Mathematicians

3. Invented methods for calculating areas, volumes, and surface areas, and formulated a principle explaining buoyancy, along with contributions to mechanics.
6. Developed a structured system of logic, including syllogistic reasoning, which became an essential tool in mathematical proof and formal logic.
9. Contributed to number theory and laid philosophical foundations influencing mathematical concepts of numbers and shapes.
11. Advanced models of planetary motion in a comprehensive astronomical text, using geometric models to predict celestial movements.
12. Created early trigonometric tables and is credited with founding trigonometry, essential for mathematical astronomy.
14. Contributed to the study and teaching of algebra and geometry, preserving and advancing mathematical knowledge from Greek sources.

1. Calculated the circumference of Earth with impressive accuracy and developed a method for identifying prime numbers.
2. Proposed early ideas on infinitesimals, offering philosophical insights that contributed to concepts of continuity and the infinite.
4. Made pioneering contributions to algebra by exploring solutions to equations, which laid early foundations for algebraic thinking.
5. Devised a formula for finding the area of a triangle given its side lengths, as well as advancements in mechanics and engineering.
7. Known for studying curves, particularly the cissoid, which he used to address problems like doubling the cube, aiding future developments in geometry.
8. Developed a theorem establishing a relationship among the sides of a right triangle, which became fundamental in geometry and trigonometry.
10. Created a systematic and logical framework for geometry, including definitions, postulates, and proofs, which became foundational for the field.
13. Used inscribed polygons to approximate the area of a circle, an early step toward integral calculus.
15. Applied deductive reasoning in geometry, including proving that a triangle inscribed in a semicircle is a right triangle, and introduced early geometric theorems.