(b. Rome, Italy, 30 January 1619; d. Rome, 12 May 1682)
Although he was never ordained, Ricci served the papal court in various capacities and on 1 September 1681 was made a cardinal by Pope Innocent XI. He was a member of the school of Galileo, although not a direct disciple; his teacher was Benedetto Castelli, whose students also included Torricelli. Torricelli himself was later a close friend of Ricci, and exerted a marked influence on Ricci’s geometrical researches.
Ricci’s only extant mathematical work is a nineteenpage printed booklet entitled Geometrica erercitatio (but more usually called by a later subtitle, De Maximis et Minimis), published in Rome in 1666. It enjoyed a wide circulation and was reprinted as an appendix to Nicolaus Mercator’s Logarithmo-technia, issued in London in 1668. The work deals primarily with two problems: finding the maximum of the product xm(a – x)n, m and n being positive integers; and applying this result to the determination of the lines tangential to the parabolas ym = kxn. It thus represents a generalization of the property by which a tangent of the ordinary second-order parabola Y2; = kx (m = 2, n = 1) meets the x-axis at a point of which the distance from the vertex (changing its sign) equals the abscissa of the point of contact. It has been suggested that Ricci’s method anticipates the so-called method of induction from n to n+1, since he begins with the values of m = n = 1, which he subsequently increases. The first explicit use of the method is, perhaps, the one set out in Pascal’s posthumous Traité du triangle arithmétique of 1665, although some possibility exists that Ricci may not have been familiar with it.
Ricci’s other mathematical contributions are contained in his numerous letters. These include his study of spirals (1644), his investigation of a family of curves more general than ordinary cycloids (1674), and the methods by which he recognized fairly explicitly that the treatments of tangents is an operation inverse to that of the calculation of areas (1668). His demonstrated competence in algebra was somewhat exceptional among the followers of Galileo, most of whom were more deeply concerned with geometrical speculation.
Ricci’s extensive correspondence with both Italian and foreign Scholars (including physicists and astronomers, as well as mathematicians) brought him considerable contemporary fame. Through such correspondence Ricci participated in the activities of the Florentine Accademia del Cimento, particularly in the final editing of its Saggi, published in 1667. He also served as an editor of the Giornale dei letterati, which was founded in Rome in the following year. As a cardinal, he discussed with Vincenzo Viviani the life of Galileo that the latter was preparing, advising him on matters that the church felt to be of some delicacy.
A curious aspect of Ricci’s career was his refusal to edit the manuscript remains of his friend and master Torricelli, who had in his will requested that Cavalieri and Ricci do so. Cavalieri died soon after Torricelli, so that the entire task devolved upon Ricci. Stating that he had too many other occupations—and that he had been away from mathematics too long—Ricci declined the undertaking. His action has been subjected to various interpretations; as a result of it, Torricelli’s complete works were published only in the twentieth century.
I. Original Works. Geometrica exercitatio [De maximis et minimis] (Rome, 1666) was summarized in Philosophical Transactions of the Royal Society, 3 (1668), 738–740; and was reprinted in Nicolaus Mercator, Logarithmotechnia (London, 1668); and in Carlo Renaldini, Geometra promotus (padua, 1670).
Ricci’s correspondence was published in the following: Bullettino di bibliografia e storia delle scienze matematiche e fisiche, 18 (1885), see index; Raffaello Caverni, Storia del metodo sperimentale in Italia, V (Florence, 1898); C. R. Dati, Lettera a Filaleti di Timauro Antiate della vera storia della cicloide … (Florence, 1663), repr. in Opere di Evangelista Torricelli, G. Loria and G. Vassura, eds., I, pt. 2 (Faenza, 1919), 441–482; Angelo Fabroni, Lettere inedite di uomini illustri, 2 vols. (Florence, 1773–1775); Christian Huygens, Oeuvres complètes, 22 vols. (The Hague, 1888–1950); Ferdinando Jacoli, Una lettera inedita del Cardinale Michelangelo Ricci a Gio. Domenico Cassini, 1895, cited in P. Riccardi, Biblioteca matematica italiana, II , sec. 7, col. 82; Giovanni Lami, ed., Novelle letterarie publicate in Firenze, XIII (Florence, 1740–1769), col. 35; Giambattista Clemente dé Nelli, Saggio di storia letteraria fiorentina del secolo XVII (Lucca, 1759), 190; Carlo Renaldini, Commercium epistolicum ab eodem cum viris eruditione (pauda, 1682); Giovanni Targioni-Tozzetti, Atti e memorie inedite dell’ Accademia del cimento, 3 vols. (Florence, 1780); Luigi Tenca, “Relazione fra Vincenzio Viviani e Michel Angelo Ricci,” in Rendiconti dell’ Istituto lombardo di scienze e lettere, Cl. di scienze, 87 (1954), 218–228; “M.A. Ricci.” in Atti e memorie dell’Accademia patavina di scienze, lettere ed arti, 68 (1956), 1–8; and “Michel Angelo Ricci,” in Torricelliana, 11 (1960), 5–13; Girolamo Tiraboschi, Storia della letteratura italiana, VIII (Venice, 1825), 554; and V. P. Zubov, “Iz perepiski mezhdu Evandzhelista Torrichelli i Mikelandzhelo Richi” (“From the Correspondence Between Evangelista Torricelli and Michelangelo Ricci”), in Voprosy istorii estestvoznaniya i tekhniki, 8 (1959), 95–101, which includes three letters, in Russian.
