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Issue No.01 - January (2010 vol.32)
pp: 34-43
<p>Two almost forgotten keyboard calculators, the first by the Milanese Luigi Torchi (1834) and the second by the Florentine Tito Gonnella (1858), demonstrate technical features much ahead of their time. In particular, Torchi's calculators seems to incorporate possibly the first direct-multiplication mechanism.</p>
Keyboard mechanical calculators, direct multiplication, 19th century, Italy
Silvio Hénin, "Two Early Italian Key-Driven Calculators", IEEE Annals of the History of Computing, vol.32, no. 1, pp. 34-43, January 2010, doi:10.1109/MAHC.2010.27
1. L. Jacob, Le calcul mécanique, Octave Doin et Fils Éd., 1911; J.A.V. Turck, Origin of Modern Calculating Machines, Western Society of Engineers, 1921 (reprinted, Arno Press, 1972); E. Martin, Die Rechenmaschinen und ihre Entwicklungsgeschichte, J. Meyer, 1925 (trans. reprinted, The Calculating Machines, their History and Development, MIT Press, 1992); M. d'Ocagne, Le calcul simplifié par le procedes mécaniques et graphiques, Gautiers-Villars, 1928, (trans. reprinted, MIT Press, 1986); R. Taton, Le calcul mécanique Pr. Universitaire de France, 1949; F. Soresini, Storia del calcolo automatico, vol. I, Confindustria, 1977; J. Marguin, Histoire des instruments et machines à calculer, Hermann, 1994; M.R. Williams, A History of Computing Technology, 2nd ed., IEEE CS Press, 1997; G. Ifrah, The Universal History of Computing, John Wiley & Son, 2001.
2. Rough and questionable estimate, from relevant literature (see reference 1); the figure refers to digital devices only.
3. M. R. Williams, "Early Calculation," Computing before the Computers, W. Aspray ed., Iowa State Univ. Press, 1990, p. 50.
4. , Low cost mechanical calculators still used dials and slides until the 1950s.
5. E. Martin pp. 33–37; M. d'Ocagne, pp. 25–27; F. Soresini pp. 45–58; J. Marguin pp. 49–62; M.R. Wiliams, 1997, pp. 124–130.
6. E. Martin pp. 53–57; M. d'Ocagne, pp. 35–37; F. Soresini pp. 83–85; J. Marguin pp. 105–112; M.R. Williams 1997, pp. 145–146; R. Taton, pp. 32–34; http:/
7. D.M. Campbell, C.A. Greated, and A. Myers, Musical Instruments: History, Technology and Performance of Instruments of Western Music, Oxford Univ. Press, 2006, pp. 306–420.
8. Pellegrino Turri (Italy) built a keyboard typewriter in 1808 to help a blind woman to write her letters; other previous inventors are mentioned in the literature, but their use of a true keyboard seems questionable (Science Museum London, The History and Development of Typewriters, H.M. Stationary Office, 1964, pp. 17–22). The first 19th century writing machines, built by the British Reverend Creed and the German Hohlfeld, made use of a piano keyboard to write music ( M. Adler, Antique Typewriters, Schiffer Books, 1997, pp. 18–20). In 1856, the American musician D.E. Hughes patented a keyboard telegraph (US patent 14,917).
9. D.D. Parmelee, Calculator,, US patent 7,074, Patent and Trademark Office, 1850; J.A.V. Turck p. 17; E. Martin p. 62; F. Soresini p. 61; J. Marguin, p. 124.
10. L. Jacob pp. 16, 48; E. Martin p. 62; M. d'Ocagne, p. 30; J. Marguin p. 123; F. Soresini p. 61., D. Roegel, "An Early (1844) Key-Driven Adding Machine," IEEE Annals of the History of Computing, vol. 30, no. 1, 2008, p. 62.
11. T. Hill, Arithmometer, US Patent 18,692, November 24, 1857; J. A. V. Turck p.22; E. Martin p. 63; J. Marguin, p. 124.
