E187 -- Theoria motus lunae exhibens omnes eius inaequalitates

(Theory of the motion of the moon which exhibits all its irregularities)

Originally published with the full title: Theoria motus lunae exhibens omnes ejus inaequalitates In additamento hoc idem argumentum aliter tractatur simulque ostenditur quemadmodum motus lunae cum omnibus inaequalitatibus innumeris aliis modis repraesentari atque ad calculum revocari possit auctore L. Eulero Impensis academiae imperialis scientiarum Petropolitanae anno 1753.

Summary:

In addition to the foreword (which was not written by Euler), it contains an “Introductio,” 18 chapters, and “Additamentum continens alias methodos investigandi motus lunae inaequalitates” as mentioned in the title.

The 18 chapters are:

De motu corporis a viribus quibuscunque sollicitati.
Investigatio virium lunam sollicitantium.
Introductio anomaliae verae lunae in praecedentes aequationes.
Investigatio inaequalitatis lunae absolutae, quae variatio dicitur.
Investigatio inaequalitatum lunae ab ejus excentricitate simplici solum pendentium.
Investigatio inaequalitatum lunae a quadrato excentricitatis ipsius ortarum.
Correctio inaequalitatum lunae hactenus inventarum.
De motu apogei lunae.
Investigatio inaequalitatum lunae a sola excentricitate orbitae solis pendentium.
Investigatio inaequalitatum lunae ab utriusque orbitae excentricitate simul pendentium.
Investigatio inaequalitatum lunae a parallaxi solis pendentium.
Investigatio inaequalitatum motum lineae nodorum afficientium.
Investigatio inclinationis orbitae lunaris ad eclipticam cum ejus variatione
Investigatio inaequalitatum lunae ab ejus inclinatione ad eclipticam oriundarum.
Accuratior investigatio inaequalitatum lunae ab inclinatione ejus orbitae pendentium.
Expositio inaequalitatum lunae hactenus inventarum.
Investigatio elementorum motus lunae.
Constitutio elementorum pro tabulis lunaribus.

The foreword indicates that this work is not an essay for a competition, which did not win the prize (see the letter from C. G. J. Jacobi to P. H. Fuss from March/April 1848; Bibl. math. 83, 1907/8, p. 302). It was actually inspired by the winning essay of Clairaut, about which Euler sent a report to the Academy.

According to C. G. J. Jacobi, Euler presented a piece with the title “Theoria motus lunae” to the Berlin Academy on April 22, 1751.

Publication:

Originally published as a book in 1753
Opera Omnia: Series 2, Volume 23, pp. 64 - 336

Documents Available:

Original Document:
The Euler Archive attempts to monitor current scholarship for articles and books that may be of interest to Euler Scholars. Selected references we have found that discuss or cite E187 include:
- Fuller AT., “Maxwell, James, Clerk Cambridge manuscripts - extracts relating to control and stability .2..” International Journal of Control, 36 (4), pp. 547-574 (1982).
- Waff CB., “Theory of moons motion (1702) - Newton, I.” Centaurus, 21 (1), pp. 64-75 (1977).

Return to the Euler Archive