Vincenzo Riccati was born in 1707 in Castelfranco Veneto, a small town about 30 km north of Padua. He was the brother of Giordano Riccati, and the second son of Jacopo Riccati.[2] He began his studies at the College of St. Francis Xavier in Bologna, under the guidance of Luigi Marchenti, a pupil of the French mathematician Pierre Varignon. He entered the Society of Jesus on December 20, 1726.[3] He taught belles lettres in the colleges of the Order in Piacenza (1728), Padua (1729), and Parma (1734). He then went to Rome to study theology. In 1739 he was assigned to the College of St. Francis Xavier of Bologna, where he taught mathematics for thirty years, succeeding his former teacher Luigi Marchenti. He was among the first members of the Italian National Academy of Sciences.[4] In 1760 he was elected Honorary Fellow of the Russian Academy of Sciences.[5]
Riccati's main research continued the work of his father in mathematical analysis, especially in the fields of the differential equations and physics. In 1746 and 1749 Riccati published two works, in which he discussed the question of the parallelogram of forces in the context of the vis viva controversy. In 1752, he published the short treatise De usu motus tractorii in constructione aequationum differentialium, in which he proved that all first-order (ordinary) differential equations conceivable at the time could be constructed using tractional motion.[6]
Riccati's main contributions to mathematics and physics were published in two volumes, Opusculorum ad res physicas mathematicas pertinentium (Bologna, 1757-1762), where he introduced the use of hyperbolic functions.[7] Vincenzo edited, in collaboration with his brother Giordano, the Works of his father and published, in collaboration with his friend and student Girolamo Saladini, the three-volume treatise Institutiones analyticae, an important textbook on calculus printed in Bologna in 1765-67. Ten years later Saladini produced an Italian translation of the work under the title Instituzioni Analitiche. Riccati's Institutiones analyticae is the fullest 18th-century Italian treatise on analytic methods in mathematics.
His contributions were in hyperbolic functions for solutions of cubics, their derivatives and exponential fiunctions. Lambert is sometimes incorrectly credited as the first to introduce the hyperbolic functions, however, he did this subsequent to Riccati's contributions in 1770. Riccati not only introduced these new functions but also derived the integral formulas connected with them. He then went on to derive the integral formulas for the trigonometric functions. Riccati with Saladini also worked on the rose curves, which was first postulated by Grandi. Like his father, Vincenzo Riccati was skilled in hydraulic engineering.[7] His efforts and implementations of flood control projects saved the regions around Venice and Bologna.
Riccati's hyperbolic addition lawsEdit
Riccati's (1757) illustration of hyperbolic addition laws.
Vincenzo Riccati (1757) introduced hyperbolic functions cosh and sinh, which he denoted as Ch. and Sh. related by with r being set to unity in modern publications, and formulated the addition laws of hyperbolic sine and cosine:
He furthermore showed that and follow by setting and in the above formulas.
WorksEdit
De usu motus tractorii in constructione aequationum differentialium (1752)
Delle forze vive e dell'azioni delle forze morte. Bologna: Lelio dalla Volpe. 1749. Retrieved 15 June 2015.
De usu motus tractorii in constructione aequationum differentialium (in Latin). Bologna: ex typographia Laelii a Vulpe. 1752. Retrieved 15 June 2015.
Lettera di un cittadino romano al padre Tommaso Gabrini. S.l.: sn. 1753. Retrieved 15 June 2015.
Lettera di Vicenzio Riccati della Compagnia di Gesù alla Signora D. Gaetana Maria Agnesi intorno alla costruzione di alcune formule senza la separazione delle indeterminate. In: Gori, Antonio Francesco (ed.), Symbolae litterariae opuscula varia, vol. 10, Florence, 1753, pp. 62–72.
De seriebus recipientibus summam generalem algebraicam aut exponentialem commentarius (in Latin). Bologna: Costantino Pisarri, Giacomo Filippo Primodi. 1756. Retrieved 15 June 2015.
Opusculorum ad res physicas et mathematicas pertinentium. 2 (in Latin). Bologna: Lelio Dalla Volpe. 1762. Retrieved 15 June 2015.
Vincenzo Riccati; Girolamo Saladini (1765). Institutiones analyticae (tre tomi) (in Latin). Bologna: Stamperia di S. Tommaso d'Aquino.
De' principj della meccanica. Venezia: Sebastiano Coleti. 1772. Retrieved 15 June 2015.
Dialogo, dove ne' congressi di più giornate delle forze vive e dell'azioni delle forze morte si tien discorso, Bologna, 1749
^"Ausländische Mitglieder der Russischen Akademie der Wissenschaften seit 1724" (Vincenzo de Riccati) (in Russian). Russische Akademie der Wissenschaften. Retrieved 2015-10-20.
