That Cawdrey should arrange his words in alphabetical order, to make his Table Alphabeticall, was not self-evident. He knew he could not count on even his educated readers to be versed in alphabetical order, so he tried to produce a small how-to manual. He struggled with this: whether to describe the ordering in logical, schematic terms or in terms of a step-by-step procedure, an algorithm.
Gentle reader, thou must learne the Alphabet, to wit, the order of the Letters as they stand, perfectly without booke, and where every Letter standeth: as b neere the beginning, n about the middest, and t toward the end. Nowe if the word, which thou art desirous to finde, begin with a then looke in the beginning of this Table, but if with v looke towards the end. Againe, if thy word beginne with ca looke in the beginning of the letter c but if with cu then looke toward the end of that letter. And so of all the rest.
It was not easy to explain. Friar Johannes Balbus of Genoa tried in his 1286 Catholicon. Balbus thought he was inventing alphabetical order for the first time, and his instructions were painstaking:
For example I intend to discuss amo and bibo. I will discuss amo before bibo because a is the first letter of amo and b is the first letter of bibo and a is before b in the alphabet. Similarly …
He rehearsed a long list of examples and concluded:
I beg of you, therefore, good reader, do not scorn this great labor of mine and this order as something worthless.
Instructions for using lists sorted according to the order of letters. Quote from The Information: A History, A Theory, A Flood by James Gleick. In turn quoting from Catholicon and Table Alphabeticall.