This chapter discusses the evolution of symbolic algebra that began in the first half of the sixteenth century. Algebra was not always called algebra. In the mid-fifteenth century some Italian and Latin writers called it Regula rei e census. The twentieth-century mathematician and science fiction author Eric Temple Bell allegedly remarked that in the mid-seventeenth century, mathematicians were able to introduce negative and rational exponents because symbolic manipulation liberated their thinking from the wilderness of words. The chapter considers the contributions of the Arab algebraist al-Qalasādi, who used letters of the Arabic alphabet to denote arithmetic operations and whose notation was clearly an attempt at symbolizing algebra through abbreviations, a first approximation to what we would consider true symbols. It also examines how Italy cultivated the seeds of algebra, citing in particular Gerolamo Cardano's Ars Magna.
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