Zeteticism is a system of scientific inquiry. The word is derived from the Greek verb ζητέω (zeteo), which means "I seek; I examine; I strive for".
Zeteticism differs from the usual scientific method in that using zeteticism one bases his conclusions on experimentation and observation rather than on an initial theory that is to be proved or disproved. A zetetic forms the question then immediately sets to work making observations and performing experiments to answer that question, rather than speculating on what the answer might be then testing that out.
For example, in questioning the shape of the Earth the zetetic does not make a hypothesis suggesting that the Earth is round or flat and then proceed testing that hypothesis; he skips that step and devises an experiment that will determine the shape of the Earth, and bases his conclusion on the result of that experiment. Many feel this is a more reasonable method than the normal scientific method because it removes any preconceived notions and biases the formation of a hypothesis might cause, and leaves the conclusion up entirely to what is observed.
Samuel Rowbotham was the first to use the term in reference to Flat Earth research. He devised the Bedford Level Experiment to determine whether the surface of water is convex, reasoning that if the water is not convex the earth cannot be a sphere. This is how he came to the conclusion that the Earth is flat. The method has been a cornerstone of Flat Earth Theory ever since.