Newton's Principia Problem

  • #1
Hello everyone, I am reading Principia Lemma 10 and I cannot understand it. Can someone please help explaining? Thank you very much.
1.png

23.png

2.png

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.
 

Answers and Replies

  • #2
Doug Huffman
Gold Member
804
111
S. Chandrasekhar Newton's Principia for the Common Reader Chapter 3, Section 15, pp 50-52 in modern integral notation.
 
  • #3
Philip Wood
Gold Member
1,221
78
I think that in modern terms, this is [itex]s = \frac{1}{2} a t^2[/itex]. So [itex]\frac{s_1}{s_2} = (\frac{t_1}{t_2})^2[/itex]. 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?
 
Last edited:
  • #4
Stephen Tashi
Science Advisor
7,570
1,465
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.
 
  • #5
Wao, thank you everyone, this helps much
 
  • #6
jtbell
Mentor
15,727
3,882
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&tag=pfamazon01-20
 
Last edited by a moderator:

Related Threads on Newton's Principia Problem

  • Last Post
Replies
2
Views
962
  • Last Post
Replies
1
Views
1K
Replies
5
Views
2K
  • Last Post
Replies
7
Views
791
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
4
Views
1K
  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
14
Views
3K
  • Last Post
Replies
4
Views
2K
Top