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Enlightening SymbolsA Short History of Mathematical Notation and Its Hidden Powers$
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Joseph Mazur

Print publication date: 2016

Print ISBN-13: 9780691173375

Published to Princeton Scholarship Online: January 2018

DOI: 10.23943/princeton/9780691173375.001.0001

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Hierarchies of Dignity

Hierarchies of Dignity

(p.133) Chapter 14 Hierarchies of Dignity
Enlightening Symbols

Joseph Mazur

Princeton University Press

This chapter discusses what Rafael Bombelli called dignità, which translates to the English word “dignity” and is equivalent to what we refer to as “exponents.” It first considers Bombelli's L'Algebra (1579), which introduces a new kind of notation for the unknown and its powers. Written in Italian, L'Algebra used equality in a different sense than we do. For Bombelli, the higher powers meant hierarchies of dignity. He was not only inventing genuine symbols when depicting dignità as little cups holding numbers, but also inventing words that were new to mathematics. The chapter also examines how the problem of finding the roots of polynomials became the problem of factoring polynomials. Finally, it looks at René Descartes's idea of using numerical superscripts to mark positive integral exponents of a polynomial in his La Géométrie.

Keywords:   exponents, Rafael Bombelli, dignità, L'Algebra, notation, equality, powers, symbols, polynomials, René Descartes

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