Isidore’s source in the De Arithmetica was Cassiodorus,[240] whom he copies with little change; while Cassiodorus’ work was apparently a bare abstract of Boethius’ translation of Nicomachus. Isidore’s account is of great brevity and contains a number of unexplained technical terms.
EXTRACTS
Preface. Mathematics is called in Latin doctrinalis scientia. It considers abstract quantity. For that is abstract quantity which we treat by reason alone, separating it by the intellect from the material or from other non-essentials, as for example, equal, unequal, or the like. And there are four sorts of mathematics, namely, arithmetic, geometry, music and astronomy. Arithmetic is the science of numerical quantity in itself. Geometry is the science of magnitude and forms.[241] Music is the science that treats of numbers that are found in sounds. Astronomy is the science that contemplates the courses of the heavenly bodies and their figures, and all the phenomena of the stars. These sciences we shall next describe at a little greater length in order that their significance may be fully shown.
Chapter 1. On the name of the science of arithmetic.
1. Arithmetic is the science of numbers. For the Greeks call number ἀριθμός. The writers of secular literature have decided that it is first among the mathematical sciences since it needs no other science for its own existence.
2. But music and geometry and astronomy, which follow, need its aid in order to be and exist.
Chapter 2. On the writers.
1. They say that Pythagoras was the first among the Greeks to write of the science of number, and that it was later described more fully by Nicomachus, whose work Apuleius first, and then Boethius, translated into Latin.
Chapter 3. What number is.
1. Number is multitude made up of units. For one is the seed of number but not number. Nummus (coin) gave its name to numerus (number), and from being frequently used originated the word.