In the last two decades, studying the possible relations between the history of mathematics and mathematics education has revealed the importance of certain foundational issues concerning the nature, relevance and validity of historical knowledge vis-à-vis problems of teaching and learning, which call for deeper exploration. Reviewing aspects of the corresponding debate points to the complementary character of many concepts (often considered as irreconcilable or antagonistic), the necessity of an appropriate didactical transposition of historical knowledge, and the need for new historical research motivated by didactical questions that contribute to a better understanding and interpretation of historical issues that are still discussed. We aim to contribute along these lines by considering as a case study what has been interpreted by many historians as an 'embarrassing mistake' of Euler in his "Vollständige Anleitungzur Algebra." Based on a well-known didactical problem in elementary arithmetic and algebra on the use of the equality notion and symbol, we argue against this interpretation. This in turn illustrates how didactical and historical research can benefit from each other and points to the need for a didactical transposition of historical knowledge, to be seen as complementary to scholarly historical knowledge rather than as a rival distortion of it.