Canon arithmeticus
{{Short description|1839 mathematical tables by Carl Jacobi}}
{{italic title}}
File:Title page of Jacobi's Canon Arithmeticus, published in 1839.png
The Canon arithmeticus is a set of mathematical tables of indices and powers with respect to primitive roots for prime powers less than 1000, originally published by {{harvs|txt|authorlink=Carl Gustav Jacob Jacobi | first=Carl Gustav Jacob|last= Jacobi|year=1839}}, with introductory text in Latin. The tables were at one time used for arithmetical calculations modulo prime powers, though like many mathematical tables, they have now been replaced by digital computers. Jacobi also reproduced Burkhardt's table of the periods of decimal fractions of 1/p and Ostrogradsky's tables of primitive roots of primes less than 200 and gave tables of indices of some odd numbers modulo powers of 2 with respect to the base 3 {{harv|Dickson|2005|p=185–186}}.
Although the second edition of 1956 has Jacobi's name on the title, it has little in common with the first edition apart from the topic: the tables were completely recalculated, usually with a different choice of primitive root, by Wilhelm Patz. Jacobi's original tables use 10 or −10 or a number with a small power of this form as the primitive root whenever possible, while the second edition uses the smallest possible positive primitive root {{harv|Fletcher|1958}}.
The term "canon arithmeticus" is occasionally used to mean any table of indices and powers of primitive roots.
References
- {{Citation | last1=Dickson | first1=Leonard Eugene | author1-link=Leonard Eugene Dickson | title=History of the theory of numbers |volume=I: Divisibility and primality | orig-date=1919 | url=https://archive.org/details/historyoftheoryo01dick | publisher=Dover Publications | location=New York | isbn=978-0-486-44232-7 |mr=0245499 | year=2005}}
- {{Citation | last1=Fletcher | first1=A. | title=Canon Arithmeticus by C. G. J. Jacobi; H. Brandt | jstor=3608400 | publisher=The Mathematical Association | series=Review | year=1958 | journal=The Mathematical Gazette | issn=0025-5572 | volume=42 | issue=339 | pages=76–77| doi=10.2307/3608400 | s2cid=246262528 }}
- {{Citation | last1=Jacobi | first1=Carl Gustav Jacob | title=Canon arithmeticus | lang=la | url=https://archive.org/details/canonarithmetic00jacogoog | publisher=Typis Academicis, Berolini | location=Berlin | series= sive tabulae quibus exhibentur pro singulis numeris primis vel primorum potestatibus infra 1000 numeri ad datos indices et indices ad datos numeros pertinentes |mr=0081559 | year=1839}}
- {{Citation | last1=Jacobi | first1=Carl Gustav Jacob | editor1-last=Brandt | editor1-first=Heinrich | editor2-last=Patz | editor2-first=Wilhelm | title=Canon arithmeticus | lang=de | orig-date=1839 | url=https://books.google.com/books?id=tsYfAAAAIAAJ | publisher=Akademie-Verlag | location=Berlin | series=Mathematische Lehrbücher und Monographien: Mathematische Monographien |mr=0081559 | year=1956 | volume=2}}
See also
- A. W. Faber Model 366, a discrete slide rule incorporating similar concepts to the Canon arithmeticus
External links
- The 1839 edition of the [https://archive.org/details/canonarithmeticu00jaco_0/page/n1/mode/2up Canon arithmeticus] at the Internet Archive
Category:History of mathematics
Category:19th-century books in Latin
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