Fragments of Ricci’s correspondence were also published in association with the following eds. of Saggi di naturali esperienze fatte nell’ Accademia del cimento: Vincenzio Antinori, ed., 3rd ed. (Florence, 1841); and Giorgio Abetti and Pietro Pagnini, eds., Le opere dei discepoli di Galileo Galilei, Edizione nazionale, I , L’Accademia del Cimento, pt. 1 (Florence, 1942).
There does not appear to be any systematic study of Ricci’s MS remains. There are quite possibly some fragments at the Bibliothèque Municipale, Toulouse; see the article by Costabel cited below. Other MSS are at the Biblioteca Apostolica Vaticana, Vatican City; Biblioteca Comunale and Museo Torricelliano, Faenza; and in the Galileiana MSS at the Biblioteca Nazionale Centrale, Flòrence. A substantial portion of the published correspondence derives from the Faenza and Florence collec-tions; see esp.: Angiolo Procissi, “I Mss. Torricelliani conservati a Firenze,” in Evangelista Torricelli nel terzo centenario della morte (Florence, 1951), 77–112. Indirect citations of Ricci and clues to the locations of other MSS can be found in various published collections of seventeenth-century correspondence, esp. B. Boncompagni, “Intorno ad alcune lettere di Evangelista Torricelli, del P. Marino Mersenne e di Francesco di Verdus,” in Bullettino di biblografia e storia delle scienze matematiche e fisiche, 8 (1875), 353–456; Correspondence du P. Martin Mersenne (Paris, 1932-); and M. C. Le Paige, “Correspondence de Renè-François de Sluse publièe pour la première fois et précédée d’une introduction,” in Bullettino di bibliografia e storia delle scienze matematiche e fisiche, 17 (1884), 427–554, 603–726.
II. Secondary Literature. On Ricci and his work, see the following: Amedeo Agostini, “Massimi e minimi nella corrispondenza di E. Torricelli con M. Ricci,” in Atti del IV Congresso dell’Unione matematica italiana, II (Rome, 1953), 629–632; Davide Besso, “Sopra un opusculo di Michelangelo Ricci,” in Periodico di matematica per l’insegnamento secondario, 8 (1892), 1–16; Pierre Costabel, “Un registre de manuscrits témoin de l’activité de Mersenne en Italie en 1645,” in Revue d’histoire des sciences et de leurs applications, 22 , no. 2 (1969), 155–162; Angelo Fabroni, Vitae italorum doctrina excellentium, II (Pisa, 1778), 220–221; Mario Glizzi, “Origini e sviluppi dell’esperienza torricelliana,” in Opere di Evangelista Torricelli, IV (Faenza, 1919), 231–294; Josef E. Hofmann, “Über die ‘Exercitatio geometrica’ des M. A. Ricci,” in Centaurus, 9 (1964), 139–193; and Ferdinando Jacoli, “Evangelista Torricelli ed il metodo delle tangenti detto ‘metodo del Roberval,’” in Bullettino di bibliografia e storia delle scienze matematiche e fisiche, 8 (1875), 265–304.
Two collections published in Faenza that deal primarily with Torricelli also include material on Ricci: Torricelliana, pubblicate dalla commissione per le onoranze a Evangelista Torricelli, III centenario della scoperta del barometro, 2 vols. (1945–1946); and the annual Torricelliana, Bollettino della Società Torricelliana di scienze e lettere (1949- ). Every issue through 15 (1964) has articles mentioning Ricci.
Other sources on Ricci include Étienne Charavay, Lettres autographes composant la collection de M. Bovet Alfred (Paris, 1885); Mario Guarnacci, Vita et res gestae pontificum Romanorum, I (Rome, 1751), cols. 189–194; Prospero Mandosio, Biblioteca romana, I (Rome, 1682), 344; Gabriel Maugain, Étude sur l’évolution intellectuelle de l’Italie de 1657 à 1750 environ (Paris, 1909); and Gaetano Moroni, Dizinario di erudizione storico-ecclesiastica, LVII (Venice, 1852), 177.