Beyträge zum Gebrauche der Mathematik und deren Anwendung III  

Year of Conception:    (varies for each part)
Year of Writing:             (varies for each part)
Year of Publication:     1772

Practical Geometry, Theory of Errors, Cartography, Astronomy


Beyträge zum Gebrauche der Mathematik und deren Anwendung. Berlin, Band III.


This volume is the third of three collections that contain essays on various topics in pure and applied mathematics.

Part I was written Mar. 1770.
Part II continues the earlier essay on "Visirkunst" of 1765, it was conceived in Dec.1765, pursued in 1766 and 1771 and finally written down July 1771.
Part III was also written Mar. 1770, its origins reach back to meditiations Feb. 1762, Lambert found the rectifying series Dec. 1766.
Part IV was written Nov. 1768 and is connected to the Beyträge of 1770, Nr. 9.
Part V gives an interpolation method, useful in extending tables, written April 1770.
Part VI is the result of years of meditations on mappings and cartography, starting around 1762. These meditations were especially intensive during the year 1770, at the end of which year the paper was probably written. It contains the famous Lambert-projection method for mapping earth.
Part VII was written April and June 1770. It reconstructs the orbit of the comet of 1769.
Part VIII is a theoretical treatise on architecture, in which Lambert develops some algebraic methods to obtain best solutions for various architectural problems. One of these problems, the optimal form of a bee hive cell (a hexagon), was found by Lambert in 1762. The rest of the text was conceived and written Sept. 1769 andFeb. 1770.
Part IX takes up the question of finding a law of mortality, births and marriages on the basis of empirical materials and graphs (a part of this can be found as an example in Beyträge 1765 Nr. 4). Lambert started working on it in Feb. 1767 and wrote the results down in Sept. 1770.

Overview of Contents:

1. Eine besondre Eigenschaft der Tangenten. pp.1-11.
2. Zusätze zur Visirkunst. pp.12-34.
3. Rektifikation elliptischer Bogen durch unendliche Reihen. pp. 35-55.
4. Verwandlung der Figuren in gleich große Recktangel. pp. 56-65.
5. Anmerkungen über das Einschalten. pp. 66-104.
6. Anmerkungen und Zusätze zur Entwerfung der Land- und Himmels-Charten. pp. 105-199.
7. Von Beobachtung und Berechnung der Cometen und besonders des Cometen von 1769. pp. 200-322.
8. Anmerkungen über die Baukunst. pp. 323-475.
9. Anmerkungen über die Sterblichkeit, Todtenlisten, Geburten und Ehen. pp. 476-569.

Reviews: ADB 1772, 495-506(6) ; GGA 1772, 979-981(4)