Who coined the term ‘polity’?

the definition of polity 

1530-40; < Latin polītīa < Greek polīteía citizenship, government, form of government, commonwealth, equivalent to polī́te-, variant stem of polī́tēs citizen

Online Etymology Dictionary

1530s, from Middle French politie (early 15c.) or directly from Late Latin polita “organized government” (see policy (n.1)).

Policy and Police ultimately derive from the same Greek word, but more directly reflect the Latin/French sense of “public order”.

Politeia is a term that gets a lot of use in Classical Greek philosophy, both Plato (it’s the term translated as The Republic) and  Aristotle (in his Constitution of the Athenians , the first comprehensive survey of political systems).

The 1530s import of the term directly from Greek/Latin, rather than via French (the tell-tale –c-) points for me to Renaissance rediscovery of the Classics….

… and looking up the OED 1st edition, I’m wrong: the 1530s instance has the same meaning as the French, “public order”. (I wonder if the French politie was a re-Latinisation? OED says it dates from 1419.)

Definition of polity (Aha! So OED content *is* free online…)

1538 STARKEY England 1.ii.51 Pepul, rude, wythout polyty, can not vse that same [riches] to theyr owne commodyte

That’s this guy: Thomas Starkey . The text is A supplicacyon for the beggers : Fish, Simon, d. 1531 : Free Download & Streaming : Internet Archive  (mislabelled)

The modern meaning “2. a. A particular form of political organization, a form of government.”, which corresponds directly to the Ancient Greek sense, seems to be first attested in:

1597 Hooker Eccl. Pol. v. lxxix. §3 We preferre..the Spartan before the Athenian Politie. – See more at: http://findwords.info/term/polit…

Looks pretty clearly like an allusion to Aristotle. That’s Richard Hooker , in his book entitled—would you believe it: Of the Lawes of Ecclesiastical Politie (which still refers to the “policy” sense). The quote is here: Online Library of Liberty

if all men be taught of nature to wish and as much as in them lieth to procure the perpetuity of good things, if for that very cause we honour and admire their wisdom who having been founders of commonweals could devise how to make the benefit they left behind them durable, if especially in this respect we prefer Lycurgus before Solon and the Spartan before the Athenian polity, it must needs follow that as we do unto God very acceptable service in honouring him with our substance, so our service that way is then most acceptable when it tendeth to perpetuity.

What is the word for the endless process of defining words within definitions?

EDITED: The term you are looking for is Definitional chain. See e.g. Introducing Semantics

Originally:

The term you are looking for is: Circular definition .

Murad Abraham points out in comments that’s not what he was looking for.

What is the answer to a multiplication problem called? Who coined the term?

Product (mathematics) . The Greek for it is the participle γενόμενον, “what has become, what has come into existence”, which I would assume was calqued into Latin as “what is produced”. The LSJ dictionary lists the participle “what has become” for product as being used in Euclid ; but the verb “becomes” for “adds up to…” is already used in Plato.

LSJ reports that δύναμαι “to be capable” was used for “is the result of multiplying two numbers” in Pappus of Alexandria , 600 years after Euclid; so “product” was not the only possible way it could have been named.