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 index	Arabic index	Recordian symbol	Explanation
1	Simple
2	Square (compound form is zenzic)	z
3	Cubic	&
4	Zenzizenzic (biquadratic)	zz	square of squares
5	First sursolid	ß	first prime exponent greater than three
6	Zenzicubic	z&	square of cubes
7	Second sursolid	Bß	second prime exponent greater than three
8	Zenzizenzizenzic (quadratoquadratoquadratum)	zzz	square of squared squares
9	Cubicubic	&&	cube of cubes
10	Square of first sursolid	zß	square of five
11	Third sursolid	Cß	third prime number greater than 3
12	Zenzizenzicubic	zz&	square of square of cubes
13	Fourth sursolid	Dß
14	Square of second sursolid	zBß	square of seven
15	Cube of first sursolid	&ß	cube of five
16	Zenzizenzizenzizenzic	zzzz	"square of squares, squaredly squared"
17	Fifth sursolid	Eß
18	Zenzicubicubic	z&&
19	Sixth sursolid	Fß
20	Zenzizenzic of first sursolid	zzß
21	Cube of second sursolid	&Bß
22	Square of third sursolid	zCß

By comparison, here is a table of prime factors:

1 − 20 1 unit 2 2 3 3 4 22 5 5 6 2·3 7 7 8 23 9 32 10 2·5 11 11 12 22·3 13 13 14 2·7 15 3·5 16 24 17 17 18 2·32 19 19 20 22·5

21 − 40 21 3·7 22 2·11 23 23 24 23·3 25 52 26 2·13 27 33 28 22·7 29 29 30 2·3·5 31 31 32 25 33 3·11 34 2·17 35 5·7 36 22·32 37 37 38 2·19 39 3·13 40 23·5

41 − 60 41 41 42 2·3·7 43 43 44 22·11 45 32·5 46 2·23 47 47 48 24·3 49 72 50 2·52 51 3·17 52 22·13 53 53 54 2·33 55 5·11 56 23·7 57 3·19 58 2·29 59 59 60 22·3·5

61 − 80 61 61 62 2·31 63 32·7 64 26 65 5·13 66 2·3·11 67 67 68 22·17 69 3·23 70 2·5·7 71 71 72 23·32 73 73 74 2·37 75 3·52 76 22·19 77 7·11 78 2·3·13 79 79 80 24·5

81 − 100 81 34 82 2·41 83 83 84 22·3·7 85 5·17 86 2·43 87 3·29 88 23·11 89 89 90 2·32·5 91 7·13 92 22·23 93 3·31 94 2·47 95 5·19 96 25·3 97 97 98 2·72 99 32·11 100 22·52

See also

• Surd

External links (references)

• Mathematical dictionary, Chas Hutton, pg 224