Tangents Via Infinitessimals
The tangent lines of the kappa curve can also be determined geometrically using differentials and the elementary rules of infinitessimal arithmetic. Suppose x and y are variables, while a is taken as a constant. From the definition of the kappa curve,
Now, an infinitessimal change in our location must also change the value of the left hand side, so
Distributing the differential and applying appropriate rules,
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