Sylvestre François Lacroix - Matematica e geometria - 1810-1813

Interesting pair of two mathematical works by Sylvestre-François Lacroix (1765–1843), published between Paris and Florence in 1810 and 1813 and altogether accompanied by 14 folded geometric plates.

The two volumes, gathered in the same lot, document well the European circulation of Lacroix’s work in the early years of the 19th century: following the French edition of the treatise on trigonometry, the Italian version of his Elements of Geometry appeared just three years later.

The first volume is the Traité élémentaire de trigonométrie rectiligne et sphérique, et d’application de l’algèbre à la géométrie, Paris, Courcier, 1810, indicated on the title page as “Cinquième édition, revue et augmentée.”

It preserves 5 folded plates, dense with geometric constructions, curves, projections and figures related to trigonometry and the application of algebra to geometry. The final plates are particularly successful, where the increasing complexity of the constructions culminates in elaborate geometric representations and solid figures.

A detail uncommon and of notable bibliographic interest is the Avis du Libraire. The publisher explicitly warns that copies lacking the author’s and bookseller’s signatures would be considered counterfeit. In the present copy are preserved two handwritten signatures in the position foreseen by the notice, both clearly visible in the photographs. For fairness, no attribution of the individual grafias is proposed beyond what is directly documentable.

The second volume is Elementi di geometria ad uso della Scuola Centrale delle Quattro Nazioni del Signore S. F. Lacroix, Florence, at Guglielmo Piatti, 1813. The title page bears the important indication “Prima versione italiana fatta sull’ottava edizione di Parigi.”

The volume preserves 9 folded plates, with a broad repertoire of plane and solid geometry constructions. The more elementary figures are followed progressively by circles and polygons, prisms, pyramids, cones, cylinders, sections and complex three‑dimensional representations. Of particular impact are the final plates, densely etched and populated with shaded geometric solids, which convey the didactic character of geometry of the era with immediacy.

Altogether there are 14 folded plates: 5 in the 1810 volume and 9 in the 1813 volume.

The conditions of the two copies differ markedly.

The Parisian 1810 volume is the best preserved of the two: it shows the natural signs of time and wear to the binding, while the plate apparatus is in decidedly better condition than in the Italian volume.

The Florentine 1813 volume shows a more lived‑in preservation, coherently documented in the photographs: browning and spreading foxing, stains and humidity drips, with areas showing traces compatible with previous mold; some pages are more yellowed, stiffened and fragile. Stains and browning also affect some of the folded plates. The binding shows evident signs of use and time.

The iconographic apparatus of the whole remains remarkable: 14 folded geometric plates through which one can follow the progression from elemental constructions to the more complex applications of solid geometry.

A bibliographically coherent set, in which Paris 1810 and Florence 1813 document two nearby moments in Lacroix’s European fortune: the French treatise with its particular system of signatures against counterfeiting and the subsequent “Prima versione italiana” of the Elements of Geometry, both enriched by an important plate apparatus.

Dimensions: volume of 1810 about 20 × 13 cm; volume of 1813 about 20 × 14 cm.