Newton’s Principia of Mathematics

In summary: The book you are recommending is Cohen and Whitman's translation of the Principia. It is a modern translation, and it has an extensive commentary by the translators. It is a book you can study in depth and then attempt to read Newton's work.
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Summary:: What kind of geometry/Math do I need to understand to read this book?

Hey people!

I would like to know what kind of geometry and/or math would I need to understand this book. I skimmed through it( The translated version by Florian Cajori) and seen that it gets technical with shapes.
 
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Principia is a 335 year old book that uses mathematical and geometrical concepts, wording, and terminology common to that era, making it very difficult for modern readers to understand. I suggest getting a version that breaks everything down into modern language if you can find one.
 
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Drakkith said:
Principia is a 335 year old book that uses mathematical and geometrical concepts, wording, and terminology common to that era, making it very difficult for modern readers to understand. I suggest getting a version that breaks everything down into modern language if you can find one.
I found a book that was translated, however I would like to know the math before I dive in. I read that it was synthetic geometry and some other geometry, maybe Euclidean?
 
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Vividly said:
I found a book that was translated, however I would like to know the math before I dive in. I read that it was synthetic geometry and some other geometry, maybe Euclidean?
I've never heard of "synthetic geometry," but Euclidean geometry is just the standard geometry like what used to be taught in the 10th grade in US high schools.

My recommendation is to not try to study calculus by way of Newton's Principia, translated or not. In another thread you mentioned that your approach was to do a deep dive in topics in your physics class, but that doesn't seem to be working out so well, as you said you were struggling with that class.

Rather than trying to make sense of the Principia my recommendation would be to focus first on whatever more modern calculus book you're studying from. After you've gotten through whatever problems are assigned to you, then you could take a stab at Newton's work.
 
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"Synthetic geometry" is what is taught in school. The other way to describe geometry is "analytical geometry", and that's of course the modern and adequate way to describe physics (and a huge part of physics is, from a mathematical point of view, indeed (analytical) geometry in a very modern sense, proposed by Riemann and Klein). Reading the Principia shows, how far you can get also with synthetic geometry, but comparing it to the way we do "Newtonian mechanics" today (which is the version by Euler, Lagrange, Laplace, et al rather than Newton).
 
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Per wiki:

Synthetic geometry (sometimes referred to as axiomatic geometry or even pure geometry) is the study of geometry without the use of coordinates or formulae. It relies on the axiomatic method and the tools directly related to them, that is, compass and straightedge, to draw conclusions and solve problems.

Only after the introduction of coordinate methods was there a reason to introduce the term "synthetic geometry" to distinguish this approach to geometry from other approaches. Other approaches to geometry are embodied in analytic and algebraic geometries, where one would use analysis and algebraic techniques to obtain geometric results.

According to Felix Klein

Synthetic geometry is that which studies figures as such, without recourse to formulae, whereas analytic geometry consistently makes use of such formulae as can be written down after the adoption of an appropriate system of coordinates.[1]
 
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Related to Newton’s Principia of Mathematics

1. What is "Newton's Principia of Mathematics"?

"Newton's Principia of Mathematics" is a book written by Sir Isaac Newton and published in 1687. It is considered one of the most influential works in the history of science, as it laid the foundation for classical mechanics and introduced the laws of motion and universal gravitation.

2. What are the main principles discussed in "Newton's Principia of Mathematics"?

The main principles discussed in "Newton's Principia of Mathematics" are the three laws of motion, the law of universal gravitation, and the concept of inertia. These principles explain the behavior of objects in motion and the force of gravity between them.

3. How did "Newton's Principia of Mathematics" impact the scientific community?

"Newton's Principia of Mathematics" revolutionized the scientific community by providing a mathematical explanation for the motion of objects and the force of gravity. It also introduced the concept of a universal law of nature, which greatly influenced the development of modern physics and astronomy.

4. What are some of the key contributions of "Newton's Principia of Mathematics"?

"Newton's Principia of Mathematics" made several key contributions to the field of science, including the development of calculus, the laws of motion, and the concept of universal gravitation. It also introduced the concept of a mathematical model for understanding and predicting the behavior of objects in motion.

5. How is "Newton's Principia of Mathematics" relevant today?

"Newton's Principia of Mathematics" is still relevant today as it laid the foundation for classical mechanics, which is still used to explain the motion of objects on Earth. It also introduced the concept of a universal law of nature, which continues to influence scientific thinking and research. Additionally, many of the mathematical principles and equations introduced in the book are still used in modern physics and engineering.

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