In 1588, the first English translation of Italian mathematician Tartaglia’s Quesiti et inventioni diverse (Venice, 1554) was published in London under the title Three bookes of colloquies concerning the arte of shooting (STC 23689). The work was an important first step in the introduction of tartaglian mathematics of movement to English audiences, at a time when black powder, cannons and other projectile weapons were already a stable of the European battle fields.
Figure 2 :Tartaglia Niccolò, 1554. Quesiti et inventioni diverse de Nicolo Tartaglia. Venetia per Nicolo de Bascarini. Google books, Public domain.
While Quesiti et inventioni had nine books dealing with multiple different branches of applied mathematics such as cartography, ballistics, and architecture, the English edition, translated by the merchant tailor Cyprian Lucar (1544–1611?), only included the first three, on the topic of ballistics. The three books were published together with an ‘Appendix’, an extensive miscellany of various English and European military authorities.
The English Tartaglia
The arte of shooting promises to teach its readers how to shoot small and large projectiles and the differences between gunpowders (sig. A.i.r). The work is a practical manual, and its didactic goals are apparent both in text and illustration. The text is constructed as a collection of short instructional dialogues between ‘Nicholas’ (Niccolò “Tartaglia” Fontana, 1499/1500–1557) and ‘Duke’ (Francesco Maria I della Rovere, Duke of Urbino, 1490–1538). The illustrations are used to exemplify and clarify the concepts discussed.
The work utilizes both diagrams and representative images. The more complex visuals contain elements of both methods of visual communication. In Figure 1, for example, the mathematical principle expressed in the text – regarding the influence of the angle of the shot on the force of the projectile – is illustrated with an image containing not only the trajectories, but also a fort, two cannons, and even some superfluous detail such as bushes and the vague form of a town in the distance. Although the corresponding source text image in Figure 2 also contains the fort and cannons, the town in the horizon has been added to the English version. No such editorial liberties have been taken with the lines communicating angles of shot, which have been reproduced exactly. The precision is somewhat curious given the fact that the angle has no bearing on the principles discussed, and no mathematical proof is offered within the attached text section.
Renaissance diagrammatics
One reason for the faithfulness in the reproduction of the angles in Figure 1 may have been the level of reverence afforded to diagrammatic representations in general. But no such reverence is afforded to the other geometric objects within the work. Indeed, while many of the illustration-diagrams have been directly copied form the Italian source text, a comparison of the images of projectile flight paths shows the geometric object has indeed not been reproduced exactly (see Figure 3).
There are seven similar diagram-images within the work, each helping explain the influence of different variants such as the angle of shot upon the flight path of the projectile. The relevant geometric object is a curve, placed at the mouth of a cannon. The devices appear to have been systematically copied, given the fact that the images have been mirrored in the English edition (note the flipped image in Figure 3 right). But although the illustrative details have otherwise been replicated quite faithfully, the curve differs visibly. The angles of shot differ, as do the curvatures. This repeats in the other diagram-images as well. This sets Figure 1 apart from the rest of the diagram-images. The attention to detail in this one specific case is especially odd, given that the purpose of the surrounding text section is somewhat introductory.
All this makes the English Tartaglia an interesting example of the English Renaissance understanding of visual communication. There are several possible reasons for the un-faithful diagrammatics of the work, including technical or material influences, as the curvatures of the more complex diagrams appear to be the first diagrams of this kind to be printed in London. The arc communicating projectile flight path was Tartaglia’s invention, and in contradiction with Aristotelian teachings of movement, according to which the projectile was in a free fall after its impetus, derived from the mover, came to an end. Perhaps the engraver had yet to learn the techniques for copying such geometric objects. But there is another possible hypothesis as well: the producer never meant to try for faithfulness, as the exact angles of the original geometric objects were not significant. This would mean that someone at the printing house or engraver’s workshop had sufficient understanding of the text to know when the angle or curvature of the geometric object carried no significance to the lesson within the text. This understanding would have led to the treatment of the geometric objects similarly to representative images: free to change and adapt in sections considered superfluous by the engraver.
Sirkku Ruokkeinen is a post-doctoral researcher in the Early Modern Graphic Literacies (EModGraL) project. She studies the use and distribution of graphic devices in England, focussing on paratextual representations of visual devices and their use in marketing, the diagrams of English military works, and the semiotics of graph representations. She has published on early modern paratextuality, book history, and graph taxonomies. ORCID | UTU
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