Center of Gravity: Barycenter

This lecture covers the concept of the center of gravity in Euler's course for first-year students, focusing on the definition and properties of the midsegment of a triangle, along with the theorem stating that the medians of a triangle intersect at a point two-thirds along each median. The instructor demonstrates the parallelism and length relationships within triangles, leading to the conclusion of the barycenter theorem. The lecture concludes with a detailed proof involving the intersection of medians and the midpoints of segments. Various geometric notations and calculations are used to illustrate the concepts.