permanence of mathematical relations principle | Poncelet's continuity principle

The metric properties discovered for a primitive figure remain applicable, without modifications other than changes of signs, to all correlative figures which can be considered to arise from the first. As stated by Lachlan, the principle states that if, from the nature of a particular problem, a certain number of solutions are expected (and are, in fact, found in any one case), then there will be the same number of solutions in all cases, although some solutions may be imaginary.

analytic continuation | conservation of number principle | duality principle | permanence of algebraic form