"If a man write a better book, preach a better sermon..."

There is an old quotation attributed to Ralph Waldo Emerson:

If a man write a better book, preach a better sermon, or make a better mouse-trap than his neighbour, tho' he build his house in the woods, the world will make a beaten path to his door.

Why are the verbs in the conditional clause in the infinitive, instead of third person singular? Old usage? Subjunctive? Neither?

Solution 1:

If a man write a better book, preach a better sermon, or make a better mouse-trap than his neighbour, tho' he build his house in the woods, the world will make a beaten path to his door.

It is the subjunctive used in older writings, of the type (pointed out by @tchrist) if A be X, then A will (the key here being the will future instead of would).

Similar to almost anything you read in the KJB:

Or if a soul swear, pronouncing with his lips to do evil, or to do good, whatsoever it be that a man shall pronounce with an oath, and it be hid from him; when he knoweth of it, then he shall be guilty in one of these.

Solution 2:

To complement medica's answer, and because I love trivia, I offer the following.

The original quote (in the OP's question) now updated is

Build a better mousetrap, and they will beat a path to your door

the popular advice is attributed to Ralph Waldo Emerson, but it was in 1889 that Sarah Yule included it in her book (p. 138 ), Borrowings, seven years after Emerson's death in April 27, 1882. In 1912 Yule stated she had copied it from a lecture delivered by the eminent American essayist in 1871. But there is no proof that he actually wrote those lines using the present subjunctive. A considerably longer version exists in Emerson's journal entry dated 1855

I trust a good deal to common fame, as we all must. If a man has good corn, or wood, or boards, or pigs, to sell, or can make better chairs or knives, crucibles or church organs, than anybody else, you will find a broad hard-beaten road to his house.

Note that Emerson used the present indicative in this instance.

^{sources: What They Didn't Say: A Book of Misquotations by Elizabeth Knowles. Bartleby.com and Wikipedia}