That's the title page of the original, there are a lot of interesting things in it. Notice it's discourse and demonstrations, mathematical demonstrations pertaining to two new sciences. I'll come back to the word Scienza. Pertaining to mechanics and local movement, by Senor Galileo etc, member of the Linsien Academy, philosopher and mathematician of the Serene Grand Duke of Tuscany, with an appendix of centers of gravity of solids.

Archimedes tying in to the center of gravity the tree of, I don't know anything about it off hand and Leiden. Leiden for those that don't know is a city outside of Amsterdam by train about a half hour twenty minutes. It's the city Decart would live in. Move into any time one of his works was being published because they were all published in Leiden and he supervised the publication.

It's the city that Huygens went to college in, the University of Leiden being a great, great university and where Huygens' papers are located. The other tricky thing that needs to be said here, he was forbidden to publish anything. Okay, so somehow, and we're not sure how, his manuscript was secreted out of Florence, carried in the 1637, period as he's going blind to Leiden, where it is published, I'm not even sure who's responsible.

Marin Mersenne has a copy of it very, very early on multiple copies of it cuz he sent one to Descartes for Descartes to comment on. You'll read that in two weeks. Descartes does not like this book much, but for interesting reasons. But how he managed to violate his house arrest and restrictions and get the manuscript out and get it all taken care of, I don't know.

At one point, I was pretty sure Mersenne had a very large hand in it. Mersenne is the one responsible for all of Descartes' publications, sitting it up in light and etc. So it could've been, but I just don't know. Do you know by any chance where but it was in violation, he was doing something that he could conceivably be given a hard time over.

Table of contents. As Stillman Drake says the Table of Contents was actually prepared by El Severe, but it's four days and then an added day on the Force of Procussion. That's one of the many nice things about this Stillman Drake translation that isn't true of the other. There are three English translations.

One was done in Newton's time by Silas Barry. But almost all copies burned in the great London fire. And the best we can tell and we here includes me in this case. Newton never saw,Two New Sciences. That makes a lot of people mad when I say that. But what Burner did was find out when the library at Cambridge first had a copy of,Two New Sciences,1745, which unfortunately is 18 years after Newton died,so, he definitely didn't see it that way, and there's no sign of any copy in Cambridge before that, and it's not clear that Salisbury copies were present in London because so many of them burned in the fire.

Okay? For those who don't know, in 1666, 67. Somebody help me. I can't quite get the date. There was massive fire in London, which was a great blessing, because it ended the plague. It killed all the bloody rats, the fire did, but the area known as Covent Garden, all of that just totally burned down, and that's where the books were.

And then there's a translation that's available, originally in Dover Press, now in Prometheus Press, by two people, both with Italian names, I don't remember. It's not a terrible translation, it's not nearly as good as Stillman Drake's. And it's, Stillman Drake has the advantage of the footnotes, the glossary, that I did remind people of after John Scott reminded me that I should have reminded people, etc.

So, the first two days are primarily about strength and materials and the next two days are about motion. Notice that we're only going to look at primarily at day three and day four. So the first one's called, Second new science of local motions and uniform and naturally accelerated.

And then,Violent motion of projectiles. The distinction between violent and natural motion is, of course, Aristotle. Violent motion is something that requires a force to initiate. My dropping an object, I need to have good objects to drop here. So my dropping an object, the motion itself, unless I throw it, is considered natural motion.

There is a third category, of course, from constrained motion, and it shows up first with inclined planes. And then, when Galileo identifies, legend has it watching the chandeliers in church swaying back and forth in the wind, came to realize what we now call pendulums were an interesting physical phenomenon.

That is Galileo, who seems to be the first to have picked that up. Okay, new sciences. Let's start with words scientia, or scienza. The term used normally even in the philosophical transactions of the royal society the royal society is engaged in natural philosophy. It's part of their name.

That of course comes out of scholastic philosophy coming out of Aristotle. And Aristotle the word physics just means nature. And so natural philosophy is the philosophy of nature and that's what it meant all through the scholastic period. And scientia by contrast, geometry is a science, sciences have a character of being absolutely secure knowledge.

Not being dominated by conjecture. Or even having conjectures a major element of it. And, of course, natural velocity tended to have a large element in it. There's a development at one time of, particularly among historians, not wanna to use the word, science, because it's a 20th century word.

The word, scientist, was invented, for those who don't know ,this it's a wonderful story. By a philosopher, William Yule describing a book written by a woman, Mary Somerville and the point he was making was that she has as much claim to being a scientist as anybody else does because the book, it's a fantastic book you'll see later, but the word scientist didn't exist before late 1830's at all.

The work scientia very much existed. And a question is what to make of it. Probably not what we call science. But something significantly more demanding than what we call science. Newton at one point you'll see actually says if geometers would pay attention to nature and natural philosophers would pay attention to geometry.

We might finally have a natural science founded on the greatest evidence and the word is scientia and he's openly contrasting it to natural philosophy. So it's a loaded word. As I said, historians at one point wanted to use natural philosophy and I was head doctrines of the Institute at a meeting.

Where people were saying we should never use the word science. I couldn't resist saying so we should call Galileo's book ,Two new Natural Philosophies. And we should call the French Academy, the Royal Academy of Natural Philosophy, which it isn't. The word was being used consciously at the time on scantia.

Is a very serious word. Not the way we use the word science which is much more lax. I put in here for my purposes now. This is my definition of a theory. It is meant to connect with every use of the word theory in classical astronomy. So here's the definition.

An interconnected system of mathematical propositions linking measurable parameters to one another into observable phenomenon from which, with appropriate additional empirical information, values of the parameters for example, one can derive answers to a wide range of questions including predictive and counter-factual questions, questions about where would Mars be if it started at such and such a time, had been appealing at such and such a time, rather than when it was.

Any number of counterfactual questions, any number of predictive questions, any number of questions about, if you change the eccentricity of Mars what difference is it going to make to the orbits, etc.? And as I say the word theory was used by Ptolemy and subsequently by an astronomy to refer to just such a framework of the individual planets.

For those who know this was a definition adapted somewhat from Duham, but I'm intentionally trying not to use Duham phrasing. And the primary influence on Sylvain Bromberger cuz it's Sylvain Bromberger who talks about question answering devices. But again I'm trying to describe what we talked about so far, because now we're gonna be looking at what it is to develop theories of strength of materials of local motion.

And what I mean here is a system of mathematical propositions, but the important thing is the parameters linking to one another.