While working on a historical novel, I believe it was "Raining Fire" set in 1833, I started to write that the hero took out a match to light the fire. I paused wondering if a match had been invented by then. Well, they had but they hadn't made there way to a woodsman in America. Here's a brief account of the history of a match during the 1800's.
In 1827, John Walker, English chemist and apothecary, discovered that if he coated the end of a stick with certain chemicals and let them dry, he could start a fire by striking the stick anywhere. These were the first friction matches. He called them strikables.
In 1830, the French chemist, Charles Sauria, created a match made with white phosphorous. White phosphorous is poisonous.
In 1855, safety matches were patented by Johan Edvard Lundstrom of Sweden. Lundstrom put red phosphorus on the sandpaper outside the box and the other ingredients on the match head.
In 1889, Joshua Pusey invented the matchbook, he called his matchbook matches "Flexibles".
And just to fill out a bit the remainder of the history I'm including a couple events in the 1900's.
In 1910, the Diamond Match Company patented the first nonpoisonous match in the U.S.
January 28, 1911 United States President William H. Taft publicly asked Diamond Match to release their patent for the good of mankind. They did then congress placed a high tax on matches made with white phosphorous.