Some additional, relevant quotations from that article are the following:
The historian of the XIXth century needs some knowledge of the progress made
by the railway engine; for this he has to depend upon specialists,
but he does not care how the engine works, nor about the gigantic
intellectual effort that went into the creation of thermodynamics.
... Similarly, the development of nautical tables and other aids to navigation is of no little importance for the historian of the XVIIth century England. But the part taken in it by Newton will provide him at best with a footnote; Newton as a keeper of the Mint, or perhaps as the uncle of a great noblemanís mistress, is closer to his interests than Newton the mathematician.
The mathematician does his reading mostly in order to be stimulated to original (or, I may add, sometimes not so original) thoughts; there is no unfairness, I think, in saying that his purpose is more utilitarian than the historianís. Nevertheless, the essential business of both is to deal with mathematical ideas, those of the past, those of the present, and, when they can, those of the future.
In reply to the question "How much mathematical knowledge should one possess in order to deal with mathematical history?"
According to some, little more is required than what was known to the authors one plans to write about; some go so far as to say that the less one knows, the better one is prepared to read those authors with an open mind and avoid anachronisms.
On using modern mathematical ideas in order to understand mathematical ideas of the past:
It is impossible for us to analyze the contents of Books V and VII of Euclid without the concept of group and even that of groups of operators, since the ratios of magnitudes are treated as a multiplicative group operating on the additive group of the magnitudes themselves
Assertions like this one are extreme cases of Weil's willingness to be anachronistic in order to support his historiographical position.
One may read this sentence as the claim that Euclid was actually thinking in terms of groups, in which case the anachronism is patent,
or as the claim that Euclid did not think in these terms, and thus that he did not understand the contens of his own book.
Calculating the Limits of Poetic License:
Fictional Narrative and the History of Mathematics
Leo Corry - Tel Aviv University