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The first true gun appeared about 1260. The Chinese had originally used a "fire arrow" which is sometimes considered the first rocket. Some considered them handheld things that just shot fire into the air and others said they were true propelled rockets.
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In the War of 1812 there were cases where the british had used "incindiary rockets" to set buildings and other ships on fire. They use over 6,000 of these "rockets." This was one of the first times rockets were used very prominently.
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In 1906, a German named Alfred Maul stook pictures of the ground by using rockets. This way of taking pictures though was disgarded after the airplane was invented.
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Goddard and Oberth were the most significant characters in before World War II rocketry, most other noteworthy events didn't happen until late 1900's with space.