Recently I found two different booklets available online, both published in 1881 in Boston, that make the dangers of the ordinary bicycle quite clear.
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As with all the illustrations in this little instruction manual, at first things seem manageable . . .
These two illustrations are from "Over the Wheel" - well, with a title like that, perhaps the emphasis on mishaps is not surprising.
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As usual as portrayed in this booklet, the rider ends up in an accident
Another booklet in a similar vein is "The Illustrated Bicycle Primer" that similarly features illustrations with cyclists crashing in various ways.
So, once the bicycle as we know it today apppeared in the late 1880s, with similar sized front and back wheels and a chain drive system, it is hardly surprising it was distinguished from its predecessor, the "ordinary" as being the "safety bicycle."
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An early "safety" bicycle
After not a very long time, the "ordinary" bicycles disappeared and the word "safety" to designate a bicycle also went out of use.