Torres Quevedo's mechanical calculator for second-degree equations with complex coefficients

Abstract

Leonardo Torres Quevedo worked intensively in analogue calculating machines during the last years of the 19th century. The algebraic calculators were calculating machines in which numbers are represented by quantities of a given physical magnitude(s). The physical result is a magnitude of a physical quantity whose measurement in the coherent unit is the result of the algebraic equation. This article shows the three-dimensional (3D) modelling, virtual reconstruction and simulation of the first mechanical calculating machine for solving second-degree equations with complex coefficients, to prove that the functionality was correct and the machine could be built. Sketches of said machine provide enough information on the shape and mechanisms of the machine. By means of the simulation, it has been possible to prove its operation and feasibility of construction so that it is possible to replicate it as a real physical model. The mechanical calculator for second-degree equations with complex coefficients constituted a major milestone in the technological development of the time and helped to originate and improve the design of other algebraic calculators like the machine for solving eighth-degree equations.