How can I better understand Newton's Principia beyond just reading the words?

[Solomon Chang]

Hello everyone, I am reading Principia Lemma 10 and I cannot understand it. Can someone please help explaining? Thank you very much.

Furthermore, is there any way of understanding the Principia in a more numerical ways rather than words like this? Just asking.
Again, thank you very much.

 

[Doug Huffman]

S. Chandrasekhar Newton's Principia for the Common Reader Chapter 3, Section 15, pp 50-52 in modern integral notation.

 

[Philip Wood]

I think that in modern terms, this is $s = \frac{1}{2} a t^2$. So $\frac{s_1}{s_2} = (\frac{t_1}{t_2})^2$. This is constant acceleration from rest. Since it's at the very beginning off the motion, the force won't have had time to change?

 

[Stephen Tashi]

It would interesting to know whether Newton is representing a graph of a function of position vs time with time on the y-axis or whether he is thinking of the curves as trajectories of an object in 2-D space.

 

[Solomon Chang]

Wao, thank you everyone, this helps much

 

[jtbell]

The English translation (of Newton's original Latin) that you are reading dates from around 1730 and can be difficult to read, even for native English speakers. This book contains a new translation from the late 1990s, along with an extensive "guide to the Principia" which is as long as the Principia itself (i.e. half the book)!

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