Chapter I – Of Mathematics in General
Summary: Defines magnitude as anything capable of increase or diminution, establishes that a number is the proportion of a magnitude to a chosen unit, and identifies algebra (analysis) as the foundational science of all mathematics.
Sources: chapter-1.1.1
Last updated: 2026-04-24
§1–2: Magnitude and the Branches of Mathematics
Magnitude (or quantity) is whatever is capable of increase or diminution — money, weight, length, and so forth. Because magnitudes are of many different kinds, mathematics splits into distinct branches, each devoted to one kind. Mathematics in general is the science of quantity, or the science that investigates means of measuring quantity (source: chapter-1.1.1).
§3–4: Measurement and the Unit
To determine any magnitude we must:
- 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).
- Express the proposed magnitude as a proportion to that unit.
This proportion is always expressed by a number. Hence: a number is the proportion of one magnitude to another arbitrarily assumed as the unit (source: chapter-1.1.1).
§5: Algebra as the Foundation
Since all magnitudes reduce to numbers, the foundation of all mathematical sciences is a complete treatise on numbers and on all possible methods of calculation. This fundamental part of mathematics is called Analysis, or Algebra (source: chapter-1.1.1).