Newton's "Principia Mathematica": Understanding the Hard Parts

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Discussion Overview

The discussion revolves around the challenges of reading and understanding Newton's "Principia Mathematica," focusing on the historical context, mathematical notation, and language used in the text. Participants share their experiences and opinions on the accessibility of the work for modern readers, as well as alternative resources for learning the concepts presented in the book.

Discussion Character

  • Exploratory
  • Debate/contested
  • Historical

Main Points Raised

  • One participant expresses difficulty in comprehending Newton's explanations despite familiarity with the underlying physics and mathematics.
  • Another participant argues that while "Principia" is historically significant, it is not useful for learning, suggesting that modern texts on calculus and mechanics are preferable.
  • A participant notes that the advanced Euclidean geometry used in "Principia" is not commonly taught today, making it harder for modern readers to engage with the text.
  • Some participants agree that the language and notation of the time contribute significantly to the difficulty of reading the book, rather than the depth of the material itself.
  • One participant mentions that reading "Principia" can be more insightful after learning mechanics through modern mathematical frameworks like calculus and linear algebra.
  • A participant shares a link to a book that may help with understanding "Principia," indicating interest in supplementary resources.

Areas of Agreement / Disagreement

Participants generally agree that "Principia Mathematica" is challenging to read due to its historical language and notation. However, there is disagreement on its value as a learning resource, with some viewing it as largely obsolete for modern education.

Contextual Notes

Participants highlight limitations in the mathematical background required to fully grasp the text, as well as the dependence on historical context for understanding Newton's work. There are unresolved questions regarding the best approaches to studying the material.

Who May Find This Useful

This discussion may be useful for students and scholars interested in the historical development of physics and mathematics, as well as those seeking alternative resources to understand classical mechanics.

arabianights
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I've been trying to read Newton's Principia Mathematica, sth I've always wanted to do since college.

i'm familiar with the physics concepts and necessary mathematics involved, but often I found it's very hard to read the book, sometimes to the point that I'm totally lost as what Newton's trying to explain.
 
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Principia is important for historical reasons, but as far as learning from it, it's pretty useless. Much better to get a book on calculus and mechanics.
 
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To understand the Principia is very hard. Usually we don't learn the math (pretty advanced Euclidean geometry, which for good reasons we use in terms of analytical geometry nowadys) used there. If I remember right, Chandrasekhar wrote a commentary on the Principia to make it better readable for the modern physicist.
 
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I agree with the others. That book is difficult to read mostly for the language and notation used at that time, not necessarily because of the depth of coverage. Don't get me wrong. Newton was one of the greatest mathematicians ever ! But, so much work has been done since and clearer expositions have been written.
 
I tried to read it, the language is very hold and difficult to understand, the exposition uses the Euclidean geometry and a lot of reasoning on geometrical figures. I think it is interesting to see these proofs after learned the mechanics with our modern language (calculus and linear algebra). For a beginner I suggest to procede in this way...

When you read the Principia you have to keep in mind that he wrote for the level of knowledge of his time ...
 

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