“The description of right lines and circles, upon which geometry is founded, belongs to mechanics. Geometry does not teach us to draw these lines, but requires them to be drawn.”
- January 4, 1643 – March 31, 1727
- Born in England (UK)
- Natural philosopher, mathematician, physicist, astronomer, theologian
- Proposed the laws of universal gravitation and motion, built the foundations of modern science, and systematized theories of natural philosophy and mathematics.
Quote
“The description of right lines and circles, upon which geometry is founded, belongs to mechanics. Geometry does not teach us to draw these lines, but requires them to be drawn.”
Explanation
In this quote, Isaac Newton is distinguishing between the fields of geometry and mechanics. He suggests that the concepts of right lines (straight lines) and circles, which are fundamental to geometry, are actually derived from mechanics—the study of forces and motion. Newton is emphasizing that geometry does not teach how to physically draw these perfect shapes, but rather assumes that they exist and that they are the idealized forms used in mathematical reasoning. In essence, geometry relies on the idealized shapes of straight lines and circles as theoretical concepts, while mechanics provides the practical foundation for understanding the forces and motions that lead to such shapes in the real world.
This reflects Newton’s broader philosophy that mathematics provides the abstract framework through which we can describe and understand the physical world. While geometry provides the theoretical tools for describing shapes and space, it is mechanics that gives us the context for how these shapes arise or are realized in nature. For example, in the study of planetary motion, gravity and the forces of attraction described by Newton’s laws of motion lead to elliptical orbits that can be approximated by circles and straight lines in certain contexts.
In modern terms, Newton’s statement underscores the relationship between pure mathematics (such as geometry) and applied mathematics (like mechanics), which describes how theoretical concepts can be used to model real-world phenomena. It reflects the idea that mathematical abstraction (geometry) and physical application (mechanics) are closely intertwined, with one relying on the other for both theoretical and practical purposes.
