  There is a simple formal correspondence between the equations of Lobachevskian trigonometry and those of standard spherical trigonometry. Based on it, Lobachevsky argued that any contradiction arising in his geometry would inevitably be matched by a contradiction in Euclidean geometry. This appears to be the earliest example of a purported proof of relative consistency, by which a theory is shown to be consistent lest another theory — whose consistency is typically taken for granted — be inconsistent.