Horses in warfare of today's English saddle. Both the Scythians and Assyrians used pads with added felt attached with a surcingle or girth around the horse's barrel for increased security and comfort. Xenophon mentioned the use of a padded cloth on cavalry mounts as early as the 4th century BC. The saddle with a solid framework, or "tree", provided a bearing surface to protect the horse from the weight of the rider, but was not widespread until the 2nd century AD. However, it made a critical difference, as horses could carry more weight when distributed across a solid saddle tree. A solid tree,
Girth (geometry) width, with the same width "w". All curves of constant width have the same perimeter, the same value "w" as the circumference of a circle with that width (this is Barbier's theorem). Therefore, every surface of constant width is also a surface of constant girth: its girth in all directions is the same number "w". Hermann Minkowski proved, conversely, that every convex surface of constant girth is also a surface of constant width. For a prism or cylinder, its projection in the direction parallel to its axis is the same as its cross section, so in these cases the girth