Traité de la trigonometrie, pour resoudre tous triangles rectilignes et spheriques. Avec les demonstrations des deux celebres propositions du Baron de Merchiston, non encores demonstrees
Traité de la trigonometrie, pour resoudre tous triangles rectilignes et spheriques. Avec les demonstrations des deux celebres propositions du Baron de Merchiston, non encores demonstrees
Traité de la trigonometrie, pour resoudre tous triangles rectilignes et spheriques. Avec les demonstrations des deux celebres propositions du Baron de Merchiston, non encores demonstrees
Written by a Scotsman in Paris
With an Early Discussion of Napier’s Logarithms
Dedicated to Robert Kerr, 1st Earl of Ancram
[MATHEMATICS] / HUME, James.
Paris, Nicolas & Jean de la Coste, 1636.

Traité de la trigonometrie, pour resoudre tous triangles rectilignes et spheriques. Avec les demonstrations des deux celebres propositions du Baron de Merchiston, non encores demonstrees.

4to [15.6 x 9.7 cm], (8) ff., 116 pp, 167 pp., 186-193 pp., (1) p. printer’s device woodcut of astronomer, (1) folding table, with woodcut arms of France on title, engraved arms of Robert Kerr, 1st Earl of Ancram (1578-1653) on verso of title, full-page woodcut arms of Hume of Godscroft, numerous woodcut and diagrams in the text, woodcut initials, headpieces, tailpieces. Bound in contemporary speckled calf, gold-tooled spine and board edges, red and blue sprinkled edges. Some rubbing and edge wear to spine and boards. Internally very well preserved.

Rare first and only edition of a treatise on trigonometry – illustrated with numerous woodcut diagrams – by James Hume of Godscroft, a Scottish mathematician living in Paris. The work includes information on logarithms as recently discovered by John Napier in 1614 (including a folding table of logarithms based on Napier’s 1619 example) and with demonstrations of two of Napier’s theorems which Hume claims are here published for the first time. Although apparently long a resident of France, James Hume’s continuing connection to the British Isles is reflected here in his dedication to Robert Kerr, 1st Earl of Ancram (1578-1653), courtier to Charles I, whose engraved arms appear on the verso of the title page.

A Scottish ex-pat, physician, and mathematician, who also published extensively on algebra, astronomy and fortification theory, Hume is credited, along with René Descartes, with introducing the modern exponential notation into mathematics (F. Cajori, pp. 204-7). Hume’s Copernican textbook, Spheres de Copernic et Ptolomee [Paris, Louys Boulenger, 1637]) has been ranked as among the earliest “informed discussion[s] about heliocentricity in France” (J. M. Lewis, p. 183). The present Traité de la trigonometrie was largely inspired by Hume’s distaste for the Trigonometriae canonicae (1633) of the mathematician and astronomer Jean-Baptiste Morin (1583-1656), with whom Hume had a bitter, long-standing. By contrast, his positive enthusiasm for the recently published works by his countryman John Napier on logarithms is evident throughout.  Hume, “whose interest in Napier would have been profound,” according the Napier’s biographer Julian Havel, has also been credited in this work on trigonometry with possibly identifying Napier’s burial site (the Church of St. Cuthbert) -- long a mystery -- and the disease Napier suffered from at the end of his life (gout).

James Hume was the son of David Hume of Godscroft (1558-1629), a figure renowned in his youth as a prodigy of neo-Latin poetry who later was a partisan and panegyrist of the Scottish house of Douglas and is today best remembered for his History of the House and Race of Douglas and Angus (1644) and the Apologia Basilica (1626), an early analytical work on Machiavelli’s The Prince. Often writing under his Latin name, ‘Scotus Theagrius,’ James Hume also published neo-Latin literature, including the Petronian farce Pantaleonis Vaticinia Satyra (1633) and several poems in his father’s De Unione Insulae Britanniae (1634), one of which accuses Morin of having plagiarized some proofs given by Hume to the Scottish mathematician John Napier (1550-1617), perhaps the very proofs included here in the Traité de la trigonometrie. Hume also published the Algèbre de Viète (1636), Les fortifications françoises (1634), and La theorie des planettes (1637). Each of these titles is today quite rare.

The Traité de la trigonometrie was apparently printed in three issues, which differ as to the number of preliminary leaves (no priority established). The present example conforms to SUDOC 042847575 and USTC 6028259.

OCLC locates U.S. examples of Hume’s Traité de la trigonometrie at the NYPL, Columbia, Harvard, and UCLA.

* Tomash & Williams H188; SUDOC 042847575; USTC 6028259; J. M. Lewis, Galileo in France: French Reactions to the Theories and Trial of Galileo; Francisque-Michel, Les Écossais en France, vol. 2, p. 292-3; E. Werdet, Histoire du livre en France, part 3, vol. 2, pp. 184-5; F. Cajori, A History of Mathematical Notations.

Price: $3,350.00

See all items in Rare Books