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MANY OF THE MULTIPLICATION techniques used in fifteenth- and sixteenth-century Europe can be traced to India, specifically through a book called Lilavati (The Beautiful) by Bhaskara (1114-85). Although many of us find mathematics to be beautiful, the name is unusual for a mathematics book. According to a translation by the fifteenth-century Persian poet Fyzi, a story lies behind the book's name. Astrologers predicted that Bhaskara's daughter, Lilavati, would have an unfortunate marriage unless she married at a certain time on a certain day. Lilavati, in anticipation of her marriage at this special time, was watching a water clock. Unfortunately, when she bent over the water clock, a pearl dropped off her headdress and stopped the water from flowing out of the clock. Lilavati missed the time for the ceremony, and because she did not want to risk an unhappy marriage, she never wed. To offer Lilavati solace, Bhaskara named his book after her because it would be a book that "will last to the latest times" (Burton 1988, p. 236; Calinger 1999, p. 279).
The five multiplication algorithms found in Lilavati appear again in European mathematics books by such authors as the Italian Fra Luca Pacioli (1445-1517), who wrote Summa de Arithmetica, Geometric, Proportioni et Proportionality in 1494. As the title indicates, Pacioli included material on arithmetic, geometry, and proportion, as well as a significant presentation on double-entry bookkeeping. The Summa begins with the basic operations, including eight algorithms for multiplication: the
scacchieri method (the chessboard); the castle method; the column method (which uses tables); the crocetta method (little cross); the quadrilateral method (a shifted chessboard plan); the gelosia method (lattice); the repegio method (multiplication by factors); and the scapezzo method (addition of partial products) (Smith 1953, pp. 107-17). All eight methods can be found in various Indian sources. Pacioli's Summa brings together mathematics from many sources without offering credit, which was "the custom of the age" (Smith 1953, p. 253). Be cause the Summa was comprehensive in tis mathematical content and the first such printed collection, it was widely read and studied.
The Lattice, or Gelosia, Method
CALLED 'SHABAKH" IN BHASKARA'S LILAVATI, the lattice, or gelosia, method is so named "because the arragement of the work resembles a lattice or gelosia," which was...