12. D. Roegel, pp. 59–65.
13. M.R. Williams 1997, pp. 149–151; J.A.V. Turck, pp. 25–26, 61–64.
14. L. Jacob pp. 27–38; J.A.V. Turck pp. 52–75; E. Martin pp. 89–95; M.R. Williams, 1997, pp. 150–151; Comptometer, .
15. P.A. Kidwell, "The Adding Machine Fraternity at St. Louis: Creating a Century of Inventions, 1880–1920," IEEE Annals of the History of Computing, vol. 22, no. 2, 2000, pp. 4–21; E. Martin pp. 113–118; M. d'Ocagne, pp. 29–32; F. Soresini, pp. 67–68.
16. M.R. Williams, 1997, pp. 149–150.
17. P.A. Kidwell p. 14; M. d'Ocagne, p. 49; E. Martin, pp. 133–134.
18. M.R. Williams 1997, pp. 129–136; E. Martin pp. 39–42; F. Soresini pp. 79–80; J. Marguin, pp. 63–67.
19. E.D. Barbour, Improvement in Calculating Machines, US patent 130,404, 1872; J.A.V. Turck p. 181; M. d'Ocagne, p. 50; F, Soresini, p. 125.
20. R. Verea, Improvements in Calculating Machines, US patent 207.918, 1878; M. d'Ocagne, p. 50; F. Soresini, p.125.
21. L. Bollée, Une nouvelle machine à calculer, French patent 201,033, 1889; L. Jacob pp. 80–84; J.A.V. Turck p. 187; M. d'Ocagne, p. 50–51; F. Soresini pp. 126–127; J. Marguin, pp. 131–134.
22. O. Steiger, Rechenmaschine, German patent 72,870, 1892; L. Jacob pp. 82–83; E. Martin pp. 119–125; M. d'Ocagne, pp. 53–54; F. Soresini, pp. 128–131.
23. Illustrations modified from R. Taton, Le calcul mécanique, p. 51.
24. F. Soresini, p. 27.
25. P. Broglia, and L. Mussio, "Il calcolo alla specola di Brera" [Computing at Brera's Observatory], L'informazione territoriale e la dimensione tempo, Proc. 7th ASITA Nat'l Conf., vol. 1, 2003, pp. 512–528.
26. S. Hénin, "La calcolatrice del falegname" [The Carpenter's Calculator], Lettera Matematica Pristem, no. 68, July 2008, pp. 39–42.
27. "Macchina aritmetica inventata ed eseguita da Luigi Torchi milanese" [Arithmetic Machine Invented and Built by the Milanese Luigi Torchi[, Gabinetto di scienze, arti ed industria, Suppl.:La Fama: rassegna di scienze, lettere, arti, industria e teatri, Milano, P. Cominazzi 1836–1840, table X.
28. The Utile Giornale ossia Guida di Milano per l'anno 1836–1881 was a 19th century commercial directory.
29. The family name Torchi is not common in Milan but is widespread in Bologna. This Luigi Torchi should not be confused with the Italian musicologist (1858–1920) bearing the same name.
30. The Lombard Institute is the descendant of a body founded by Napoleon I in 1797, originally as the Royal Institute of Sciences, Letters, and Arts. Its goal was to promote the scientific and industrial development. The Prizes were awarded to the most distinguished entrepreneurs for their improvements in the trades and production.
31. Collezione degli Atti delle Solenni Distribuzioni de' Premi d'Industria fatte in Milano e in Venezia, Imperiale e Regia Stamperia, 1839, pp. 61–63.
32. Gabrio Piola (1794–1850) was a renowned Italian mathematician, today remembered for the Piola-Kirchhoff stress vector. Francesco Carlini (1783–1862) was director of the Brera Astronomical Observatory (Milan) since 1832; he was also chairman of the Lombard Institute from 1833–39 and 1844–46. He is remembered for the Théorie du mouvement de la Lune, published with Giovanni Antonio Amedeo Plana. Paolo Brambilla taught geometry and algebra at the high school "S. Alessandro" in Milan.
