Add punctuation: Even the concept of an infinite series for example one which increases according to definite powers of variables is in my opinion only permissible with the reservation that in every special case on the basis of the arithmetic laws of constructing terms or coefficients certain assumptions must be shown to hold which are applicable to the series like finite expressions and which thus make the extension beyond the concept of a finite series really unnecessary
Even the concept of an infinite series, for example one which increases according to definite powers of variables, is in my opinion only permissible with the reservation that in every special case, on the basis of the arithmetic laws of constructing terms (or coefficients), ... certain assumptions must be shown to hold which are applicable to the series like finite expressions, and which thus make the extension beyond the concept of a finite series really unnecessary.