An Illustration of Arithmetic from the Margarita Philosophica

This illustration of arithmetic is from the Margarita Philosophica which first came out in 1503. Arithmetic is illustrated by a beautiful lady holding a book in each hand. Sitting at two tables are Boethius and Pythagoras. In the 15th century people thought that these two men had done the most important work in the theory of arithmetic.

Boethius was born in Rome in A.D. 475 and died in Pavia in Italy in 524. He was one of the cleverest men of his day. He translated texts from Greek to Latin and wrote commentaries on the works of Greek philosophers like Aristotle and Plato. He also wrote two important works about mathematics: one was about arithmetic and one was about geometry. These works were quite basic but were used a lot in Europe for many centuries for teaching maths.

Pythagoras is a famous Greek mathematician. He was born about 570 B.C. and died about 475 B.C. Everything that Pythagoras wrote has already been destroyed but he is still remembered for many important discoveries in mathematics. We know about the discoveries he made because many of the mathematicians who lived after him wrote about them. The thing that Pythagoras is most remembered for is 'Pythagoras's Theorem'. Everyone who studies maths learns Pythagoras's Theorem. It says that in a right-angled triangle the square on the hypotenuse is equal to the sum of squares on the other two sides.

In the illustration Boethius and Pythagoras are shown sitting at two tables. On one table Boethius is doing a calculation using Hindu-Arabic numerals. On the other table Pythagoras is doing a sum using a simple abacus or a counting board. Hindu-Arabic numerals are the numerals we use today and are sometimes just called Arabic numerals, as opposed to Roman numerals. They were invented in about 200 B.C. in northern India, more than 200 years after Pythagoras died. However, they were not very popular until Arabic mathematicians started using them in about A.D. 800. They still weren't used in Western Europe until about 300 years later.

The illustration is supposed to show how much better Arabic numerals are than a simple abacus for doing calculations in arithmetic. In the Middle Ages it was thought that Boethius had invented Arabic numerals, which is why he is shown in this picture, although we now know that Arabic numerals didn't get to Western Europe until long after Boethius had died