Prime factor exponent notation


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 indexArabic indexRecordian symbolExplanation
1Simple-
2Square z-
3Cubic&-
4Zenzizenzic zzsquare of squares
5First sursolidszfirst prime exponent greater than three
6Zenzicubicz&square of cubes
7Second sursolidBszsecond prime exponent greater than three
8Zenzizenzizenzic zzzsquare of squared squares
9Cubicubic&&cube of cubes
10Square of first sursolidzszsquare of five
11Third sursolidcszthird prime number greater than 3
12Zenzizenzicubiczz&square of square of cubes
13Fourth sursoliddsz
14Square of second sursolidzbszsquare of seven
15Cube of first sursolid&szcube of five
16Zenzizenzizenzizenziczzzz"square of squares, squaredly squared"
17Fifth sursolidesz-
18Zenzicubicubicz&&-
19Sixth sursolidfsz-
20Zenzizenzic of first sursolidzzsz-
21Cube of second sursolid&bsz-
22Square of third sursolidzcsz-

By comparison, here is a table of prime factors:

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