TITLE: Theorems first published in textbooks?
QUESTION [31 upvotes]: According to Wikipedia, the Bohr-Mollerup Theorem (discussed previously on MO here) was first published in a textbook. It says the authors did that instead of writing a paper because they didn't think the theorem was new. 
What other examples are there of significant theorems that first saw the light of day in a textbook? (I'm assuming Wikipedia is right about Bohr-Mollerup.) 
I recognize that the word "significant" is imprecise; I have in mind theorems that mathematicians have picked up on and used in their own work, but I'm open to other interpretations.

REPLY [4 votes]: Intersection theory has of course a long tradition, starting from the work of Schubert, Poincaré and many more, but the book Intersection theory by Fulton is by now considered the gold reference. Many results in the book were new at the time. Citing from the introduction

Several theorems are new or stronger than those which have appeared before, and some proofs are significantly simpler. Among the former are a new blow-up formula, a stronger residual intersection formula, and the removal of a projective hypothesis from intersection theory and Riemann-Roch theorems; the latter includes the proof of the Grothendieck-Riemann-Roch theorem. Some formulas from classical enumerative geometry receive a first modern or rigorous proof here.