I've read the following quote on Wanner's Analysis by Its History:
... our students of mathematics would profit much more from a study of Euler's Introductio in analysin infinitorum, rather than of the available modern textbooks.
(André Weil, 1979; quoted by J.D. Blanton, 1988, p. xii)
I got the mentioned book (there is a translated version published by Springer) and it seems a nice read. The translator mentions in the preface that the standard analysis courses puts low emphasis in the ordinary treatise of the elements of algebra and also that he fixes this defect.
My concern at the moment is that the book may be dated but André Weil said it's a worthy read, I'd like to know if someone already read Euler's book and some modern introduction to analysis to make a fair comparison. It's important to notice that although the book is a translation, the translator made some edits in several parts of the book, I guess that with the intention of making it a readable piece for today's needs.