Magnitude
Summary: The foundational concept of Euler’s algebra — anything capable of increase or diminution — which mathematics seeks to measure by comparing it to a chosen unit.
Sources: chapter-1.1.1
Last updated: 2026-04-24
Definition
Magnitude (or quantity) is whatever is capable of increase or diminution (source: chapter-1.1.1). Examples: a sum of money, a weight, a length of rope.
Measurement
To measure a magnitude, choose a known magnitude of the same kind as the unit (e.g., a foot for length, a pound for weight, a crown for money), then express the ratio of the proposed magnitude to the unit. This ratio is always a number. Hence:
A number is nothing but the proportion of one magnitude to another arbitrarily assumed as the unit.
(source: chapter-1.1.1)
Implications
- All magnitudes reduce to numbers.
- The choice of unit is arbitrary; the resulting number changes when the unit changes.
- Different species of magnitude require different units.
- The science of measuring all quantity is called Algebra or Analysis — see ch1.1.1-mathematics-in-general.