The Planetary Theory of François Viète 1. The Fundamental Planetary Models

The treatise was evidently rediscovered by Libri G. , who gives a summary of its contents based upon the Paris manuscript (Libri 1865, iv, 297–305). Libri also remarks (p. 22, n. 1) that Delambre had followed Boulliau in reporting the treatise lost. If it was not known to Boulliau, it must have been all but lost in the mid-seventeenth century. More recently, Viète's planetary theory has been considered by Schofield C. (1965, 295), Swerdlow N. (1973, 470–1, 482, 501) and Whiteside D. T. (1974, 3–4, 16–17), the last being the most thorough and penetrating.

The four manuscripts are listed by Hoffmann J. E. (Viète 1646 (repr. 1970), p. X*, n. 15).

That F₁ and F₂ were the property of the same person, that is, of the second hand of F₁, may explain why they are together in the Magliabechiana collection. I know nothing of the history of either manuscript.

The reference to the French tables in Apollonius Gallus shows that Viète intended to publish an astronomical work and may, in fact, already have developed a good part of his planetary theory. But the reference to Apollonius Gallus in the Ad harmonicon shows that the autograph manuscript itself must be from 1600 or later.

There is some confusion about both the title and the number of books in the treatise. The title is given as Ad harmonicum coeleste libri quinque priores in F₁, F₂, and R, although the title in F₁ is not in Viète's hand, and as Ad harmonicon coeleste libri quinque priores in P. Since harmonicon rather than harmonicum has been the conventional title since Libri, who followed P, I have continued to use it although harmonicum, which is the way the title is given by the Elzevirs, may well be correct. How the contents of the treatise were to form part of five books I do not know, nor do I know what was to follow the libri quinque priores. The surviving treatise could be more than the second book, but how much more or where the divisions fall is unclear.

In his Relatio Kalendarii vere Gregoriani (Viète 1646, 494) of 1600, Viète uses, with a small correction in epoch position, Copernicus's 1717-year period of the anomaly of precession. The Copernican precession with some correction is also used in the rough notes in F₁. On Viète's solution to the problem of finding the epoch of the anomaly in Copernicus's precession theory, see Swerdlow 1975, Appendix 1.

De mundi aetherei recentioribus phaenomenis, 1588 (Brahe 1915–, iv, 157).

Swerdlow 1973, 471–8.

Swerdlow 1973, 458, n. 2.

The bracketed words in this definition are exchanged, surely by error, in F₁ and the other manuscripts, and here they have been put back where they must belong.

The proof is given in Swerdlow 1973, 470, and Whiteside 1974, 16, n. 6. See also Boyer 1947–48. The well-known cancelled passage on f. 75r of Copernicus's autograph manuscript shows that he too was aware of this method of generating an ellipse. Tycho uses the double epicycle model of the first anomaly in the Progymnasmata, and this could have drawn Viète's attention to it, although it seems more likely that he had already developed his model before the publication of the Progymnasmata.

Whiteside D. T. points out (1974, 4) that quite remarkably the Mercury model of Qutb ad-Dīn ash-Shīrāzī, described by Kennedy E. S. (1966, 373–5), produces exactly this equation of centre with an altogether different vector linkage.

Boyer C. 1947–48. “Note on Epicycles and the Ellipse from Copernicus to Lahire”, Isis, xxxviii, 54–56.

Brahe I. 1915–. Opera omnia, ed. Dreyer I. L. E. (Hauniae).

Copernicus N. 1543. De revolutionibus orbium coelestium libri VI (Norimbergae (repr. New York, 1965)).

Copernicus N. 1973. Nicolai Copernici Opera omnia, i. Nicolai Copernici De revolutionibus codicis propria auctoris manu scripti imago phototypa (Varsoviae-Cracoviae).

Kennedy E. S. 1966. “Late Medieval Planetary Theory”, Isis, lvii, 365–78.

Kennedy E. S. and Roberts V. 1959. “The Planetary Theory of Ibn al-Shātir”, Isis, 1, 227–35.

Libri G. 1865. Histoire des sciences mathématiques en Italie (deuxième édition, Halle).

Schofield C. 1965. “The Geoheliocentric Mathematical Hypothesis in Sixteenth Century Planetary Theory”, British journal for the history of science, ii, 291–6.

Swerdlow N. 1973. “The Derivation and First Draft of Copernicus's Planetary Theory: A Translation of the Commentariolus with Commentary”, Proceedings of the American Philosophical Society, cxvii, 423–512.

Swerdlow N. 1975. “On Copernicus's Theory of Precession”, The Copernican achievement, ed. Westman R. S. (forthcoming).

Viète F. 1646. Opera mathematica recognita F. à Schooten (Lugduni Batavorum; repr. with foreword by Hoffmann J. E. , Hildesheim, 1970).

Whiteside D. T. 1974. “Keplerian Planetary Eggs, Laid and Unlaid , 1600–1605”, Journal for the history of astronomy, v, 1–21.