33. "Atti della solenne distribuzione de' premj d'agricoltura ed industria fatta il dì 4 ottobre 1834" [Proceedings of the Solemn Distribution of Prizes for Agriculture and Industry Made on October 4th 1834], Biblioteca Italiana, vol. 76, 1834, pp. 462–467; "Catalogo degli oggetti d'arti e manifatture esposti nelle sale dell'I. R. Palazzo di scienze ed arti di Brera," [Catalogue of the Objects of Art and Manifacture Exhibited at the Royal Imperial Palace of Sciences in Brera], Annali Universali di Statistica, vol. 5, no. 81, 1838,p. 200; Nuovo Dizionario Universale Tecnologico o di Arti e Mestieri, vol. XVI, 1836, pp. 236–237.
34. G.B. Carta, "Biografia degli italiani illustri nelle scienze, lettere ed arti del secolo XVIII…" [Biographies of Illustrious Italians in Sciences, Letters and Arts in the 18th and 19th Century], Annali Universali di Statistica, vol. 45, 1835, p. 208.
35. "Aritmetiche machine" [Arithmetic Machines], Concorsi a premj d'industria agricola e manifatturiera, Archivio Storico dell'Istituto Lombardo di Scienze e Lettere, title VI, folder 5/34, 1834.
36. Like most astronomers, Carlini was sensitive to the long and boring calculations required to compose the astronomical tables.
37. In 1850 the rental of a single room in Milan was 100 lire per year, and the salary of an unskilled worker was 20–30 lire per month. G. Bigatti, La città operosa. Milano nell'Ottocento, Franco Angeli, 2000.
38. "Per la costruzione in metallo della macchina pei conteggi inventata da Luigi Torchi, 1839–1840" [For the Construction in Metal of the Computing Machine Invented by Luigi Torchi, 1839–1940], Archivio Storico dell'Osservatorio Astronomico di Brera, Archivio Amministrativo Nuovo (1831–1848), C41: f 157. A 041/022 AAN. See also P. Broglia, p. 521.
39. "Esposizione delle Industrie Lombarde 1838" [Exhibition of the Lombard Industries 1838], Annali Universali di Statistica, vol. 58, n. 81, 1838, p. 204.
40. Giovanni Virginio Schiaparelli (1835–1910) was a well-known astronomer, mostly remembered for his observations of Mars' surface.
41. Collezione degli Atti…, p. 212.; D. Sacchi, "Nuovo meccanismo per rimontar le correnti inventato ed eseguito da Luigi Torchi" [A New Mechanism to Sail Upstream Invented and Built by Luigi Torchi], Gabinetto di scienze, arti ed industria, Suppl. La Fama: rassegna di scienze, lettere, arti, industria e teatri; P. Cominazzi 1836, table IV; Memorial Encyclopédique, no. 59, Nov. 1835.
42. A. Parrochetti, "Livello a pendolo, invenzione di Luigi Torchi" [Pendulum Level, Invention of Luigi Torchi], Giornale dell'ingegnere, architetto ed agronomo, vol. 6, 1858, pp. 121–123.
43. , Dorr Eugene Felt built the Comptometer prototype when he was 22, like Torchi. Coincidentally, Felt's prototype, the Macaroni Box, was built with wood and iron wire, and both Torchi and Felt had just a low-grade education.
44. E. Martin pp. 53–57; M. d'Ocagne, pp. 35–37; F. Soresini pp. 83–85; J. Marguin pp. 105–112; M.R. Williams 1997, pp. 145–146; R. Taton, pp. 32–34.
45. P. Govi, "Aritmometro del Sig. Thomas di Colmar" [Arithmometer by Mr. Thomas de Colmar], Giornale dell'Ingegnere, Architetto ed Agronomo, vol. 2, 1835, p. 413.
