 So something has the same speed in the same direction, that means it has the same velocity, so velocity is the vector that has the speed and the direction of that speed, and so that's a nice statement of Galileo's discovery. It is now typically called the law of inertia, or most commonly Newton's first law. Newton came along much later and used Galileo's work as the basis on which he built his laws and mechanics, and Newton's laws and mechanics enabled him to quantify exactly what happens when you do have forces. So in the Aristotelian worldview, a book sliding across a desk comes to rest because that's what books do, books like everything else on earth should be at rest. In the Galilean Newtonian point of view, a book sliding across a table stops because there's friction, and if the book falls off the edge of the desk and falls toward the ground, there are two explanations for that. In the Aristotelian worldview, the book is mainly made of earth, which means it wants to be as close to the earth as possible, and so it goes down, and in the Galilean Newtonian point of view, it experiences a force called gravity. And the reason that the Galilean and Newtonian point of view really supplanted all those old ideas is that the force of gravity also explains why the moon acts the way it does, and why the moons of Jupiter act the way they do, and the celestial bodies. And so we have this common theory that describes everything that we see on earth in terms of gravitation and everything in the sky, and so the fact that the Newtonian laws were both universal and quantitative enabled people to explain everything that they used to be able to explain and more meant that those ideas supplanted the old ones rapidly.