<< How old is the term "Golden section"? Jeff Miller's web page on the earliest occurrences of mathematical terms has a rather definite reference to a textbook in German by Ohm, of 1835, where the term "Goldener Schnitt" is used; he has another quotation: a certain Baravalle claimed that sectio aurea was used by Leonardo da Vinci. >>
There's a long discussion of the situation at the end of
Roger Herz-Fischler, A Mathematical History of Division in Extreme and Mean Ratio, Waterloo: Laurier: 1987, reprinted by Dover under the different title A Mathematical History of the Golden Section [alas!], date?
(I have copies of both, but cannot now find either of them.) An opening section of an article of mine also discusses the issue:
A generalisation of the golden section, Fibonacci Quarterly 20 (1982), 146-158.
The situation, at least in 1987, was what Peter Flor says: the first *known* use of 'golden section' was in Ohm's book of 1835. (That is Martin Ohm, the younger brother of Georg Ohm of Ohm's Law.) But Ohm's use of it is so easy and straightforward that it is not impossible that it had been used elsewhere, though nothing more was known about that in 1987. The first use in English seems to be in Chrystal, Introduction to Algebra, 1890.
On the other hand, I am sceptical that Leonardo used 'sectio aurea'. I can't remember what R H-F says, but I knew of nothing *in Latin* before D'Arcy Thompson, On Growth and Form, 1st ed (only) 1917!
The story is quite complicated - indeed as is the history of the construction itself - and I can best recommend Roger H-F's book to you, for this and 1000 other things about the construction.