In answering this question, it is helpful to make a distinction between, on the one hand, what Reeder calls the "inferential moves" that Euler makes (see related thread Euler's mathematics in terms of modern theories?), and on the other, the mathematical objects he manipulates (infinitesimals, infinite integers, etc). This allows Reeder to observe that modern infinitesimal theories are far more successful in formalizing Euler's procedures ("inferential moves") than are $\epsilon,\delta$ techniques.

Traditional scholars like Ferraro (see thread linked above) were trained on the basis of conceptual frameworks that are inadequate to the task of making such an evaluation, and tend to receive the work of scholars like Laugwitz with hostility.

Laugwitz argued for an essential coherence of infinitesimal reasoning in both Cauchy and Euler, modulo certain "hidden lemmas" that need to be made explicit to meet a modern standard. I would adopt an optimistic position that many of Euler's greatest contributions are immediately publishable in contemporary journals, provided minimal changes are made so as to clarify the nature of the objects as well as the "hidden lemmas".

The verdict is still out on whether the MATHEMATICAL community (as opposed to that of the HISTORIANS of mathematics) will in the end side with Reeder's analysis or Ferraro's analysis.

In answering this question, it is helpful to make a distinction between, on the one hand, what Reeder calls the "inferential moves" that Euler makes (see related thread Euler's mathematics in terms of modern theories?), and on the other, the mathematical objects he manipulates (infinitesimals, infinite integers, etc). This allows Reeder to observe that modern infinitesimal theories are far more successful in formalizing Euler's procedures ("inferential moves") than are $\epsilon,\delta$ techniques.

Traditional scholars like Ferraro (see thread linked above) were trained on the basis of conceptual frameworks that are inadequate to the task of making such an evaluation, and tend to receive the work of scholars like Laugwitz with hostility.

Laugwitz argued for an essential coherence of infinitesimal reasoning in both Cauchy and Euler, modulo certain "hidden lemmas" that need to be made explicit to meet a modern standard. I would adopt an optimistic position that many of Euler's greatest contributions are immediately publishable in contemporary journals, provided minimal changes are made so as to clarify the nature of the objects as well as the "hidden lemmas".

The verdict is still out on whether the MATHEMATICAL community (as opposed to that of the HISTORIANS of mathematics) will in the end side with Reeder's analysis or Ferraro's analysis.