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As @Dave L Renfro noticed, the distinction between series and sequence is not old, and it was possible for the same author to use the two terms with different meanings (also in the same article). Consider e.g. Gauss's Theoria Residuorum Biquadraticorum Commentatio Prima & Commentatio Secunda, we have some examples: article 5 cunctos numeros $1, 2, 3 \... 6 The origins of all of the companion terms parabola, hyperbola, and ellipse were coined by Apollonius of Perga, in his classic text "On Conic Sections." (He was born about 262 BC, approximately 25 years after the birth of Archimedes.) The terms we use are direct descendants of the Greek words. Now, the reason they have the names they is that in the ... 15 As to why the conic section got called ellipse, the introductory chapter of Toomer, Diocles, On Burning Mirrors is interesting. He does not give a conclusive answer, but here's an excerpt, p. 7: Apollonius found symptomata for all three curves, and defined them by the method of "application of areas", which was the standard Greek procedure for formulating ... 8 This may not be "etymological", but may perhaps shed some light on the relationship between E/P/H things in mathematics: A. Rastegar, EPH-classifications in Geometry, Algebra, Analysis and Arithmetic (2015). 34 The origin of all these uses is very different. Joe Silverman explained the genesis of the sequence ellipse$\rightarrow$elliptic integral$\rightarrow$elliptic function$\rightarrow$elliptic curve. Another large class of occurences of the word "elliptic" is connected with "trichotomies", that is classifications of some objects into three classes. Such ... 47 Your saying "elliptic functions are the functions on elliptic curves over$\mathbb C\$" is somewhat misleading, I think. First came elliptic integrals measuring arc-length on an ellipse. These are generalizations of the inverse trig functions (take the ellipse to be a circle). The inverse functions to the elliptic integrals are elliptic functions. It was ...