For material on related topics, see Calculus. Laterally related topics: Archimedes' Method and Surface Area.
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Miller, G. A. Gerbert's Letter to Adelbold. School Science and Mathematics 21 (1921), 649--53.
Gerbert puts circles and squares inside an equilateral triangle, and attempts to explain why they give different answers for the area. We think of these answers as estimates, but Gerbert's letter contains no hint of a limiting process. Reprinted in Swetz, Frank J., From Five Fingers to Infinity. Closely related topics: The Abacus, Gerbert, Pope Sylvester II, and The Measurement of Area and Volume.