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:But a more rigorous mathematical proof based on the equation for elasticity is desired:
 
:But a more rigorous mathematical proof based on the equation for elasticity is desired:
   −
::P<ref>ed</ref>=(%change in Q)/%change in P)
+
::P<sub>ed</sub>=(%change in Q)/(%change in P)
    
::If the new P and Q are denoted by P<sub>2</sub> and Q<sub>2</sub>, and the old P and Q are denoted by P<sub>1</sub> and Q<sub>1</sub>, then:
 
::If the new P and Q are denoted by P<sub>2</sub> and Q<sub>2</sub>, and the old P and Q are denoted by P<sub>1</sub> and Q<sub>1</sub>, then:
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