Jacek Rodzeń

This article aims to analyze (from autopsy) mathematical motifs in the frontispieces to selected seventeenth-century Polish technical-military treatises (by Adam Freytag, Kazimierz Siemienowicz and Józef Naronowicz-Naroński). The frontispiece is considered here an iconographic source for the history of science and technology. The rationale for investigating this topic is the process of the progressive mathematization of technical knowledge in Europe in the 15th-18th centuries. It is the first study of this subject with regard to Polish technical-military writing. Only one other article is devoted to this issue (Delphine Schreuder, When Mars Meets Euclid. The Relationship between War and Mathematical Sciences in Frontispecies of Fortification Treatises, 2021), but it does not cover the works of Polish authors. There are also several general studies (mainly in art or architectural history) on frontispieces to fortification treaties (Armin Schlechter, Engraved Title Pages of Fortification Manuals, 2014, Jeroen Goudeau, Harnessed Heroes: Mars, the Title-page, and the Dutch Stadtholders, 2016). The analysis of the typographic compositions of the discussed frontispieces revealed three main motifs: 1. the connection between the art of war and mathematical knowledge, as far as the knowledge of fortification and artillery is concerned; 2. the degree to which those disciplines - both of which combine the practice of the battlefield with theory - were mathematicized; 3. the crucial importance of drafting and measuring instruments for these sciences. The article’s final section addresses the issue of the rhetorical and persuasive function of the frontispieces.

The paper presents engineering interests of Isaac Newton, including some of his technical inventions. So far, this topic has not been studied in a broader manner and in more depth. This article discusses Newton’s youthful passions against the backdrop of the so-called mathematical magic literature. His two inventions, i.e. variants of the reflecting telescope and the marine octant are also discussed. Finally, an example is provided of the involvement of the author of Principia in a discussion around the steam engine and the ship powered by such engine designed by Denis Papin.

Isaac Newton is known primarily as an outstanding mathematician and physicist. Less known are his interests in alchemy, theology, and history. Yet, we still know very little about his interest in engineering and about how he designed and created several scientific instruments (e.g. a variant of the reflecting telescope, a variant of the rotary slide rule). Among them, there is also a navigational octant built by Newton in 1699. This device is an example of an ingenious solution in the field of early modern catadioptrical instruments.

This paper presents examples of mathematical models which have almost passed into oblivion, yet a few decades ago still played a significant role in the teaching of mathematics. In the late nineteenth century such devices started to be produced on a large scale for schools and universities. The Jagiellonian University Museum has three such models in perfect condition in its collections.