10

Irrational numbers were used by the ancient Greeks when they were discovered. The earliest texts did not survive but there are plenty of them in Euclid. Though they are not called numbers. The theory of proportions of Eudoxus-Euclid is equivalent to the theory of real numbers. Euclid's book X contains some very complicated theory of some irrational numbers. ...


5

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 \...


4

Regarding the headline question, Newton, in his text Universal Arithmetick, gave what Leo Corry states may be the first definition of number that included both positive and negative integers, fractions, and irrationals. Here is Newton's definition: By number we understand, not so much a Multitude of Unities as an abstracted ratio of any Quantity, to ...


2

Cauchy was indeed the first, although his version was weaker than the modern one. An intuitive geometric interpretation of the theorem, along with a proof motivated by it, is due to Bonnet. A very well sourced and illustrated account of history of the mean value theorem is A brief history of the mean value theorem by Besenyei, which describes many ...


1

I don't understand French, but it seems that Legendre is the key person who coined these terms. You can use DeepL (www.deepl.com) to translate French. So if one can decipher the definition of le module then l'angle du module will begin to make sense. Module itself is from Latin so there is no difference in French/German/ or English. Can we make sense if we ...


Only top voted, non community-wiki answers of a minimum length are eligible