46. "Descrizione della macchina presentata all'I. R. Istituto dall'Ing Giuseppe Mozzoni con petizione 26 Febbraio 1847" [Description of the Machine Presented to the Imperial Royal Institute by Eng. Giusppe Mozzoni with Letter of February 26th, 1847], Archivio Storico dell'Istituto Lombardo di Scienze e Lettere. Concorsi a premj d'industria agricola e manifatturiera, no. 107/58, 1847.
47. A. Hyman, Charles Babbage: Pioneer of the Computer, Princeton Univ. Press, 1982, pp. 182–190; M.G. Losano, La macchina analitica. Un secolo di calcolo automatico, Milan, Etas Kompas, 1973.
48. "Aritmetiche Macchine," jury report, 1834, signed by G. Piola, F. Carlini, P. Brambilla .
49. M.R. Williams, 1997, pp. 137–142.
50. J. Marguin pp. 75–76; M.R. Williams, 1997, pp. 142–144.
51. M. d'Ocagne p. 5; J. Marguin, p. 32.
52. Collezione degli Atti…, p. 61.
53. R. Macii, and E. Borchi, "Tito Gonnella, inventore nella Firenze dell'800" [Tito Gonnella, Inventor in 19th Century Florence], Convegno nazionale su strumenti e cultura scientifica nell'Ottocento, E. Borchi, R. Macii, F. Vetrano eds., Tip. Idealpress, 1997.
54. T. Gonnella, Teoria e descrizione d'una macchina colla quale si quadrano le superfici piane, [Theory and Description of a Machine to Square Plain Surfaces], 1825; T. Gonnella, Opuscoli matematici, etc . [Mathematical Booklets], Tip. Mazzoni, 1841.
55. Exposition Universelle du 1851. Travaux de la Commission Française sur l'Industrie des Nations [Universal Exhibition of 1851. Works of the French Commission for the Industries], vol. III, Imprimerie Impériale, 1855, p. 23.
56. A.G. Bromley, "Analog Computing Devices," Computing before Computers, W. Aspray ed.,. Iowa State Univ. Press, 1990, pp. 159–199; G.A. Carse, and J. Urquhart, "Planimeters," Handbook of the Napier Tercentenary Celebrations, or Modern Instruments and Methods of Calculation, M. Horsburgh ed., Bell, 1914 (reprinted Tomash, 1982), p. 190; F. Soresini vol. III, p. 35; C. Care, "A Chronology of Analogue Computing," The Rutheford J., vol. 2, 2006–7.
57. T. Gonnella, "Descrizione di due macchine aritmetiche per l'addizione immaginate e costrutte da Tito Gonnella", [Description of Two Machines for the Addition Invented and Built by Tito Gonnella], Tip. Calasanziana, 1859.
58. F. Soresini, pp. 61–62.
59. T. Gonnella, 1859, pp. 32–33. Filippo Corridi was chairman of Accademia Toscana d'Arti e Manifatture and director of Istituto Tecnico Toscano.
60. D.D. Parmelee US patent 7,074, 1850. As D. Roegel underscores (p. 59), Parmelee's patent already proposed the use of circles instead of the straight rod.
61. J. Marguin p. 117; E. Martin p. 60; M. d'Ocagne, p. 37.
62. T. Gonnella, 1859, p. 33.
63. No copy of Gonnella's "Descrizione" has been found in the online catalogues of the main European National Libraries, http:/
64. V. Castelnuovo, Storia economica d'Italia: dall'Ottocento ai giorni nostri [Economical History of Italy, Since 19th Century to our Days], Einaudi, 1995; L. Villari, Romanticismo e tempo dell'industria, [Romanticism and Industry], Donzelli, 1999.
65. In 1959 Olivetti exported 30% of its calculator production. Near US$ 6 million of Italian calculating machines were exported to the US that year. J.W. Cortada, Before the Computer, Princeton Univ. Press, 1993, pp. 251–255.
66. Several other names have been encountered in the course of the present study, but for most of them information is scant or unreliable.
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