…call a curve, a straight line then is defined as the shortest distance between two points. In other words, he's following Euclid. He reads page one, straight lines, shortest distance between two points. Okay, we got that. So that's the way straight lines…

…triangle, three lines, three straight lines. and measure the angle in here, and in here, and in here, for instance, according to Euclid and measurements, so forth. I mean, according to the geometry in a flat space, flat plane like this, the sum of the…

…distance then, huh? Boy, now he actually goes to the trouble of measuring the radius, and to his horror, if he's read Euclid, he discovers that his predicted radius that its actual measured radius exceeds the predicted radius by some excess. So we can…

…And you measure the surface area by laying out distances on the surface of the sphere and just measuring the area. And according to the Euclid, the area is The area is supposed to be 4 pi times the square of the radius. What we're going to do is we…

…defined. I'll let this guy get away with masses, and I'll let him get away with defining positions in time, because maybe Euclid took care of geometry. But I want a precise definition of force. You will never get it. First, because this law isn't…

…or something. If you use one of those things to do surveying, are you measuring a real line in the sense of a Euclid? That's an approximate idea. The crosshair has some width. And it can't have no width. And so whether Euclidean geometry can be used…

…question. From a scientific standpoint, not a mathematical standpoint, that is an experimental standpoint, we need to know whether the laws of Euclid apply to the geometry that we use in measuring land. And so we make an hypothesis that it does, and it…

…precise. You see, it does more or less, because none of our lines are really line. But whether or not those lines of Euclid, which are abstract, apply to the lines of experience, that's a question for experience. And it's not a question that can be…

…theory when mechanics is a description of nature. We can always make a mathematics just like you can make a mathematics of Euclid. But you can't make a mathematics of the world Because sooner or later, you've got to find out whether the axioms apply…

…a different kind of a distance. And it seems to agree with other measurements of the distance. And the space is sort of what Euclid thought it was. And so the two types of definitions of distance agree. Well, it's a good thing that they do agree on…

…quantities were available so that you could solve elaborate equations and so on. Everything was prepared for calculating things out. But Euclid discovered that there was a way in which all of the theorems of geometry could be ordered from a set of…

…one of the, it's reputed, I don't know if it's true, that when one of the kings was trying to learn geometry from Euclid, he complained that it was difficult. And Euclid said that there's no royal road to geometry, and there's no royal road It's not…

…know if it's true, that when one of the kings was trying to learn geometry from Euclid, he complained that it was difficult. And Euclid said that there's no royal road to geometry, and there's no royal road It's not the job, if we cannot, as people who…