Land surveying tube in early Judaism

B. Erubin 43b describes a special tube of Rabban Gamaliel, with which he was able to measure distances of up to two thousand cubits on a plane, and which he would also use to measure the depth of ravines. With this tube, he could also measure angles, or at least set the tube on a specific angle to measure distances using congruent triangles. Although the method of measurement presented in the Talmud is not clear, very few sages thoroughly studied or interpreted the measurement method. Some have understood the method, on the basis of their own contemporary mathematical knowledge, while others simply laconically quoted their predecessors without understanding the earlier sages' explanations. Notably, in Rabban Gamaliel's period, optical lenses were not in use. Instead, a hollow tube was adapted to allow the measurement of a fixed distance. There are diverse opinions on how this tube was used to measure distance, depth, and height. In this paper we address the measurement methods of the Geonic sages and their subsequent interpreters and assess the methods they propose.