I would agree with Alexandre Eremenko's answer. The early calculus in fact was not inconsistent, as elaborated below.
Joël's answer is based on a premise that "the question is not precise enough to get a definite answer", and "does not make real sense, because 'arguments' are not results". This premise is historically incorrect. In fact, in the historical literature the claim of inconsistency of the early calculus is very specific and precise. It is routinely based on Berkeley's analysis of the typical calculations such as that of the derivative of a power, or the derivative of the product of two functions. The alleged inconsistency is presented as follows. Berkeley claims that (1) $dx$ is nonzero at the start of the calculation; (2) $dx$ is assumed to be zero at its conclusion; (3) in any consistent reasoning, $dx$ cannot be simultaneously zero and nonzero; (4) therefore the procedures of the calculus were inconsistent, Q.E.D.
Berkeley, however, did not read Leibniz carefully enough. Leibniz explicitly and repeatedly clarifies that he is working with a generalized notion of equality, where expressions equal up to a negligible term are also held to be equal. In modern terminology, this means that Leibniz is working with a binary relation which is not equality on the nose, but rather approximate equality in a suitable sense. It is in this sense that Leibniz writes formulas like $2x+dx=2x$ (note that he did not use our "=" symbol). Leibniz might not have been "rigorous" by modern standards, but he was not inconsistent, either. In fact, Leibniz's procedures were more soundly based than Berkeley's criticisms thereof. Philosopher David Sherry and I presented our analysis last year in the Notices of the AMS at http://www.ams.org/notices/201211/
Felix Klein wrote in 1908 that there were in fact not one but two separate tracks for the development of analysis: (A) the Weierstrassian one, in the context of an Archimedean continuum; and (B) the track exploiting indivisibles and/or infinitesimals. The B-track was eventually popularized by Abraham Robinson.
Everybody is familiar with the great accomplishment of Weierstrass in developing rigorous foundations for analysis, which is beyond dispute. However, historian Carl Boyer (and many others), in describing Cantor, Dedekind, and Weierstrass as "the great triumvirate", adds an anti-infinitesimal spin to their accomplishment. Namely, the traditional historical literature seeks to couple their "rigorous" accomplishment to the elimination of "inconsistent" infinitesimals, as if pursuing the A-track depended on the elimination of the B-track (Dunham's "rotten foundations"). It is the coupling of Weierstrass's accomplishment to an ill-informed critique of infinitesimals (both classical and modern) that constitutes the historical misconception pointed out by Vickers and others.