Post #676533

Here's the first paragraph of the preface to Euler's pre-calculus textbook (Introductio ad analysin infinitorum, 1748) as translated from Latin by ChatGPT. The more things change, the more they stay the same! "I have very often observed that by far the greatest part of the difficulties which hinder students of mathematics in approaching the analysis of the infinite arises from this source: although they scarcely grasp common algebra, they nevertheless attempt to apply their minds to that more sublime art. From this it comes about that they not only remain standing, as it were, at the threshold, but even form distorted notions of that infinite, whose understanding is here brought to their aid. Now, although the analysis of the infinite requires not only a thorough knowledge of algebra but also an acquaintance with all the methods thus far discovered, there nevertheless exist many questions whose development is capable of preparing the minds of learners for that higher science—yet these are either omitted from the usual elements of algebra, or are not treated with sufficient care. For this reason, I do not doubt that the material I have assembled in these books will abundantly supply this deficiency. For I have taken care not only to set forth more fully and distinctly those matters which the analysis of the infinite strictly requires than is commonly done, but also to work through quite a number of problems by which readers may gradually—and almost without realizing it—render the idea of the infinite familiar to themselves. Moreover, I have here resolved many problems 1/2