Juan de Ortega (mathematician)

Juan de Ortega (born Palencia, Spain, c. 1480; died c. 1568),[1] was a Spanish mathematician. He wrote some of the earliest works on commercial arithmetic, and discovered an improved method for calculating square roots.

Frontispiece of Ortega's Tratado

Life

Very little is known of Ortega's life.[2] He was a member of the Dominican Order in Aragon,[2] and he taught arithmetic and geometry in Spain and Italy.[1]

Mathematical contributions

For his work on arithmetic Ortega drew on that of Boethius and of 13th-14th century mathematicians.[1]

A widely known[3] publication among Ortega's works was Tratado subtilissimo de Aritmetica y de Geometria ("Most refined treatise on arithmetic and geometry") (Barcelona, 1512). The work was published in Spain, France and Italy, and translated into several languages.[2] The Tratado was innovative[3] in focusing on the practical, in particular commercial, application of arithmetical and geometrical techniques.[2] In later editions[4] this work also introduces a novel approximation method for calculating square roots,[5] which appears to be largely based on the Pell equation and thereby the best available technique,[6] even though no general solution of this equation is known to have been found until much later.[1]

Another textbook by Ortega was Cursus quattuor mathematicarum artium liberalium ("Course of four mathematical arts") (Paris, 1516).[1]

References

1. M A Catala, "Ortega, Juan de", Biography in Dictionary of Scientific Biography (New York 1970-1990).
2. David E. Smith (1958). History of Mathematics. Courier Corporation. p. 344. ISBN 978-0-486-20429-1.
3. Comissão Nacional para as Comemorações dos Descobrimentos Portugueses (1994). Las relaciones entre Portugal y Castilla en la época de los descubrimientos y la expansión colonial (in Portuguese). Universidad de Salamanca. p. 226. ISBN 978-84-7481-792-8.
4. "Biografia de Juan de Ortega" (in Spanish). Biografías y Vidas. Retrieved 17 November 2017.
5. Edward Smedley (1845). Encyclopædia metropolitana; or, Universal dictionary of knowledge, ed. by E. Smedley, Hugh J. Rose and Henry J. Rose. [With] Plates. p. 436.
6. Benito, Manuel; Escribano, Jose Javier; Fernández, Emilio; Sánchez, Mercedes (5 December 2012). "Fray Juan de Ortega's approximations, 500 years after". arXiv:1212.1125 [math.HO].

Further reading

• "Ortega biography". MacTutor archive. School of Mathematics and Statistics, University of St Andrews, Scotland.