In his 1557 work The Whetstone of Witte, British mathematician Robert Recorde proposed an exponent notation by prime factorisation, which remained in use up until the eighteenth century and acquired the name Arabic exponent notation. The principle of Arabic exponents was quite similar to Egyptian fractions; large exponents were broken down into smaller prime numbers. Squares and cubes were so called; prime numbers from five onwards were called sursolids.
Although the terms used for defining exponents differed between authors and times, the general system was the primary exponent notation until René Descartes devised the Cartesian exponent notation, which is still used today.
This is a list of Recorde's terms.
Cartesian index Arabic index Recordian symbol Explanation 1 Simple 2 Square (compound form is zenzic) z 3 Cubic cꝭ 4 Zenzizenzic (biquadratic) zz square of squares 5 First sursolid ß first prime exponent greater than three 6 Zenzicubic zcꝭ square of cubes 7 Second sursolid Bß second prime exponent greater than three 8 Zenzizenzizenzic (quadratoquadratoquadratum) zzz square of squared squares 9 Cubicubic cꝭcꝭ cube of cubes 10 Square of first sursolid zß square of five 11 Third sursolid Cß third prime number greater than 3 12 Zenzizenzicubic zzcꝭ square of square of cubes 13 Fourth sursolid Dß 14 Square of second sursolid zBß square of seven 15 Cube of first sursolid cꝭß cube of five 16 Zenzizenzizenzizenzic zzzz "square of squares, squaredly squared" 17 Fifth sursolid Eß 18 Zenzicubicubic zcꝭcꝭ 19 Sixth sursolid Fß 20 Zenzizenzic of first sursolid zzß 21 Cube of second sursolid cꝭBß 22 Square of third sursolid zCß
By comparison, here is a table of prime factors:
+ 1 − 201unit22334225562·377823932102·511111222·31313142·7153·516241717182·3219192022·5+ 21 − 40213·7222·1123232423·32552262·1327332822·72929302·3·531313225333·11342·17355·73622·323737382·19393·134023·5+ 41 − 604141422·3·743434422·114532·5462·2347474824·34972502·52513·175222·135353542·33555·115623·7573·19582·2959596022·3·5+ 61 − 806161622·316332·76426655·13662·3·1167676822·17693·23702·5·771717223·327373742·37753·527622·19777·11782·3·1379798024·5+ 81 − 1008134822·4183838422·3·7855·17862·43873·298823·118989902·32·5917·139222·23933·31942·47955·199625·39797982·729932·1110022·52
See also Surd
External links (references)