[Theō’ric transformation] is an operation of necessary, or rather, of compulsive reasoning, (granted the premisses the interpreter of the reasoning is compelled to assent to the conclusion,) which formal logic cannot possibly take into account, since from the point of view of formal logic there is no essential distinction between it and the most obvious corollarial transformation. Yet the key to mathematical methodeutic lies hidden here. It will consist in the transformation of the problem, – or of its statement, – due to viewing it from another point of view.

…every difficult mathematical theorem evidently involves some transformation of thought of which formal logic can take no account, although it is perfectly evident and undeniable, when it is suggested. This transformation, which creates an ens rationis, may appropriately be termed a “theo’ric” transformation.

It is not quite so true as Kant thought it to be that deduction is purely explicative; but the amplificative element that a certain kind of deduction, called theo’ric transformation, affords, consists, after all, only in new forms of conceiving old facts.