I'm still going through some old papers and books that I have yet to really document. Many of them seem to have some bearing on one of the most important inputs to the theatrum machinarum: engineer's sketchbooks.
Sketchbooks are a well-studied element of the history of technology. Unfortunately, the purview of the most popular studies is limited to the hagiography of early engineering: Leonardo, Francesco di Giorgio, and Taccola. The sketchbook genre was very long lived and had ongoing significance. We can take the starting point to be Villard's famous book. An arbitrary end point could be the anonymous military sketchbook that was part of the Rosenwald collection and is held by the Library of Congress (Daniela Lamberini attributes the work to a member of the circle of Giulio Parigi). There are even sketchbook versions of Besson's work and some manuscript versions of Ramelli's designs.
One interesting contribution to the sketchbook genre is the book of Jacques Gentillâtre. He was born in 1587 and worked in the atelier of Jacques II Du Cerceau--why do these guys just keep cropping up?--at the side of a young Salomon de Brosse. He left Paris in 1603 to work as an architect and engineer in Sedan, Lorraine, and in Franche-Comte [nb. he would have overlapped with Errard and may have known him. This fact might explain the remarkable resemblance between some of his sketches and Errard's hodometer]. He served as an "architect and fortficateur" in Montbeliard in the service of the duc de Wurtemberg and then worked for the Seigneurie de Geneve. He appears in Lyon in 1622 but all traces of him end in 1623.
He maintained a sketchbook between about 1615 and 1625 which seems to have been intended as a manual of practice for architects and engineers (MS. fr. 14727). Like the Rosenwald book, it contains a variety of sections, many of which are incomplete. The writing is elegant but the vocabulary and syntax are limited. But its the many images that draw the reader's attention. It has four main sections: mathematics, fortresses and machines of war, buildings, and mechanical inventions. His use of mathematics is remarkable for the time. The book opens with long mathematical tables for common activities like multiplication and addition. He then provides six books on geometry that includes guidance on surveying and instruction on weights, measures, and forces. He then continues with sketches of fortifications and of war machines. Chatelet-Lange notes that influence of Errard's book on fortification but seems unaware of his earlier book on machines. Gentillatre mentions several earlier authors on fortification, but not Errard. He then moves into civil architecture and borrows liberally from Vitruvius.
In addition to Jean Martin's Vitruvius, Gentillatre also borrows from Palladio, Alberti, Durer, Vignole, and Jacques I Du Cerceau: Livre d'architecture (1559 and 1582). In addition to architecture, he focusses on the trades, devoting pages to both masonry and carpentry. Gentillatre demonstrates solutions to complicated geometrical problems like the masonry design of spherical niches or spiral staircases, and the wooden falsework to support masonry spans, arches, and bridges. He then devotes a few pages to perspective and optics and then moves on the machines, borrowing several designs from Salomon de Caus. Chatelet-Lange notes that his machine descriptions are dry and scientific. In this manner, he emulates de Caus but differs from both Ramelli and Besson.
Notably, Chatelet-Lange claims that Genillatre's work is syptomatic of an overall shift in architecture and the affiliated work of the early engineers. The importance of mathematics and science is gradually recognized as a great art. This trend is reflected not just in the sketch book of Gentillatre but also in the prefaces of Besson and Ramelli, and in a manuscript by de Caus that describes a conversation between an architect, an engineer, and a mathematician. This trend towards mathematization is most reflected in the emerging science of mechanics, fortification, and land surveying. Overall, the work has a whimsical nature. Chatelet-Lange compares the depictions to the "fantastic and anecdotic" depictions of Sambin and Boillot. Similarly, the work of both Gentillatre and the modern engineers is completely free from depictions of ruins or ancient orders. In their pages, the Renaissance man recreated the ideals of antiquity.
L. Châtelet-Lange: 'L’Architecture entre science et pratique: Le Cas de Jacques Gentillâtre', Actes du colloque. Les Traités d’architecture de la Renaissance: Tours, 1981. Paris, Picard : 1988. pp. 397–406