Beyträge zum Gebrauche der Mathematik und deren Anwendung II
Year of Conception: (varies for each part)
Year of Writing: (varies for each part)
Year of Publication: 1770
Subject: Practical Geometry, Trigonometry, Number Theory, Equations, Astronomy
Publication: Beyträge zum Gebrauche der Mathematik und deren Anwendung. Berlin, Band II in zwei Theilen.(2)
Description:
This volume is the second of three collections that contain essays on various topics in pure and applied mathematics.
Part I and II are connected to Lambert's table project, viz. a table of factors and of prime numbers, later the same year pursued with the publication of Zusätze zu den logarithmischen und trigonometrischen Tafeln. The conception of these texts lies in the year 1766.
Part III describes and applies a conversions of numbers into (continued) fractions and of series into continued fractions. It contains a method to speed up the convergence of certain series that Lambert often applies in other (mathematical or astronomical) works. The essay continues an old string in Lambert's thought, but the structure of the text may have arisen around Mar. 1766.
Part IV and V were both written down Oct. 1766. Part IV, conceived Nov. 1758, shows how to derive sines and cosines from a table of sines ascending per three degrees. Part V gives a popular account that the quadrature of the cercle is impossible on heuristic grounds. Lambert would follow up on this paper in his famous article on the irrationality of pi.
Part VI describes an instrument and tricks to measure with certain accuracy distances on paper, a method Lambert conceived of in Feb. 1757 and often used throughout his carreer. The paper itself seems to have been written down in Sept. 1766.
Part VII was conceived Oct. 1763, written down Oct. 1766, it studies foursided figures.
Part VIII was conceived Aug. 1757, reconsidered Dec. 1765 and written down Mar. 1768. It treats of the theory of equations.
Part IX was conceived Feb. 1758, written down Mar. 1766 and describes a mechanical method to integrate surfaces by enclosing them by polygons "ad mentem Archimedis".
Part X was written Mar. 1766 and continues Lambert's study of practical geometry ("Gnomonik", "Feldvermessen").
Part XI continues Lambert's earlier occupation with the doctrine of balance, it was conceived Nov. 1765, written down a year later.
Part XII is part of Lambert's preoccupation with practical and popular astronomy in general, and with Tobias Mayer moon tables in particular. Materials for this article were collected June 1765, the text itself written down Jan. 1766.
Overview of Contents:
1. Theilung und Theiler der Zahlen pp.1-41
2. Vorschlag die Theiler der Zahlen in Tabellen zu bringen. pp.42-53
3. Verwandlung der Brüche. pp.54-132
4. Algebraische Formeln für die Sinus von drei zu drei Graden. pp.133-139
5. Vorläufige Kenntnisse für die, so die Quadratur und Rektifikation des Cirkuls suchen. pp.140-169
6. Einige Anmerkungen von Ausmessung der Winkel und Linien auf dem Papier. pp.170-174
7. Anlage zur Tetragonometrie. pp.175-183
8. Anmerkungen über die Verwandlung und Auflösung der Gleichungen. pp.184-249
9. Quadratur und Rektifikation der krummen Linien durch geradelinichte Vielecke, welche um dieselbe und in denselben beschrieben werden können. pp. 250-313
10. Anmerkungen und Zusätze zur Gnomonik. pp. 314-362
11. Gedanken über die Grundlehren des Gleichgewichts und der Bewegung. pp. 363-628
12. Zergliederung und Anwendung der Mayer'schen Mondstafeln, nebst 58 Blättern, Tafeln für Neu- und Vollmonde. pp. 629-815
Reviews: ADB 1770, 322-333(6) Part I and II are connected to Lambert's table project, viz. a table of factors and of prime numbers, later the same year pursued with the publication of Zusätze zu den logarithmischen und trigonometrischen Tafeln. The conception of these texts lies in the year 1766.
Part III describes and applies a conversions of numbers into (continued) fractions and of series into continued fractions. It contains a method to speed up the convergence of certain series that Lambert often applies in other (mathematical or astronomical) works. The essay continues an old string in Lambert's thought, but the structure of the text may have arisen around Mar. 1766.
Part IV and V were both written down Oct. 1766. Part IV, conceived Nov. 1758, shows how to derive sines and cosines from a table of sines ascending per three degrees. Part V gives a popular account that the quadrature of the cercle is impossible on heuristic grounds. Lambert would follow up on this paper in his famous article on the irrationality of pi.
Part VI describes an instrument and tricks to measure with certain accuracy distances on paper, a method Lambert conceived of in Feb. 1757 and often used throughout his carreer. The paper itself seems to have been written down in Sept. 1766.
Part VII was conceived Oct. 1763, written down Oct. 1766, it studies foursided figures.
Part VIII was conceived Aug. 1757, reconsidered Dec. 1765 and written down Mar. 1768. It treats of the theory of equations.
Part IX was conceived Feb. 1758, written down Mar. 1766 and describes a mechanical method to integrate surfaces by enclosing them by polygons "ad mentem Archimedis".
Part X was written Mar. 1766 and continues Lambert's study of practical geometry ("Gnomonik", "Feldvermessen").
Part XI continues Lambert's earlier occupation with the doctrine of balance, it was conceived Nov. 1765, written down a year later.
Part XII is part of Lambert's preoccupation with practical and popular astronomy in general, and with Tobias Mayer moon tables in particular. Materials for this article were collected June 1765, the text itself written down Jan. 1766.
Overview of Contents:
1. Theilung und Theiler der Zahlen pp.1-41
2. Vorschlag die Theiler der Zahlen in Tabellen zu bringen. pp.42-53
3. Verwandlung der Brüche. pp.54-132
4. Algebraische Formeln für die Sinus von drei zu drei Graden. pp.133-139
5. Vorläufige Kenntnisse für die, so die Quadratur und Rektifikation des Cirkuls suchen. pp.140-169
6. Einige Anmerkungen von Ausmessung der Winkel und Linien auf dem Papier. pp.170-174
7. Anlage zur Tetragonometrie. pp.175-183
8. Anmerkungen über die Verwandlung und Auflösung der Gleichungen. pp.184-249
9. Quadratur und Rektifikation der krummen Linien durch geradelinichte Vielecke, welche um dieselbe und in denselben beschrieben werden können. pp. 250-313
10. Anmerkungen und Zusätze zur Gnomonik. pp. 314-362
11. Gedanken über die Grundlehren des Gleichgewichts und der Bewegung. pp. 363-628
12. Zergliederung und Anwendung der Mayer'schen Mondstafeln, nebst 58 Blättern, Tafeln für Neu- und Vollmonde. pp. 629-815
; GGA 1770, 726-728(4)