Del III: Matematikk og fysikk: Frederich Arentz Undersøgning, hvorledes man paa den korteste Maade kan opløse saadanne Æqvationer,som inneholde flere eller mange ubekiendte Størrelser tillige

Abstract

Frederich Christian Holberg Arentz was born in 1736 and died in 1825. He graduated in theology at the University of Copenhagen in 1756, and then studied philosophy and mathematics at the University of Copenhagen, and physics and mathematics in Leiden. From 1760 to 1825 he was a high school teacher and from 1781 rector of the Cathedral School in Bergen. He became a remarkably learned person in several diciplines, and he was awarded a titular professorship in 1806. He was elected a member of DKNVS in 1774.

Arentz published three mathematical treatises in DKNVS Skrifter, one in 1788 and the other two in the volume for 1824─1827. These last two are of little interest today. The first one has in English translation the title «Investigation on how one in the shortest manner can solve such equations, which contain several or many unknown quantities». Here Arentz developes independently of earlier authors a method equivalent to Cramer’s rule for solution of systems of equations, without explicit determinant notation. He constructs tables for calculation of the denominators of the solutions of n equations with n unknown variables, for n =1,2,3,4,5,6. (The numerators then follow by the stated rule.) Since there are n! terms in each denominator, there are 720 terms when n=6, and the corresponding table covers five pages in the treatise.