Geometry & physics 1920s (contd.)

0:00 This is very interesting. It is the same way of thinking that we find in Poincaré to define the dimension. A solid body is one in which there is only one boundary, that is to say that there is only one thing that is the boundary. In a way, because a surface can always be considered as the boundary of something else. We say that a body cannot be considered as the boundary of something else. The plane, the cut, is defined this way as a cut of gasoline such that it is the same relation on both sides of a surface that is not flat, that is to say that it is not the same relation because it has a straight side and a concave side, so it behaves differently. And at the same time, it is a cut of a plane that has the same relation on both sides. So it goes on the straight side and on the concave side. For Witten, all of them are at least locally immediate. As a consequence of this definition, if C is on one side defined by A and B, then there is a point B on the other side that is in the same relation C to B, that is, congruent to D to B. So if now A to B congruent to Z to A to B implies that Z coincides with B. X is to say that X and Z, here they are, are adjacent to each other, adjacent to each other with a B, that is to say that they are not the same.

2:30 So, let's say that we can meet at the same point, because the three of them are on the same side, and they can still be on the same side. Of course, we already have the movement of a right and a left. Of course, we pass over it and we show it. For example, with the help of these... Only 2Z is possible, thanks to the calculative demonstration. Suppose there is a 3 on a point and we find a contradiction with a right. We cannot have the same relation with 3 points. Then, if 2Z touches the point of contact of the adjacent linear, a right and a Z can have more than 2 points of contact because there is a calculation, There are some very specific applications, but we won't go into too much detail, we will focus on the very first elements. The third text, which is the last one, dates from 1698 and was sent to Auden Krausser, who was the author of Pascal's Masseurité. I am honored to be able to present my Calculum Citus in front of you, because so far our Calculum has been completely different, and therefore our elementary geometry is de-analytical, without this, the analysis depends on the mathematical physics of the human body.

5:00 With them, we can go back up the ladder. Well, then he will start to say that it works well and that everything that is imaginable must depend on analysis. This new analysis develops the idea of similitude. The reduction of the problems of geometry and algebra is always prolix. There is a number, a prolixity, a difficulty to pass from the equation to the instruction. That's a number. We will discuss what Descartes knew, what Descartes knew precisely about the problem of mathematics. So, he talks about the analysis of the senses, the two. But in saying that, it does not refer to a calculation and it does not concern the first principles. We assume the elements. The analysis that he has discovered is at the same time different from the analysis of the senses and different from the analysis of the body. Equalities are the same, and similarities are the same, but there is no general notion for them to be adapted to their own research. And, as we can see, by the fault of philosophers who are content with basic definitions, especially in metaphysics. This is not the first philosophy. Philosophers are content with basic definitions. It's exactly the same thing. Here is its definition.

7:30 Its semblance, the things observed in themselves, are a mystery. The term, if you want to call it that, is singular, isolated. Quantity can only be defined by the comparison of two things. And so, from this idea, he wants to demonstrate that it is based on a fundamental idea, rather than a theory, that triangles with angles are central and that central triangles have proportional sides. For this, they pose an action, but of a physical nature. What cannot be discerned by determinants, i.e. by sufficient data, cannot be seen in an absolute way. This is the action of the law. Consequently, we have two triangles with the same angles, which easily show that we cannot discern them. We cannot discern the data, the angles, and that these data are sufficient. We follow them all the time, and we cannot discern them, and by this time, they are no longer there. And then, in the beginning, we also saw that the sides were proportional, because if they were not proportional, we could discern them. So that the circles are in relation to the squares in the graph, simply by building the square is considered a circle, and then by saying, well, if we have a circle, we build a transcript, but we cannot discern the data. So, the data are similar and therefore the answers are the same. So, this is the kind of reasoning that we can create. So, as I said many times before, this is a programmatic work rather than a theoretical one. Of course, this has nothing to do with Priemann and Poincaré's analysis, rather, in the course of the evolution of mathematics, what has played the role, what has fulfilled the role of the analysis of mathematics is the calculation of the Paris centric of Moëtius and the vector calculation of Gaël.

10:00 Finally, I would like to say that, I don't know if I can push this idea further, but it would be interesting to compare this project of Euclid, to write a new foundation of geometry with its characteristics, with the project of Ibn al-Haitham in the Treaty of the Columns. In which, in the late 10th and early 11th centuries, Wilton Abraham wrote new foundations for geometry to take into account the use of geometric transformations. This is something else that Pellein-Liske does, since he considers it to be the same thing. It would certainly be interesting to compare in detail the treatment of the products. Thank you very much. If you like, you missed the fact that the two sides of the circle have two sides. It's demonstrable in this construction. The intersection of a right side and a left side is the same. That is to say, there is a topology hidden somewhere in the tree. So there is a relationship between the two. What I said is that it shows that a right cannot meet a circle of more than two. In this text, there is no problem of existence.

12:30 He says that if there is a right of existence, there cannot be a left of existence. It is in another text where he analyzes definition by definition a text that he has articulated too early. In which he analyzes all the definitions that are at the beginning of the first book of the elements of physics. And in his critique of the definition of the cancer diabetis, I remind you that Keven has published the number of the definition of the diabetis, it is the definition 17 in the second edition that he has, in which he defines the cancer diabetis as... A finger passing through the center, meeting the circle in two points and dividing it into two equal parts. So, he says, well, that's it, there's too much in there. First, it would be enough to say that it passes through the center. Because we can demonstrate, at that moment, what the circle meets. And he demonstrates, in general, in his commentary, that a finger that is one point inside the circle necessarily meets the circle in two points. This snake is a continuity principle because it has an interior point and an exterior point because we can prolong it indirectly. And then we can prolong it indirectly on one side of the interior point and on the other side of the interior point because it is this snake. Two points. So it demonstrates that. And then it also demonstrates, in this snake by the way, it calculates by its characteristic. The definition of the right is that everything that can be done on the right side can be done on the identical side of the other side. And that's what shows that the two sides are equal. Any questions? I would like to ask a question. Do you have any knowledge of how to work with these components? Well, he sent a piece to the Eglise, to Vigas, but Vigas was not at all interested in it.

15:00 Everyone knows it completely. Vigas had this book in his hand too, he did only mathematical methods. And, well, it was really interesting. On the contrary, Rosenhausen considered that mathematics was preserved as a treasure, all the packages of mathematics he had used, and consequently, well, he didn't make anything of it himself, but he considered that, at the same time, there is a whole correspondence between Rosenhausen from 1698, there is an important correspondence between Rosenhausen and mathematics. This is a series in which we can see a series of problems that the author does not understand too well, so he asks questions and the author is the guide and he speaks like that. But it is not the same as the others. It has been known to publish the other problems of the Eiris. This edition, this is a reprise by Horst of the edition of Guérin which dates from 1840. We are in the 40s of the 10th century. And does his calculation give him the means to define a code? No, no, you can see from what I said that he immediately turned to the analysis of principles rather than to the resolution of problems here. He hoped to talk more about it later, but he won't be able to. That's all. Well, thank you to all the speakers, to all the speakers. Thank you for your attention.

17:30 Thank you for your attention. Subtitles by the Amara.org community Very good. Thanks to Rishi Muscovini, who worked on the transmission of the optical vision of mathematics into mathematics. Thank you, thank you. You're very kind, but for me it's a little more ergodic.