Robert Jones’s A Treatise on Skating, first published in 1772, is generally considered the first book on skating. It went through several editions between 1772 and 1855, with numerous additions and changes over time.
Aimed at beginners, it has two parts: a section on basic skills, including choosing and putting on skates, stroking and edges, and a section on more advanced maneuvers, such as the spiral line and the flying Mercury (shown in the cover image). It provides a nice overview of what skating was like back in the day. People didn’t do fancy jumps or spins, or even figures. The advanced skaters seemed most interested in dramatic body positions as they glided across the ice.
In 1855, W. E. Cormack updated Jones’s Treatise in response to an unspecified event that occurred three years earlier. I think this may have been the publication of Cyclos’s book, which was the first attempt at systematizing skating. Later, Henry Vandervell and T. Maxwell Witham took this further with A System of Figure Skating in England while Demeter Diamantidi, Max Wirth, and Karl von Korper did the same in Austria with Spuren auf dem Eise. These books laid the foundation for the schedule of compulsory figures, which was the foundation of figure skating for nearly a century.
Based on Cormack’s comments, I think there may have been some resistance to systematizing what had previously been an abstract art, just as there has been resistance to creating a code of points for scoring skating in the ISU judging system.
The link above is to my edition of Jones’s book, which includes both the full text of the original an Cormack’s updates.
Robert Jones. 1772. A Treatise on Skating. London: J. Ridley.
John Cyclos [George Anderson]. 1852. The Art of Skating with Plain Directions for the Acquirement of the Most Difficult and Elegant Maneuvers. Glasgow: Thomas Murray and Son.
Henry Eugene Vandervell & T. Maxwell Witham. 1869. A System of Figure Skating: Being the Theory and Practice of the Art as Developed in England, with a Glance at its Origin and History. London: Horace Cox.
Demeter Diamantidi, Karl von Korper, and Max Wirth. 1881. Spuren auf dem Eise: die Entwicklung des Eislaufes auf der Bahn des Wiener Eislauf-Vereines. Vienna: Alfred Holder.