[thaumasiotes]

> But is it even clear that Euler's usage of "functiones pares" etymologically corresponds with our "even functions"?

Well, the etymology of "even" doesn't trace to the Latin word "par", or any cognate or ancestor of it. Is it clear that Euler's usage of "pares" is the same sense as our "even functions"? Pretty clear.

The "words" Latin dictionary ( http://archives.nd.edu/whitaker/words.htm ) includes the following gloss of 'par': "s:even, divisible by two". Perseus ( http://www.perseus.tufts.edu/hopper/morph?l=par&la=la#lexico... ) seems to cite this sense back to Horace, glossing the phrase "ludere par impar" as "play 'even and odd'".

I'll also note that par and impar are the Spanish equivalents today of even and odd.

All that, together with the fact that it was translated into English as "even", seems like a pretty strong case that that's what Euler meant.

[pash]

Yep, I looked it up too, and indeed par and impar seem to have been the standard Latin terms for even and odd in the mathematics of the era. See, e.g., Clavius's 1574 translation of Euclid's Elements [0].

0. https://books.google.com/books?id=4Ks7AAAAcAAJ&pg=PA8&lpg=PA...