According to Wikipedia, the [Bohr-Mollerup Theorem](https://en.wikipedia.org/wiki/Bohr%E2%80%93Mollerup_theorem) (discussed previously on MO [here](https://mathoverflow.net/questions/23229/importance-of-log-convexity-of-the-gamma-function)) 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.



Theorems first published in textbooks?
I recall that, and Wikipedia independently confirms that L'Hôpital's rule first appeared in a textbook, apparently the first textbook on differential calculus: [*Analyse des Infiniment Petits pour l'Intelligence des Lignes Courbes*](https://en.wikipedia.org/wiki/Analyse_des_Infiniment_Petits_pour_l%27Intelligence_des_Lignes_Courbes) published by Guillaume de l'Hôpital and made up of content mostly provided by Johann Bernoulli, who was on retainer to l'Hôpital, more or less, for this purpose.


