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 (compound form is zenzic)z
3Cubic&
4Zenzizenzic (biquadratic)zzsquare of squares
5First sursolidszfirst prime exponent greater than three
6Zenzicubicz&square of cubes
7Second sursolidBszsecond prime exponent greater than three
8Zenzizenzizenzic (quadratoquadratoquadratum)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:

1 20
1unit
22
33
422
55
62·3
77
823
932
102·5
1111
1222·3
1313
142·7
153·5
1624
1717
182·32
1919
2022·5
21 40
213·7
222·11
2323
2423·3
2552
262·13
2733
2822·7
2929
302·3·5
3131
3225
333·11
342·17
355·7
3622·32
3737
382·19
393·13
4023·5
41 60
4141
422·3·7
4343
4422·11
4532·5
462·23
4747
4824·3
4972
502·52
513·17
5222·13
5353
542·33
555·11
5623·7
573·19
582·29
5959
6022·3·5
61 80
6161
622·31
6332·7
6426
655·13
662·3·11
6767
6822·17
693·23
702·5·7
7171
7223·32
7373
742·37
753·52
7622·19
777·11
782·3·13
7979
8024·5
81 100
8134
822·41
8383
8422·3·7
855·17
862·43
873·29
8823·11
8989
902·32·5
917·13
9222·23
933·31
942·47
955·19
9625·3
9797
982·72
9932·11
10022·52

See also


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