This presentation examines the teaching of applied mathematics at the University of Wittenberg during the eighteenth century, a period characterised by significant transformations in higher education and scientific culture. While the history of mathematics has often focused on theoretical developments, less attention has been paid to the institutional contexts in which mathematical knowledge was taught and adapted to practical purposes.

Drawing on lecture catalogues, disputations, university records, and contemporary textbooks, the study analyses the place of applied mathematics within Wittenberg’s curriculum between 1700 and 1800. Particular attention is given to subjects such as surveying, cartography, military engineering, mechanics, and astronomy, as well as to the relationship between pure and applied mathematics in academic instruction.

The presentation investigates how professors responded to growing demands for practically useful knowledge and how mathematical teaching reflected broader developments associated with the German Enlightenment. It argues that applied mathematics increasingly served as a bridge between traditional scholarly learning and emerging forms of technical, administrative, and professional expertise.

By situating Wittenberg within wider educational and intellectual networks, the study contributes to a deeper understanding of the role of universities in the transmission of practical knowledge and highlights the importance of mathematical instruction in processes of institutional and societal change during the eighteenth century.

While semicircular arches have dominated Roman architecture, their low span-to-rise ratio of 2 is disadvantageous for the building of bridges. Basket-handle arches, which have been in wide-spread use since the 17th century, improve upon this. From a mathematical perspective, such arches are half ovals. We present two geometrical constructions for basket-handle arches with three centres which do not appear in the literature on ovals, one attributed to Heron of Alexandria and one to Huygens by Ernest Degrand and Jean Résal in their book "Ponts en maçonnerie" (1887). It remains an open question, however, who in fact did invent these constructions and when, as neither Heron's nor Huygens's opera omnia appear to contain either of them.

The concept of a cubic equation was entirely unknown in antiquity. Yet:

The famous problem of doubling the cube concerned the insertion of two mean proportionals between two arbitrarily given lengths, an approach introduced by Hippocrates of Chios (470–410 BC). From a modern perspective, this amounts to solving a cubic equation, more precisely a pure cubic equation. A mixed cubic equation arises in a problem presented by Archimedes: the division of a sphere by a plane section. Archimedes derives an equation for a proportion. This equation again can be transformed into a cubic equation. A third type of a cubic equation emerges from the trisection of an angle. However, this insight was not fully recognized until François Viète (1593). Viète explicitly stated that the methods enabling the solution of the Delian problem and the trisection of an angle are sufficient to solve all cubic equations. In doing so, he drew upon the ancient method of neusis, which he legitimized through a postulate of his own. In demonstrating the application of this approach, however, he just gave an example.

The absence of solutions to cubic problems in Archimedes’ work prompted Eutocius, in his commentary, to present a series of solutions to the Delian problem, twelve in total. The first of these solutions is attributed to Plato, the philosopher. In this construction, the endpoints of an L-shaped line are connected by a broken line consisting of two consecutive right-angle turns.This Platonic approach to solving the Delian problem might also be applied to the other problems handed down from antiquity: the trisection of an angle, the construction of a regular heptagon or a nonagon, and the problem of dividing a sphere. Each of these problems can be traced to a cubic equation, by means of a triple proportion. In every case, the solution can then be obtained by a broken line segment “in the Platonian manner”. The incorporation of this method into ancient geometry (in the Euclidean sense) might be achieved by a postulate modeled after Viète’s neusis-postulate, as a supplementum geometriae.

Like the classical method of neusis, the broken-line construction is concerned with the determination of an inclination. The “Platonic Postulate,” however, surpasses all other postulates considered in this context.

Following Viète, Newton likewise states that the general solution of cubic equations is covered by a neusis postulate. Yet in both cases the method was worked out only for particular examples. The fundamental difficulty lies in the restriction to lengths, that is, to positive quantities. This requires a distinction of many separate cases (Omar Khayyam 19; Cardano 18; Viète 4; Newton 8). In the method employing right-angled broken line segments, negative values are included, both for the coefficients and for the solutions, in a natural manner, by the direction the segments are laid off. As a result, the description of the configuration determining the required length (the “construction”) becomes remarkably transparent, even in the broadest sense.

Finally: The method “in the tradition of Plato” can be extended to equations of any higher degree. In such cases, only the number of bends in the broken-line segments increases.