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Lucky you! (or me :-) ). This question was answered a while back on Math.SE I found his original thoughts in the translated version of "Institutiones calculi differentialis cum eius usu in analysi finitorum ac doctrina serierum, volume 1", chapter 7. The translation is called "Foundations of Differential Calculus" and a link is found here https://...


The earliest reference I can find to "banana brackets" is in: G. Malcolm. Data structures and program transformation. Science of Computer Programming, 14(2-3):255-280, October 1990. Where they are clearly crescent-moon/banana shaped symbols: ⦅...⦆. The later style using $($ and $|$ seems to be a typographic practicality, and is used by ...


On page 10 of that book the author wrote The most important example of a ground field is the field of common rational numbers for which I use the freely invented symbol 9... where he uses the symbol in question instead of the 9 that I used above.


When introducing the older terminology in the previous sentence, Peano describes it thus: ... signifie "il y a des a", "les a existent"... It seems likely this is the source of the inverted "E".

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