The Cross Staff is an angle measuring instrument that also makes it possible to determine the height of or distance to objects based on the intercept theorem. The instrument itself has been known since the Medieval Age for both land-based and sea-based measurements and is attributed to a development by Levi ben Gershon (also: Gersonides, 1288 – 1344). It consists of a wooden rod onto which spacers are applied and several adapters that are extended in the transverse direction. These adapters can be placed continuously variable on the base rod.
Hence the determination of an angle is always possible if the adapters can be positioned on the rod in such a way that a targeted object is just covered. A length dimension can also be determined, but the prerequisite for this is that any length in the triangle is known. Then and only then mathematics give you the proportions of the secondary triangle stretched over the cross staff.
The replica of a Cross Staff, which is available in the HistoLab, is the result of a student's work. It becomes frequently used in our courses on the experimental history of physics. The staff consists of a base rod of 78 cm in length and, as was customary at the beginning of modern times, has four different adapters of different sizes available as attachments.
Maximilian Curtze, Abhandlung des Levi ben Gerson über Trigonometrie und den Jakobsstab, Bibliotheca Mathematic, 12, 1898, S. 97 – 112
Wolfgang Torge, Geschichte der Geodäsie in Deutschland, de Gruyter Verlag, Heidelberg, 2. Auflage, 2008, S.32ff.