The earliest bicycles, like Lallement's bicycle, did not have brakes as such, but back pressure on the pedals provided some braking. Later bikes used a brake pad that pushed against the tire, like the brakes found on wagons of the day. Later bikes used pads that pressed agains the rim of the wheel, like the centerpull brake. Another type of brake is the cantilever brake, in which the brake arm is pivotally attached to the bike frame, with the brake pad placed between the pivot (the fulcrum of the lever thus formed) and the end of the brake arm. This type of brake is thus a class two lever. Although this cantilever brake is from 1939, they really became popular when added braking power was needed on bikes that were being made for off road use.
The rest of the bike technology posts are in the Bicycle Technology section.