Complete Instruction in Algebra

established (which is called the measure, or the unit), and thus depends solely upon our discretion; afterwards, that one determines in what proportion the given quantity stands to this measure, which is always indicated by numbers, so that a number is nothing other than the proportion in which one quantity stands to another, which is assumed as the unit.

From this it is clear that all quantities can be expressed by numbers, and therefore the foundation of all mathematical sciences must be placed in the fact that one considers the theory of numbers, and all types of calculations that can occur therein, precisely, and treats them completely.

This fundamental part of mathematics is called Analytic analysis or Algebra.

In analysis, therefore, solely numbers are considered, by which quantities are indicated, without concerning oneself with the particular kind of quantity, as is done in the remaining parts of mathematics.

Arithmetic or the art of calculation deals particularly with numbers, but it extends only to certain types of calculations that occur frequently in common life; on the other hand, analysis encompasses in a general way everything that may occur regarding numbers and their calculation.