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Although the large number of constructions may be accomplished this way , we know of three problems dating from Greek era nnoindent that cannot be solved in that way : nquad duplication ( doubling ) of a cube −− to find a side of a cube whose volume is twice that of a given cube ; nquad tris ection of an angle −− to find one third of a given angle ; squaring a circle −− to construct the square that has the same area as a given circle . Unsolved problems of that kind initiated a completely new way of thinking −− how would it be possible to prove that certain pro b lems could not be s o lved $ ? $ nquad The nnoindent answer is in modern algebra and group theory . nquad The problem of solving algebraic equations dates far back in the past and for a long time it was the central content of algebra . Descriptions of solving certain simple algebraic equations had appeared nnoindent as early as 2000 years B . C , for example in Egypt , nquad during the Middle Dynasty , in the London papyrus known as Ahmess calculation , nquad and on Babylonian tiles , nnoindent approximately at the same time . nquad The Babylonians were able to solve quadratic equations , while in the XVI century Girolamo Cardano , Nicolo Tartaglia , Lodoviko 52 .. A period Grozdani acute-c sub comma G period Vojvodi c-acute nnoindentFerari comma52 n ..quad ScipioneA .del Grozdani Ferro and many $ nacute othersf werecg dealingf , g with$ G solving . Vojvodi cubic and $ nacutefcg $ quadratic equations period nnoindentFor a longF time e r a commar i , nquad .. the questionScipione concerning del Ferro the possibility and many to solve others algebraic were dealing with solving cubic and quadraticequations by equations radicals remained . open in algebra period For an algebraic equation we shall say that it is solvable by radicals if its solutions may be obtained by using rational For a long time , nquad the question concerning the possibility to solve algebraic operations open52 parenthesisA .