^Roero, C.S. (2015). "M.G. Agnesi, R. Rampinelli and the Riccati family: A cultural fellowship formed for an important scientific purpose, the Instituzioni Analitiche". Historia Mathematica. 42 (3): 296–314. doi:10.1016/j.hm.2014.12.001. hdl:2318/1514382.
BibliographyEdit
Michieli, Adriano Augusto (1943–44). "Una famiglia di matematici e poligrafi trevigiani: i Riccati. II. Vincenzo Riccati". Atti del R. Istituto Veneto di Scienze Lettere ed Arti. 103 (2): 69–109.
Indorato, Luigi; Nastasi, Pietro (1991). "Riccati's proof of the parallelogram of forces in the context of the vis viva controversy". Physis. 28: 751–767.
"Vincenzo Riccati". Science and Its Times: Understanding the Social Significance of Scientific Discovery. Vol. 4. Gale Group. 2000. p. 264. ISBN9780787639365. Retrieved 14 August 2023.
Capecchi, Danilo (2012). History of Virtual Work Laws: A History of Mechanics Prospective. Springer. ISBN9788847020566.
Tournès, Dominique (2004). "Vincenzo Riccati's treatise on integration of differential equations by tractional motion (1752)". Oberwolfach Reports. 1: 2739–2741.
External linksEdit
Wikimedia Commons has media related to Vincenzo Riccati.
vincenzo, riccati, castelfranco, veneto, january, 1707, treviso, january, 1775, venetian, catholic, priest, mathematician, physicist, 1707, 1775, born, 1707, january, 1707castelfranco, veneto, venetian, republicdied17, january, 1775, 1775, aged, treviso, venet. Vincenzo Riccati Castelfranco Veneto 11 January 1707 Treviso 17 January 1775 was a Venetian Catholic priest mathematician and physicist Vincenzo RiccatiVincenzo Riccati 1707 1775 Born 1707 01 11 11 January 1707Castelfranco Veneto Venetian RepublicDied17 January 1775 1775 01 17 aged 68 Treviso Venetian RepublicBurial placeTreviso CathedralNationalityItalianKnown forHyperbolic functionsScientific careerFieldsMathematician and physicistInstitutionsCollege of San Francesco Saverio Bologna Pontifical Gregorian UniversityAcademic advisorsJacopo RiccatiNotable studentsGian Francesco Malfatti 1 Girolamo SaladiniNotesHe is the son of Jacopo Riccati and the brother of Giordano Riccati Contents 1 Life 2 Contributions 3 Riccati s hyperbolic addition laws 4 Works 5 See also 6 References 7 Bibliography 8 External linksLife EditVincenzo Riccati was born in 1707 in Castelfranco Veneto a small town about 30 km north of Padua He was the brother of Giordano Riccati and the second son of Jacopo Riccati 2 He began his studies at the College of St Francis Xavier in Bologna under the guidance of Luigi Marchenti a pupil of the French mathematician Pierre Varignon He entered the Society of Jesus on December 20 1726 3 He taught belles lettres in the colleges of the Order in Piacenza 1728 Padua 1729 and Parma 1734 He then went to Rome to study theology In 1739 he was assigned to the College of St Francis Xavier of Bologna where he taught mathematics for thirty years succeeding his former teacher Luigi Marchenti He was among the first members of the Italian National Academy of Sciences 4 In 1760 he was elected Honorary Fellow of the Russian Academy of Sciences 5 Riccati s main research continued the work of his father in mathematical analysis especially in the fields of the differential equations and physics In 1746 and 1749 Riccati published two works in which he discussed the question of the parallelogram of forces in the context of the vis viva controversy In 1752 he published the short treatise De usu motus tractorii in constructione aequationum differentialium in which he proved that all first order ordinary differential equations conceivable at the time could be constructed using tractional motion 6 Riccati s main contributions to mathematics and physics were published in two volumes Opusculorum ad res physicas mathematicas pertinentium Bologna 1757 1762 where he introduced the use of hyperbolic functions 7 Vincenzo edited in collaboration with his brother Giordano the Works of his father and published in collaboration with his friend and student Girolamo Saladini the three volume treatise Institutiones analyticae an important textbook on calculus printed in Bologna in 1765 67 Ten years later Saladini produced an Italian translation of the work under the title Instituzioni Analitiche Riccati s Institutiones analyticae is the fullest 18th century Italian treatise on analytic methods in mathematics After the suppression