In this article several theorems of the theory of Gamma-lines for meromorphic functions are extended to the more general setting of algebroid functions. We recall the definition of algebroid function of order k and how it can be considered as a function defined on a Riemann surface of k sheets. In this way, we prove the so called tangent variation principle for algebroid functions, previously proved for meromorphic functions by Barsegian, and we get several consequences of this result. We also extend a proposition on proximity properties of meromorphic functions.
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