Chapter I – Of the Addition of Compound Quantities
Summary: Explains how to add compound expressions by removing parentheses, preserving each term’s sign, and then combining only like terms. (source: chapter-1.2.1)
Sources: chapter-1.2.1
Last updated: 2026-04-26
§256–260: Writing and Performing the Sum
Euler represents the sum of compound expressions with parentheses, for example . (source: chapter-1.2.1)
To perform the addition, he removes the parentheses and writes every term with its proper sign:
(source: chapter-1.2.1)
The same rule applies when some terms are negative, so adding to gives
(source: chapter-1.2.1)
Euler also states that the order of the terms may be changed without changing the sum, provided the signs are preserved. (source: chapter-1.2.1)
§261: Reducing the Sum by Combining Like Terms
After the terms are written out, entirely similar terms may be combined into a shorter expression. (source: chapter-1.2.1)
Examples include:
(source: chapter-1.2.1)
Euler distinguishes these from unlike terms such as , which cannot be reduced to a single term. (source: chapter-1.2.1)
§262: Sum Plus Difference
Euler observes that adding the sum and difference of two numbers gives twice the greater:
(source: chapter-1.2.1)
He then illustrates the same method on longer algebraic expressions containing powers and radicals. (source: chapter-1.2.1)