From Difference Engine to General-Purpose Idea

When people talk about early computers Babbage's Analytical Engine is bound to come up. Designed back in the 1830's it's definitely older than any other example of the art. But it also has a lot of strikes against it. The machine was purely mechanical. It only really did math. It stored numbers in decimal instead of binary. Worst of all, it only ever existed as designs on paper. So should we call this beast a computer? Or is it something else entirely? Selected Sources: https://www.fourmilab.ch/babbage/sketch.html - Sketch of the Analytical Engine, and Lovelace's Notes https://web.archive.org/web/20210226094829/http://athena.union.edu/~hemmendd/Courses/cs80/an-engine.pdf - Bromleys low level description of the engine https://sci-hub.se/10.1007/978-3-642-61812-3_2 - On the Mathematical Powers of the Calculating Engine, by Charles Babbage https://archive.org/details/bub_gb_Oi3IhTZyVCAC/mode/1up - The Ninth Bridgewater Treatise, Babbage