“Permanence of Mathematical Relations Principle”的概念、定义、习题解题方法及翻译-数学辞典

单词

Permanence of Mathematical Relations Principle

释义

Permanence of Mathematical Relations Principle

The metric properties discovered for a primitive figure remain applicable, without modifications other than changes ofsigns, 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 anyfinite number of variables holds for all real values of the variables, then it also holds by Analytic Continuation forall complex values (Bell 1945). This principle is also called Poncelet's Continuity Principle.

See also Analytic Continuation, Conservation of Number Principle, Duality Principle, Permanence ofAlgebraic Form

References

Bell, E. T. The Development of Mathematics, 2nd ed. New York: McGraw-Hill, p. 340, 1945.

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