Cnidus and Athens · c. 408-c. 355 BCE
Eudoxus of Cnidus
Eudoxus of Cnidus was Greek mathematician and astronomer. His theory of proportion handled incommensurable magnitudes, and his method of exhaustion anticipated integral reasoning.
Biographical and historical reference works document Eudoxus of Cnidus’s role and the mathematical work summarized on this page.
3-5, 6-8, 9-12, College
The person and the work
Biography
Eudoxus of Cnidus was Greek mathematician and astronomer associated with Cnidus and Athens. His theory of proportion handled incommensurable magnitudes, and his method of exhaustion anticipated integral reasoning.
The proportion theory became the foundation of Book V of Euclid’s Elements. Together, these contributions connect fractions, ratios, and percentages, geometry and measurement, and calculus and change to the working problems, tools, and questions of the period.
Mathematical contribution
What this hero added or preserved
Core mathematical work
His theory of proportion handled incommensurable magnitudes, and his method of exhaustion anticipated integral reasoning.
Method, teaching, or application
The proportion theory became the foundation of Book V of Euclid’s Elements.
Why this matters
The larger lesson
Eudoxus of Cnidus shows that mathematics grows through proof, calculation, observation, design, teaching, or careful records. The lasting lesson is that fractions, ratios, and percentages, geometry and measurement, and calculus and change can turn a difficult question into a method another person can inspect and reuse.
Place the work in time
Timeline
- c. 408
Life and working period
Eudoxus of Cnidus worked as Greek mathematician and astronomer in Cnidus and Athens.
- Legacy
Lasting mathematical connection
The proportion theory became the foundation of Book V of Euclid’s Elements.
Key idea
Proportion preserves a relationship
Eudoxus of Cnidus’s work connects quantities by ratio. Scaling both parts by the same factor keeps the relationship unchanged.
The ratio 3:5 scaled by 6 becomes 18:30.
Try it yourself
Scale a ratio
Scale the ratio 3:5 by a factor of 6.
- Multiply the first term by the scale factor.
- Multiply the second term by the same factor.
- Confirm that both ratios simplify to the same value.
Show the answer
The scaled ratio is 18:30.
Math at work
Scientists and astronomers use the same habits
Scientists and astronomers use fractions, ratios, and percentages to plan, compare, test, or communicate decisions. Eudoxus of Cnidus’s work provides a historical example of that connection.
Keep curiosity alive
A little-known fact
The proportion theory became the foundation of Book V of Euclid’s Elements.
Eudoxus of Cnidus matters because of only one famous formula or anecdote.
The documented record is broader: His theory of proportion handled incommensurable magnitudes, and his method of exhaustion anticipated integral reasoning.
Keep exploring
Connected learning paths
Related math terms
- Ratio
- Proportion
- Percentage
- Angle
Practice these ideas
- Fractions & DecimalsWork with fractions, decimals, percentages, and conversions.
- Pre-AlgebraBridge arithmetic and algebra with integers, ratios, and equations.
- GeometryExplore shapes, angles, area, perimeter, volume, and classification.
- Advanced GeometryPractice coordinate geometry, transformations, vectors, and solids.
- Basic CalculusPractice introductory limits, derivatives, and integrals.