# Mathematical Treasure: Langsdorf on Kaestner's Analysis of Finite Quantities

Author(s):
Frank J. Swetz (The Pennsylvania State University)

Karl Christian von Langsdorf (1757-1834) was a German mathematician, engineer, and natural scientist. He studied mathematics at Göttingen with Abraham Kästner (1719-1800) beginning in 1774 (Wikipedia) and earned the D.Phil. in 1781 (Mathematics Genealogy Project). Among his many publications was the two-volume Erläuterungen der Kästnerischen Analysis endlicher Grössen (1776-1777), which roughly translates into English as Explanations of Kästner’s Analysis of Finite Quantities.

The book discusses problems in geometry and the use of numerical methods to solve algebraic problems.

Obviously, a reader of this book was expected to have knowledge of mathematics including algebra. On the first page, the author discussed the solutions to a set of simple equations. From the equation $x^2+z^2=b,$ von Langsdorf solved for $x,$ obtaining $x=\sqrt{b-z^2}.$ Note that the radical sign is inserted by hand in the text.

These images were obtained through the courtesy of ETH-Bibliothek Zürich. The book may be viewed in its entirety at e-rara: http://dx.doi.org/10.3931/e-rara-14892.

Index to Mathematical Treasures

Frank J. Swetz (The Pennsylvania State University), "Mathematical Treasure: Langsdorf on Kaestner's Analysis of Finite Quantities," Convergence (February 2018)