In this paper, I examine aspects of the methodological debate that originated in 2010, when the distinguished historian of mathematics Sabetai Unguru reviewed Roshdi Rashed’s edition of the Arabic translation of Apollonius’ Conics. In his review, Unguru criticized what Rashed calls ‘l’usage instrumental d’une autre mathématique pour commenter une oeuvre ancienne’. I consider this debate very important and will try to place it within in the discussion of the so-called ‘geometric algebra’ that goes back to the seventies, by tracing the contributions of the main figures who took part in it.

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