A collection of four manuscripts (plus two additional leaves) devoted to fortification (beautifully illustrated with 16 pen and ink drawings of barriers and building tools and equipment); plain and solid geometry and its applications, with problems and solutions, possibly from an examination (with 14 line diagrams plus 2 on an added leaf); maritime navigation, triangulation, determination of longitude, compass corrections and correcting a course for currents, with problems and solutions, possibly from an examination (with about 50 line diagrams); and the surveying of land and dikes and the conversion of measurements, with problems and solutions, possibly from an examination (with a double-page sundial, and a similar sundial on an added leaf).
Ad 1. [Fortification barriers, and tools and equipment for building fortifications].
[The Netherlands], [ca. 1645].
[A]2 = 2 ll., [4] pp. Illustrated with 16 fine pen and ink drawings.
Text in Dutch (pp. 1-3) and French (p. 4), with 16 fine pen and ink drawings, shaded to show contours. The first two illustrations, not num,bered or lettered, show barriers. The first is made from an array of wooden stakes with horizontal iron spikes at the top. The second is a wooden beam with sharp wooden stakes radiating from it, called "vriese cavailliers" (literally "Frisian cavalry", still used in World War II and still called a "friese ruiter" in Dutch, a "cheval de fries" in English and a "cheval de frise" in French). The remaining illustrations show shovels, a pick, an adze, knives, a hoe and two views of a wheelbarrow (one from directly above, the other nearly from the side, with a scale). Although the manuscript has no title, it appears to be complete as it survives, with the 14 drawings of equipment, or elements within the drawings, lettered A-Y, including W but without J or U. The notes give quite detailed explanations, often with exact measurements. The manuscript devotes about 130 words to the array of stakes, for example: "dit sijn baricades die men somwijls steeckt ... inde gaten van de retrenchements van 6, 7 a 8 voet breet alwaer men uut en in gaet ende oock wel inde bressen als men den tijt niet en seyt om die te repareren en men steeckt se wel 3 a 4 dick achter de andere maer de uutwendigste sijde moet altijt diepper in de aerde sijn ende dan de tweede dieper als de dorde ...". It is not clear why the manuscript switches to French for the last page, but the neat semi-gothic cursive is quite rounded and may show some French influences (including the form of the final s).
Ad. 2. [Problems and solutions for a course in plane and solid geometry, perhaps an examination].
[The Netherlands], [ca. 1685].
[B]-[C]4 (- C1.4, with C4 probably blank) = 6 ll., 12 pp., plus 1 loose leaf on a different paper stock (1, [1 blank] pp.), possibly in the same hand and perhaps intended as an addition to the manuscript. Illustrated with 14 line diagrams plus 2 on the added leaf.
An extensive fragment (6 of 8 or 9 written leaves?) of a course in Latin on plane and solid geometry, with applications to architecture and other fields. It opens with "Theor. 1e. Propos. 4ta." and the first "Problem" is numbered 4, so there was probably at least one leaf preceding those that survive, but the first 6½ pages conclude modus 1 and the numbered theorems, propositions, problems, modi and lemmas suggest that modi 2-6 are complete except for the lost C1, which contained most of modus 5 (its heading, at the foot of B4v, has been struck through). So the manuscript may have originally collated [A]2 [B]-[C]4 = 10 ll., with C4 and possibly A1 blank. The heading to modus 6 notes that it is taken from the Jesuit Juan Bautista Villalpando (his 1604 work on the Tempel in Jerusalem) and the text cites Claude Richards annotated Euclid (first published at Antwerp in 1645) for Villalpando and Christoph Grienberger. The heading for the missing modus 5 indicates that it was taken from Thomas Hobbes, perhaps from his Quadratura circuli, ... (Oxford, 1669). The appendix to modus 1 notes that it is taken from Archytam Tarentinum (by Johann Andreas Schmidt & Johann Georg Metz, Jena, 1683).
Ad. 3. [Maritime navigation, including the determination of longitude, compass corrections and correcting a course for currents].
[The Netherlands], [ca. 1730?].
[A]10 [B]12 = 22 ll., [44] pp. Illustrated with about 50 line diagrams
A series of problems and solutions concerning maritime navigation, including triangulation, taking bearings, determination of latitude and longitude, compass corrections and corrections for currents, extensively illustrated with line diagrams. One of the examples uses the Cape of Good Hope.
Ad. 4. [The surveying of land and dikes, the conversion of measurements, and sundials].
[South Holland?], [ca. 1747].
[A]-[B]2 = 4 ll., with 3 slips pinned to A2r & v (quire A with 4 pp. of text plus the rectos of the slips), plus 1 loose leaf on a different paper stock (1, [1 blank] pp.), possibly by the same hand, closely related to the manuscript. Illustrated with a double-page sundial drawn across B1v & B2r (B1r & B2v blank), and a similar sundial on the added leaf.
The problems on the conversion of measurements uses examples with various "roeden" as used in Putten (South Holland), Hondsbos (North Holland), Rijnland (South Holland) and other administrative districts, as well as the province of South Holland itself, but they show a tendency to covert to South Holland units, suggesting the manuscript was written there. It notes that "onse" (our) roed comprises 12 voeten and our "onse" voet 12 duimen, which would fit the South Holland and several other units, but not, for example the Amsterdam units.
Ad 2 lacks 2 or possibly more leaves of text, as noted, the lower outside corner of A3 has been torn off, with the loss of a small bit of text, and the surviving leaves C2 and C3 are no longer conjugate. In ad 4, A1 and A2 are no longer conjugate, and the added leaf with the full-page sundial has a tear into the sundial and a large transparent brown stain. Many of the leaves have tattered edges or small stains. In spite of these defects, the manuscripts form valuable primary sources for education in applied mathematics. The splendid drawings in ad 1, with extensive accompanying text, provide very detailed information about barriers used against enemy infantry and cavalry ca. 1645, and about the tools and other equipment used to build fortifications at that time, and the two sundials in the ca. 1747 manuscript are especially interesting, as is the watermark commemorating the establishment of the Princes of Orange as hereditary stadtholders.