Arithmetic manuscript for the Real Academia Militar de Matemáticas de Barcelona.
[Manuscript]/ [Mathematics] / [Real Academia Militar de Matemáticas de Barcelona]. Elementos de la Aritmetica. S.l. [Barcelona]: s.n. [18th century, after 1739]. 8vo manuscript [14.4 x 10.0 cm], 191 pp. [in fact 195 pp., as pp. 40-43 are repeated in numeration], [1] p., [2] ff. Bound in contemporary calf, gold-tooled spine, blue sprinkled edges. Spine and boards much rubbed, minor edge wear. Occasional staining especially in first and last leaves, but not affecting legibility, occasional toning, pen trials and remnants of red wax seal in last two leaves, neatly written throughout.
18th-century Spanish manuscript of the (unpublished) “Elements of Arithmetic” developed expressly for the use of students at the Real Academia Militar de Matemáticas de Barcelona. The manuscript’s introduction alludes to the establishment of the mathematics curriculum on 22 July 1739, discusses the intentions of the program, and lists more advanced mathematical topics one was to pursue after mastering these “Elements.” This volume carries the inscription of a certain Josef Mariano Isidro de Araquistain (“Del Bac.r en L.s D. Josef Mariano Ysidro de Araquistayn, y Pasante de Abogado”), who perhaps is the one who wrote out the manuscript.
Maria Rosa Massa-Esteve, who has studied the establishment of the mathematical curriculum at the Real Academia Militar de Matemáticas de Barcelona, writes, “In 1739, a Royal Ordinance set up the rules of the Royal Military Academy of Mathematics and established the contents of the course in pure and ‘mixed’ mathematics to be taught in academies. The mathematical course prepared by Pedro Lucuce (1692-1779) [was] taught for almost 40 years in this Academy [and] the generation of engineers trained in this Academy enjoyed an excellent scientific and technical level, and its repercussion and influence can be appreciated in its civil and military works […] Although the course was never published, it has been preserved in several manuscripts, written by different students from the Academy of Barcelona and from two other centers in Oran and Ceuta” (Maria Rosa Massa-Esteve, “Teaching Mathematics at the Barcelona Royal Military Academy of Mathematics (1739-1803),” pp. 143 & 154).
The contents of our manuscript are as follows: [Introduction] (pp. 1-60); “Elementos de la Aritmetica” (pp. 7-11); “Tratado I de la Aritmetica” (pp. 11-12); “Libro I De la Arithmetica” (pp. 13-72); “Libro II Del algorihtmo literal” (pp. 72-96); “Libro III De la razon y proporcion en com[u]n” (pp. 97-110); “Libro IV De las Reglas de Proporcion” (pp. 111-46); “Libro V De las Potencias y raices de los numeros y singular[en]te de la comp[osicio]n y resolucion de num[ero]s quadrados y cubicos” (pp. 147-74); “Libro VI De Las Progresiones” (pp. 175-91); [five pages on money, weights, measures, index, and pen trials].
OCLC and KVK locate similar manuscripts at the Universidad de Sevilla (MS A 333/024) and Barcelona Biblioteca de Catalunya (MS 3474).
*Maria Rosa Massa-Esteve, “Teaching Mathematics at the Barcelona Royal Military Academy of Mathematics (1739-1803),” in The Algebrization of Mathematics during the 17th and 18th Centuries: Dwarfs and Giants, Centres and Peripheries, Davide Crippa & Maria Rosa Massa-Esteve, eds., pp. 141-70.