Hi everyone and welcome back to my channel. Today
I am channeling my inner Newton by sitting here under a
Passion fruit vine and I'm going to be looking through something
that actually really excites me and that is
Newton's great work
It is in Latin the Philosophae Naturalis Principia Mathematica
Or translated to english the mathematical principles of natural philosophy.
So this is a super important book to the history of science. It is where we were introduced to Newton's laws
You know talking about motion things like the inverse square law
You know laws of gravity that
Keep large bodies in orbit and some really nice insights just about the physical world.
So this was first published in 1687
Although this version here is not own original
It has since being translated into English by Andrew Motte and then revised by Florian Cajori.
So that's a copy that I have here
and in this video
we're just going to be taking a look through this book and having a look at some of these key insights and at some of
The science in the way that it was first presented to us
The writing of this book kind of came about after Newton was visited by his friend Edmund Halley after Halley's Comet frame
And Halley wanted to know from Newton. You know, what are your thoughts on?
You know, what motion?
heavenly bodies would follow if they're governed by this invest square law that they were starting to think about and Newton said, you know,
I've already worked it out. They're going in ellipses and I'll send you my calculations
so in writing up
you know all of his thoughts and calculations around that it eventually evolved into this book which ended up laying kind of a
Foundation for classical mechanics that we still learn and use today it apparently took Newton about one-and-a-half
Years of solid focused work to work on this manuscript and get it out there
He had to put some of his side interests like alchemy on hold for a little bit
To get this out and we're very glad that he did. It's very important and I'm really excited to have a look at it
So, let's see what's inside
so here it is the book which helps to bring the tools of mathematics to physics and
help to bring us a really great period of science the book starts off with a page of
Definitions where Newton is defining things like mass momentum inertia and centripetal force
These just set up the rest of the book and then we go into the axioms or laws of motion
Now these are arguably the most famous
aspects of this book and these are Newton's laws one two, and three listed here and
These are still laws that you would learn about in any physics class or a lecture today
And they're still very useful and relevant
Now we'll come back to reading through some of these laws to see how Newton laid them out
I will come back to that in a minute, but we'll just have a look at what's in the rest of this book
So after the axioms and explaining them a bit
We get on to book one of three in this work, which is the motion of bodies now
That's pretty much what it sounds like it's you know
How things move and how you can describe the motion of pretty much everything
Although in this first book. We're only talking about the motion of bodies
Moving through free space, you know
There's no resisting medium and that leads us into what book two is about
Which is the motion of bodies in resisting mediums?
So I guess you have a little bit more to consider here and yet he really talks about
Every case that you can think of when you want to know about motion. There's also
plenty of
diagrams and
Mathematical explanations, which I guess are good because the language in this book
I must say can be a little confusing at the best of times
You know, it was originally written in Latin and it's been translated to English here
but even then I find it very difficult sometimes to figure out what's going on and what they actually you referring to so
Maybe the diagrams do actually help out quite a bit
Now there is actually a third book which I don't have included here in my copy
Which is on the system of the world and it's more about astronomy and applying these
concepts of motion to astronomy
But since I don't have that one here
We're just going to be talking about books 1 & 2
so I've taken us back to the
Definitions page just to have a little read of some of these to see what the language is like
So for the first definition here
It's actually talking about mass and he says the quantity of matter is the measure of the same
Arising from its density and bulk conjointly
now this language about the measure of the same could actually be read as the
Quantity of matter is the measure of matter
Arising from its density and bulk conjointly, which to me makes a little bit more sense when you read it that way
So that's mass
And then we have another definition here. It reads in a very similar way
The quantity of motion is the measure of the same
arising from the velocity and quantity of matter conjointly so that there is actually talking about
momentum so you'll still see the definition of momentum given in textbooks everywhere as
Usually P for momentum is equal to m*v
Which is matter and velocity, so nothing has really changed there in physics
we then go on to talk about what is actually
Inertia, or as it's called here an innate force of matter
It is a power of resisting by which everybody as much as in it lies
Continues in its present state whether it be of rest or of moving uniformly forwards in a right line
So that's just talking about inertia. We haven't got onto any of Newton's laws yet
These are just setting up definitions for what we're going to go and talk about so
We've got some other things like an impressed force or a centripetal force
There's also quite a lengthy discussion at the end of these definitions
where Newton
splits up the definition of centripetal force into its absolute quantity, its
Accelerative quantity and its motive quantity and then has a bit of a long-winded
discussion here about
what is
Absolute true and mathematical time or the same with you know?
