History of Science and Engineering Annotation << Back The Second Part of Jacob Hermann's Speech «On the Origin and Development of Geometry» at a Meeting of the St. Petersburg Academy of Sciences on August 1, 1726. Continuation. Started in the Previous Issue Sinkevich G.I. Speaking at an open session of the St. Petersburg Academy of Sciences in the presence of Catherine I and her retinue, Jacob Hermann expressed admiration for the genius of the founder of the Academy, Peter I, who invited foreign scientists to the Academy, as well as the wisdom and patronage of the continuer of his work, Empress Catherine I. After this obligatory part, Hermann spoke about the history of ancient geometry and the development of its ideas up to the 16th century. In the second part of the speech published here, Hermann sums up the role of ancient geometry and moves on to the period of the origin and formation of infi nitesimal analysis. He begins with the research and discoveries of F. Vieta, J. Napier, moves on to the geometry of indivisibles of B. Cavalieri and E. Torricelli and the development of their methods in the works of Gregory of Saint-Vincent. Together with the works of H. Huygens and B. Pascal, they formed the basis of the teachings of G.-W. Leibniz. Hermann talks about the role of R. Descartes, describing in detail the method in his "Geometry". Analyzes the works of B. Pascal on calculating quadratures, primarily the cycloid, and dwells in detail on his mystifi cation with a reward for solving problems on the cycloid. Considers the geometric method of Wallis series, admits that with its help it was possible to solve most of the problems of that time, "one can conclude about the superiority of this method and its wide generality. However, it is regrettable that this method is only conditionally geometric, approximate, Fermat and others objected to it." Points to the latest achievements of J. Bernoulli, R. de Montmort, B. Taylor, as well as academicians of the St. Petersburg Academy of Sciences H. Goldbach and F. Mayer, who discovered methods for summing any series of fi gurate numbers. Herman concludes this reasoning with the words: "In my opinion, the geometric method of summing all types of quantities changing according to a certain law should be highly valued when a simple contemplation reveals the type of the desired sums, for this has a special elegance, which we almost never encounter in the arithmetic consideration of these issues. Many examples of this geometrical method are found in the works of Cavalieri, Stefani de Angelis, and Guido Grandi, as well as in the extensive work of Gregory of Saint Vincent on conic sections, and especially in the Lectionibus Geometricis of Isaac Barrow, where there are many rudiments of higher geometry." Having summed up this period, Hermann passes on to the generalized method of Leibniz, published in 1684. Hermann talks about the works of I. Newton, beginning with his "Mathematical Principles of Natural Philosophy" of 1687; he points out the differences in the methods of Leibniz and Newton, and concludes: "Life is such that both the method of differential calculus in the style of Leibniz and the method of fl uxions of Newton are beautiful in that they lead us to truths unattainable by previous methods, and even when the truth follows from other considerations, they provide confi rmations." Hermann's speech is the speech of an eyewitness of the process of creation of mathematical analysis and discussions around it, he cites many mathematical facts, names and events, which he witnessed, maintaining objectivity and impartiality. He talks about the role of the Bernoulli brothers in the dissemination of Leibniz's teaching, about numerous applied problems that were the stimulus for the development of this teaching, as well as about the famous dispute about priority between the followers of Newton and Leibniz. Keywords: Jacob Hermann, St. Petersburg Academy, ancient mathematics. DOI: 10.25791/intstg.11.2024.1509 Pp. 03-19.