Newton’s Principia of Mathematics

[Vividly]

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.

 

[Drakkith]

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.

 

[Vividly]

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?

 

[jtbell]

I suggest you use the translation by Cohen and Whitman. The translation is more modern than Cajori's, and it comes with an extensive commentary by the translators, which takes up half the entire book.

https://www.amazon.com/dp/0520088174/?tag=pfamazon01-20

 

[Mark44]

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.

 

[vanhees71]

"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).

 

[Drakkith]

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]