An unpublished manuscript primer on arithmetic and commercial mathematics, composed, calligraphed, and decorated by the mathematician Louis André Simon as a commission for l'écolier Jean-Antoine Bech, young son of the Duc de l'Entrecasteaux. The text begins with two one-page livrets—a multiplication table and a list of the names of increasingly large numbers—after which follows chapters on basic arithmetic, interest computations, currency conversions, commission income, the mathematics of discounted merchandise, profit-sharing, company structures, and concludes with a short treatise on "the question of  bankruptcy." Each section contains sample calculations, and some include word problems for the student to solve. Nearly half the 593 pages are decorated with Simon's colorful, whimsical birds, potted flowers, paisleys checky, and swirling tracery. Nothing is known about young Bech, though we know of two other manuscripts in Simon's hand. The earlier of these is a copy of the 1737 third edition of jurist Claude Poquet de Livonnière's Regles du droit françois, which Simon enlarged from the original unillustrated duodecimo into a thick folio illuminated with seven naïve portraits—one of Louis XV—and dozens of polychrome figures, blooms, and delicate ornamentation. That manuscript, preserved in the Juvenile Jurisprudence collections at the Lillian Goldman Law Library at Yale, is not signed, but an accompanying letter by the bookseller Sanders of Oxford, dated 1746, attributes the MS to Louis André Simon, and notes that it was produced for the young son of the Duc de l'Entrecasteaux—perhaps Jean-Antoine Bech's father. Clearly Simon was connected to the House of Entrecasteaux in some capacity, if nearly forty years later he was commissioned by the same family for another major book. (The other manuscript, also an original work on commercial arithmetic, is signed by Simon but not dated. It comprises 41 lessons in two folio volumes, and is illustrated much like our book. That manuscript is held at the Houghton Library at Harvard as MS Typ 382.) Our manuscript, only the third known work by Simon, is the most significant, having been signed and dated by both Simon and the young charge for whom it was created. Not only a signal, handsome manuscript by a little-known artist and mathematician, but an enigmatic witness to an unstudied aspect of the relationship between student and teacher in pre-Revolutionary France.

Contents:
1-2. Decorative frontis
3-8. General title 
9-10. Address from teacher to student
11-14. Definition of arithmetic
15-44. On addition
45-70. On subtraction
71-82. On multiplication
83-98. On division
99-138. On reduction
139-148. On invoicing
149-174. On interest
175-230. Currency conversion and computation
231-238. Currency multiplication
239-256. Sundry computation tables
257-298. Computation of grain prices
299-318. Calendarial calculation
319-400. The rule of threes
401-412. On tariffs
413-454. On "company rules" (profit sharing)
455-476. Regula falsi (solving for simple unknowns)
477-488. Rules of compounds
489-496. Rules for bartering
497-500. On discounts
501-520. Règle de part
521-556. On commissions
557-564. On the question of bankruptcy
565-592. Sundry notes and mathematical rules
593. Conclusion: addresses to student and teacher 

Folio, 341 x 204 x 45 mm (binding), 339 x 200 x 39 mm (text block), leaves watermarked "J M" in block letters, countermarked with a small bunch of grapes (Gaudriault 1468, suggesting Joseph Montgolfier, c1788, ref. Archives nationales de France 1478 III, 2), 297 ff., leaf comprising pp 523-4 removed, three preliminary blank leaves, collation impracticable but generally gathered in cahiers of 16, 18, or 20 leaves, text justification 152 x 310 mm, centered between two vertical double guidelines, occasional modern penciled pagination, without catchwords, text in a single hand in iron-gall ink, polychrome watercolor and bodycolor illustrations of birds, flowers, and occasional figures accomplished in the same hand. Period mottled sheepskin, undecorated and unlettered, edges of text block stained vermilion, worn, with old scoring to upper board and small areas of loss of leather, first and last free ends wanting, inner hinges separating (but board attachments firm), acid migration from turn-ins discolors margins of first and last leaves, minor worming to margins of upper pastedown; scattered staining, fingersoiling, and blemishes to text block, last few leaves toned and a bit tired.

Provenance: From the library of Jean-Antoine Bech of Entrecasteaux, son of the Duc de l'Entrecasteaux, who—according to the title page—commissioned the work from artist and mathematician Louis André Simon, who completed the manuscript 27 September 1785.

Entrecasteaux: 1785.

Item #358