Advanced calculus; . der the figure and the equivalent circuits AC Aand AC A described as indicated by the large arrows. It is clearthat either may be modified little by little, as indicated in theproof above, until it has been changed into the other. Hence the C change in the value of / around the two circuits is the same. Or, as another proof,it may be observed that the combined circuit AC ACA, where the second isdescribed as indicated by the small arrows, may be regarded as a reducible circuitwhich touches itself at A. Then the change of / around the circuit is zero and /must lose as much o
Advanced calculus; . der the figure and the equivalent circuits AC Aand AC A described as indicated by the large arrows. It is clearthat either may be modified little by little, as indicated in theproof above, until it has been changed into the other. Hence the C change in the value of / around the two circuits is the same. Or, as another proof,it may be observed that the combined circuit AC ACA, where the second isdescribed as indicated by the small arrows, may be regarded as a reducible circuitwhich touches itself at A. Then the change of / around the circuit is zero and /must lose as much on passing from A to A by C as it gains in passing from A toA by C. Hence on passing from A to A by C in the direction of the large arrowsthe gain in /must be the same as on passing by C. It is now possible to see that any circuit ABC may be reduced to circuits aroundthe portions cut out of the region combined with lines going to and from A and theboundaries. The figure shows this; for the circuit ABCBADCDA is clearly.
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