The present contribution concerns a text in the form of handwriting, written in French. The year is known, given on the first page - 1846, but the author not. The present authors believe that the manuscript was written by Hervé Faye (Hervé Auguste Étienne Léopold Alban Faye, 1814-1902), a French astronomer and geodesist. The manuscript belongs to a collection of 24 manuscripts which is a property of the Mathematical Institute of Serbian Academy of Sciences and Arts in Belgrade. The entire collection has been digitized and it is deposited in the Virtual Library of the Faculty of Mathematics in Belgrade. The manuscript containing almost 600 pages is subjected to an analysis which is reported here.