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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.
This principle was formulated by Poncelet, 
and amounts to the statement that if an analytic identity in any
finite number of variables holds for all real values of the variables, then it also holds by Analytic Continuation for
all complex values (Bell 1945). This principle is also called Poncelet's Continuity Principle.
See also Analytic Continuation, Conservation of Number Principle, Duality Principle, Permanence of Algebraic Form
References
Bell, E. T. The Development of Mathematics, 2nd ed. New York: McGraw-Hill, p. 340, 1945.