  In this note we present a method for constructing CMC-1 surfaces in
hyperbolic 3-space $\bfH^3(-1)$ in terms of holomorphic data first introduced
in Bianchi's Lezioni di Geometria Differenziale of 1927, therefore predating by
many years the modern approaches due to Bryant, Small and others. Besides its
obvious historical interest, this note aims to complement Bianchi's analysis by
deriving explicit formulae for CMC-1 surfaces and comparing the various
approaches encountered in the literature.

Differential Geometry;History and Overview