Absolute true and mathematical space or motion and I think he's just trying to clear up confusion
about I guess what exact properties he is referring to for the rest of the book, so
Yeah, this is a pretty long section here
Which I'll admit is not the easiest to follow but we get to this page our laws of motion
Let's see if you can recognize these laws for number one. We have that
every body
continues in its state of rest or a uniform motion in a right line unless
It is compelled to change that state by forces and impressed upon it
So yeah
That actually makes sense and there's just a little explanation here and then we have law two. So
the change of motion is proportional to the motive force impressed and
Is made in the direction of the right line and which that force is impressed. Now
I believe this second law could be written in a more familiar way as F is equal to
M*a. So a super important
equation in physics. I guess this is it written out and it's a long-winded original form. But you know, that's actually kind a
revolutionary law because it is so useful in so many areas of physics and it's neat to see
You know Newton talking about it in sort of his own words here
so law number three
It also might be a little familiar for you it is that too every action
there is always opposed an equal reaction or the
mutual actions of two bodies upon each other are
Always equal and directed to contrary paths
And again, I think that one's not too hard to understand especially if you've seen it recently in your own classroom
So yeah, then we just have a few
corollaries
Newton, you know giving some
little bits of evidence or
Justification for his reasoning here, but we won't go through all of those now
We'll just go to the start of book one
So book one starts with a mathematical look at something called the method of first and last ratios
which to my understanding is like a
geometrical form of
infinitesimal calculus
So even though I believe Newton had already
Come up with his sort of, you know version of calculus as we know it today by the time he wrote this book
He doesn't feature calculus in here and instead publishes calculus at a much later time
Now whether he did that to make, you know these proofs and things more understandable to other
Scientists and physicists at the time. I'm not sure or maybe he just wasn't ready to share some of his other
You know theories and workings as of yet. But anyway, he he proves a lot of these things very geometrically
And it's pretty impressive and interesting to just have a look at how some of these things are done
So this is you know a mathematical discussion here
And then we get into section two of book one which says here the determination of centripetal forces
so a lot of these first few propositions is talking about the relationship between centripetal forces and
things like areas or
You know circular motion and the radius of a path, that would be traveled
So these actually relate to what we now know as Kepler's laws and Kepler did actually come before
Newton so
I think that Newton is building on some of those laws from Kepler
here in the section. As we move through two propositions five to ten
We start to hear about the inverse square law
Which you know says that centripetal force varies as the inverse square of the distance to the center
Now, I think it comes up here in proposition six. We see it just mentioned at the end here that
the centripetal force in the middle of an arc will be directly as the verse sine and inversely as
The square of the time and we've got a little semicircle diagram down here
Now it's a little bit hard to understand there
But you probably have encountered an inverse square law in a more familiar way as written like one over R squared
And lots of things like, you know, in this case we could be talking about, you know, a gravitational attraction
Varying in strength as an inverse square law
So the further away from it you get it drops off quite steeply because it's the inverse of the square
So that's kind of what we're talking about in this section
here and basically we just get a lot of stuff about
Elliptical orbits the motion of you know planets or other bodies
We get lots of things about centripetal force
And I think I'll just have a little skip through the rest of these
So coming to book two
The first section of it talks about the motion of bodies that are resisted in the ratio of the velocity
So, you know resistance that is in direct proportion to velocity
Which is not an alien concept to any physicist nowadays
So we talk about that a bit through some more propositions and some more geometrical arguments
section two here then goes on to talk about the motion of bodies that are
Resisted as the square of their velocities
we have a few more sections here before we get on to section five which is
hydrostatics
essentially the density and compression of fluids
So that's pretty cool. We're even talking about fluid dynamics here and then for the next section, which is
Section six
We get the motion and resistance of pendulous bodies
So that is the effects of air resistance on pendulums
And I think that Newton did a lot of experiments so did other physicists at the time with pendulums
So it makes sense that
They get their own little sections
so yeah, that's pretty interesting that he was able to look at resistance and pendulums and you can see
That through his diagrams here
Like this is all really impressive stuff and I'm quite excited to see it laid out because I've never really seen it laid out
in the way
it was initially presented before now one important aspect of this book and it's stressed by Newton and
like at the start and and through a lot of the language is that he's for example with all of his work about
gravitation, he's not trying to
Provide any explanations or reasoning as to you know?
How gravity works and why you know bodies attract each other gravitationally
He he doesn't you know?
give an explanation and he doesn't try to give an explanation of that. So there is sort of a
famous quote from Newton and it came at the end of book 3 in this work where he essentially says I
frame no hypotheses, so
There he says he's not claiming to
To really have any understanding of how gravity works and I guess you could argue
We still don't really know how gravity works but here in this book
Newton is doing his best to show you the effects of it and how it will affect
Motion and how things will move under it
So I think I'm going to leave my little review of the book here
But because I was so excited to get a copy of this book and to wade through it. I'm going to upload another video
Hopefully tomorrow where I'm just going to read the book and nothing else
So I'll see how far I can get through it without getting too tired
But maybe you can watch that if you want to maybe you know put into your subconscious
Some of Newton's words and some of those phrasing or you just want to you know
Hear more about this language. So thanks for watching this video
I hope you found it a little bit interesting and I'll see you next time.