing the suckers of an octopus:

[T]oward the base of the arm they are larger and not in contact, but they soon become approximate, and gradually lessening in size they become very minute at the tips....

"Proximate," however has a usage that its cousin lacks -- next or previous in order. This may be temporal (as in the "proximate future," something that will happen next as opposed to remote events to come), or causal

The jury had to determine the proximate cause of the collision

or with respect to process, particularly in chemistry, in which "proximate analysis" of a compound means determining the compound's precursors.

Both words have synonymous adverbial forms -- "proximately" and "approximately."

Both words have synonymous noun forms, but with different morphemes -- "proximity," "proximateness" and "approximation."

Only "approximate" is a verb.