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Answer(s) to the question What is a 3rd-order Fresnel lens? are disappointing to me, in that the term 3rd order does not refer to anything like a third-order series expansion.

But this leads me to a new question: When did the use of an expression like "third order approximation" come into use in naming such a thing as a third-order series expansion?

And if it can be narrowed down sufficiently, is there any idea of who it was who first used it this way?

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    $\begingroup$ According to Jeff Miller: ORDER (degree) is found in English in 1706 in Ditton, Fluxions 22: "An Infinitesimal of another Order or Degree" and ibid. 123: "These sorts of [Exponential] Quantities are of several Orders or Degrees" [OED]. $\endgroup$ – Michael Bächtold Apr 16 at 15:07
  • $\begingroup$ @MichaelBächtold that certainly sounds exactly like what I'm after. OED means he is quoting the Oxford English Dictionary? $\endgroup$ – uhoh Apr 16 at 15:11
  • $\begingroup$ With "lenses, divided into four orders based on their size and focal length" Fresnel used the original Latin meaning of ordo, row, line, rank, which predates the order of approximation by centuries, see Online Etymology Dictionary. $\endgroup$ – Conifold Apr 16 at 18:16
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    $\begingroup$ @uhoh Yes, OED means Oxford English Dictionary. jeff560.tripod.com/sources.html $\endgroup$ – Michael Bächtold Apr 16 at 21:06
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    $\begingroup$ No, I haven't read that. It is a little ambiguous in the post what "such a thing" refers to. In any case, no harm in people finding out both things. $\endgroup$ – Conifold Apr 16 at 23:01

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