Compound Quantities
Summary: Compound quantities are algebraic expressions made of several terms joined by plus or minus signs, and Euler treats them as the basic objects of Section II. (source: chapter-1.2.1, source: chapter-1.2.2, source: chapter-1.2.3, source: chapter-1.2.4)
Sources: chapter-1.2.1, chapter-1.2.2, chapter-1.2.3, chapter-1.2.4
Last updated: 2026-04-26
Definition
Expressions such as and are treated as single quantities even though they contain several terms. Euler encloses them in parentheses when he wants to show that the whole expression is being added, subtracted, multiplied, or divided. (source: chapter-1.2.1, source: chapter-1.2.2, source: chapter-1.2.3, source: chapter-1.2.4)
Basic Operations
Addition of compound quantities is performed by dropping parentheses and preserving each term’s sign. (source: chapter-1.2.1)
Subtraction is performed by changing the signs of every term in the expression being subtracted. (source: chapter-1.2.2)
Multiplication distributes each term of one compound quantity across every term of the other. (source: chapter-1.2.3)
Division is straightforward when the divisor is simple, but for a compound divisor it may require a term-by-term search for the quotient or else remain an unreduced fraction. (source: chapter-1.2.4)
Importance
This section marks a shift from arithmetic with single numbers and fractions to symbolic manipulation of general expressions. (source: chapter-1.2.1, source: chapter-1.2.2, source: chapter-1.2.3, source: chapter-1.2.4)