Theoria motuum planetarum et cometarum continens methodum facilem exaliquot observationibus orbitas cum planetarum tum cometarum determinandi. Una cum calculo, quo cometae, qui annis 1680 et 1681 itemque ejus, qui nuper est visus, motus verus investigatur

First edition of Leonhard Euler’s first book devoted entirely to astronomy, published in Berlin by Ambrosius Haude in 1744, with no date printed on the title-page. Quarto, illustrated with an allegorical frontispiece after F. H. Frisch, engraved by Berot, and four folding plates of astronomical and geometrical diagrams. The frontispiece was printed on leaf A4, which would normally have contained pages 7 and 8, and was then placed facing the title-page: the pagination consequently passes directly from 6 to 9, with no loss of text. 185 pages, numbered through 187.

Modern half ivory vellum, smooth spine without lettering, comb-marbled paper boards, red edges. A few small spots of foxing, chiefly towards the end of the volume.

The frontispiece, deliberately occupying a leaf otherwise intended for text, provides an emblematic introduction to the scientific programme of the book. Two winged figures display the solar system beneath the motto “Sapientissimi Opus” - the work of the All-Wise - an image of celestial order whose motions are precisely what the calculations that follow seek to explain.

The Theoria motuum planetarum et cometarum was Euler’s first book devoted entirely to astronomy. Its title already states its ambition: to provide a method by which the orbits of both planets and comets might be determined from a limited number of observations. Recorded as Eneström 66, it has long been recognised as one of Euler’s fundamental works on the calculation of orbits.

The problem arose directly from Newtonian mechanics. In the Principia, Newton had treated geometrically the motion of a body subjected to the attraction of another and had applied his theory to cometary trajectories. Euler now translated this mechanics into the language of analysis. In the Theoria he gave a complete mathematical treatment of the two-body problem consisting of a planet and the Sun, while developing methods by which an orbit could be derived from observations. Historians of cometary orbit determination have accordingly identified Euler’s work of 1744 as the first fully analytical method no longer dependent upon geometrical constructions.

The significance of this development was clearly understood by Jérôme de Lalande. In his Bibliographie astronomique of 1803 he summarised the historical position of the book in a single sentence: « Ce livre est le premier où l'on ait traité analytiquement les orbites des planètes et des comètes » [This is the first book in which the orbits of planets and comets were treated analytically].

Euler did not leave his method at the level of abstraction. He applied it to two comets whose juxtaposition is particularly revealing. The first was the Great Comet of 1680-1681, one of the celestial objects to which Newton himself had applied his theory of gravitation in the Principia. More than sixty years after Newton, Euler thus returned to the same body, but with the new instruments of mathematical analysis.

The second is described on the title-page simply as “ejus, qui nuper est visus” - the comet recently observed. It was the spectacular Great Comet of 1743-1744, now designated C/1743 X1 and commonly known as the Klinkenberg-Chéseaux comet. Discovered in late 1743, it reached perihelion on 1 March 1744 and became one of the most striking astronomical phenomena of its age. The Theoria thus tests Euler’s new method against both a canonical object of Newtonian mechanics and the most immediate astronomical event of his own time.

This double application gives the full title of the work its meaning. Euler was not merely presenting a general theory of celestial motion, but demonstrating how a small number of observations could be transformed through calculation into orbital parameters. The passage from geometrical construction to analytical calculation made the method systematic and helped establish orbital determination as one of the central applications of mathematical analysis to astronomy. Modern historical studies of cometary orbit calculation place Euler’s 1744 method precisely at this turning point.

The book appeared at a moment when Euler’s own career was entering a new phase. Invited by Frederick II, he had left St Petersburg for Berlin in 1741. The reorganisation of the Prussian learned society was completed in 1743 with the creation of the Académie Royale des Sciences et Belles Lettres, which held its first session in its new form in January 1744. Euler was appointed Director of its Mathematics Section; Maupertuis, whom Frederick had been courting for several years, was not formally appointed President until May 1746.

The Theoria motuum therefore appeared at the beginning of Euler’s great Berlin period, in the very year in which the reorganised Academy began its work. Published by Ambrosius Haude, it was one of Euler’s first major books after settling in Prussia and brought astronomy within the analytical programme that he had already done so much to advance in mechanics.

A rare copy of the first edition of Euler’s first astronomical treatise, complete with its allegorical frontispiece and four folding plates, in which he provided a general analytical treatment of planetary and cometary orbits and applied it in turn to Newton’s Great Comet of 1680-1681 and to the newly observed comet of 1743-1744: one of the works that decisively brought celestial mechanics into the domain of mathematical analysis.