Number theory
While the word "algorithm" goes back only to certain readers of al-Khwārizmī, careful descriptions of methods of solution are older than proofs: such methods (that is, algorithms) are as old as any recognisable mathematics—ancient Egyptian, Babylonian, Vedic, Chinese—whereas proofs appeared only with the Greeks of the classical period.
An interesting early case is that of what we now call the Euclidean algorithm. In its basic form (namely, as an algorithm for computing the greatest common divisor) it appears as Proposition 2 of Book VII in "Elements", together with a proof of correctness. However, in the form that is often used in number theory (namely, as an algorithm for finding integer solutions to an equation formula_78,
or, what is the same, for finding the quantities whose existence is assured by the Chinese remainder theorem) it first appears in the works of Āryabhaṭa (5th–6th century CE) as an algorithm called
"kuṭṭaka" ("pulveriser"), without a proof of correctness.
Anarchism
The word "anarchism" is composed from the word "anarchy" and the suffix -ism, themselves derived respectively from the Greek , i.e. "anarchy" (from , "anarchos", meaning "one without rulers"; from the privative prefix ἀν- ("an-", i.e. "without") and , "archos", i.e. "leader", "ruler"; (cf. "archon" or , "arkhē", i.e. "authority", "sovereignty", "realm", "magistracy")) and the suffix or ("-ismos", "-isma", from the verbal infinitive suffix , "-izein"). The first known use of this word was in 1539. Various factions within the French Revolution labelled opponents as anarchists (as Maximilien Robespierre did the Hébertists) although few shared many views of later anarchists. There would be many revolutionaries of the early nineteenth century who contributed to the anarchist doctrines of the next generation, such as William Godwin and Wilhelm Weitling, but they did not use the word "anarchist" or "anarchism" in describing themselves or their beliefs.