On Avienna's "The Arithmetic"
Abu Ali al - Husain ibn Abdullah ibn Sina, also known under the Latinized name Avicenna is a very well known Muslim polymath of the eleventh century. He is born c. 980 near Bukhara (Uzbekistan) and died 1037 in Hamadan (Iran). His major fields of expertise are medicine and philosophy and his book The Canoon of Medicine was the major textbook in medicine for hundreds of years. He also wrote The Book of Healing, which is an encyclopedic - ca. 28 books in almost all sciences of his era. It contains volumes of medicine, philosophy, logic, geology, biology, music, astronomy as well as arithmetic and geometry.
In this lecture we analyze the first essay of Avicenna's volume of The Healing Book, on arithmetic. We first introduce the contents of the essay, which involves, but is not limited to, numerical sequences, their sums and properties, theories on perfect, abundant and deficient numbers as well as amicable pairs. We also introduce some first order difference equations and their solutions as demonstrated in the mentioned article. Then we investigate the methodology of Avicenna and the originality of his works in mathematics. For the last task we make comparisons with Avicenna's work and the works of some Muslim and Greek ma thematicians.