The Ordinary is the official name for the old-fashioned bicycle with the massively oversized front wheel (sometimes called a "high-wheeler"). The idea was invented by James Starley of Coventry, England, and the first Ordinary manufactured was a brand called the Ariel manufactured in England in 1872; before this time, there had only been the velocipede, a wood-and-iron bicycle (even the wheels) which could weigh up to 100 pounds and had its pedals on the front wheel. Ordinaries were made of lighter tubular steel and had tires of solid rubber with wire spokes in the middle, making them both lighter to lift and less bone-rattling to ride. The pedals were still on the front wheel, but the large circumference of the front wheel made the same amount of pedaling go farther, since gears were not used until the rear-wheel-driven safety bicycle of the 1890s. The rider had to sit up high, above the large wheel, just to reach the pedals and still be sitting upright; the small back wheel was just for balance.

The first American Ordinaries were manufactured in 1877, and within a few years they became a craze in the U.S.; the League of American Wheelmen was founded in 1880 and immediately started to campaign for better road surfaces and were quite effective in getting roads paved. ("Wheelmen" is quite accurate; the long skirts of the era prevented women from riding an Ordinary unless they were daring enough to wear pants.) It required courage for anyone to ride an Ordinary; their brakes were not all that effective and a lot of riders were pitched over the straight front handlebars when they ran into an obstacle. Or they just fell off; even getting on wasn't all that easy. But Ordinaries were still popular enough that accessories such as chain and lock sets, bike stands, bells or whistles to announce that you were coming, saddlebags, odometers, and oil lanterns for night riding could all be bought by 1879.

At the time, these were just called bicycles; the names Ordinary or high-wheeler came into use around 1890 as the safety bicycle with two wheels the same size came into use. "Penny-farthing" was another name for the Ordinary in England, since the two wheels looked like a penny and a farthing coin next to one another. The Japanese name for the Ordinary was "daruma jitensha" or "ichirinsha." As this shows, the Ordinary spread all around the world; by 1884 Australia had 30 bicycling clubs. However, the increased ease and reduced risk of the safety bicycle meant that in the 1890s, the Ordinary became obsolete.

Sources:
Ierley, Merritt. Wondrous Contrivances: Technology at the Threshold. New York: Clarkson Potter Publishers, 2002.
http://www.exploratorium.edu/cycling/timeline.html
http://www.fi.edu/pieces/payton/slide2.htm
http://www.cycle-info.bpaj.or.jp/english/learn/bcc02.html
http://www.phys.uri.edu/~tony/bicycle/bikehist.html
http://www.phm.gov.au/hsc/bike/history.htm