of the Society of Jesus Riccati retired to his family home in Treviso where he died on January 17 1775 Riccati was a friend and correspondent of Maria Gaetana Agnesi and Ramiro Rampinelli 8 Contributions EditHis contributions were in hyperbolic functions for solutions of cubics their derivatives and exponential fiunctions Lambert is sometimes incorrectly credited as the first to introduce the hyperbolic functions however he did this subsequent to Riccati s contributions in 1770 Riccati not only introduced these new functions but also derived the integral formulas connected with them He then went on to derive the integral formulas for the trigonometric functions Riccati with Saladini also worked on the rose curves which was first postulated by Grandi Like his father Vincenzo Riccati was skilled in hydraulic engineering 7 His efforts and implementations of flood control projects saved the regions around Venice and Bologna Riccati s hyperbolic addition laws Edit nbsp Riccati s 1757 illustration of hyperbolic addition laws Vincenzo Riccati 1757 introduced hyperbolic functions cosh and sinh which he denoted as Ch and Sh related by C h 2 S h 2 r 2 displaystyle Ch 2 Sh 2 r 2 nbsp with r being set to unity in modern publications and formulated the addition laws of hyperbolic sine and cosine C A r C B C h f B E S h f C D C h p D F S h p C M C h f p M N S h f p C K r 2 C G C h f S h f 2 C H C h p S h p 2 C P C h f p S h f p 2 C K C G C H C P C h 2 S h 2 r r C h f p C h f C h p S h f S h p r S h f p C h f S h p C h p S h f r displaystyle begin matrix CA r CB Ch varphi BE Sh varphi CD Ch pi DF Sh pi CM Ch overline varphi pi MN Sh overline varphi pi CK frac r sqrt 2 CG frac Ch varphi Sh varphi sqrt 2 CH frac Ch pi Sh pi sqrt 2 CP frac Ch overline varphi pi Sh overline varphi pi sqrt 2 CK CG CH CP left Ch 2 Sh 2 rr right hline Ch overline varphi pi frac Ch varphi Ch pi Sh varphi Sh pi r Sh overline varphi pi frac Ch varphi Sh pi Ch pi Sh varphi r end matrix nbsp He furthermore showed that C h f p displaystyle Ch overline varphi pi nbsp and S h f p displaystyle Sh overline varphi pi nbsp follow by setting C h p C h p displaystyle Ch pi Rightarrow Ch pi nbsp and S h p S h p displaystyle Sh pi Rightarrow Sh pi nbsp in the above formulas Works Edit nbsp De usu motus tractorii in constructione aequationum differentialium 1752 Delle forze vive e dell azioni delle forze morte Bologna Lelio dalla Volpe 1749 Retrieved 15 June 2015 De usu motus tractorii in constructione aequationum differentialium in Latin Bologna ex typographia Laelii a Vulpe 1752 Retrieved 15 June 2015 Lettera di un cittadino romano al padre Tommaso Gabrini S l sn 1753 Retrieved 15 June 2015 Lettera di Vicenzio Riccati della Compagnia di Gesu alla Signora D Gaetana Maria Agnesi intorno alla costruzione di alcune formule senza la separazione delle indeterminate In Gori Antonio Francesco ed Symbolae litterariae opuscula varia vol 10 Florence 1753 pp 62 72 De seriebus recipientibus summam generalem algebraicam aut exponentialem commentarius in Latin Bologna Costantino Pisarri Giacomo Filippo Primodi 1756 Retrieved 15 June 2015 Opusculorum ad res physicas et mathematicas pertinentium 2 in Latin Bologna Lelio Dalla Volpe 1762 Retrieved 15 June 2015 Vincenzo Riccati Girolamo Saladini 1765 Institutiones analyticae tre tomi in Latin Bologna Stamperia di S Tommaso d Aquino De principj della meccanica Venezia Sebastiano Coleti 1772 Retrieved 15 June 2015 Dialogo dove ne congressi di piu giornate delle forze vive e dell azioni delle forze morte si tien discorso Bologna 1749See also EditJohann Heinrich Lambert Girolamo Saladini List of Roman Catholic scientist clericsReferences Edit O Connor John J Robertson Edmund F Gian Francesco Malfatti MacTutor History of Mathematics Archive University of St Andrews Vincenzo Riccati University of St Andrews Scotland Agostini Amedeo Coletti Luigi 1936 RICCATI Enciclopedia Italiana Retrieved 19 July 2018 Natucci 1984 p 401 Auslandische Mitglieder der Russischen Akademie der Wissenschaften seit 1724 Vincenzo de Riccati in Russian Russische Akademie der Wissenschaften Retrieved 2015 10 20 Tournes 2004 pp 2739 2741 a b Indorato amp Nastasi 1991 p 753 Roero C S 2015 M G Agnesi R Rampinelli and the Riccati family A cultural fellowship formed for an important scientific purpose the Instituzioni Analitiche Historia Mathematica 42 3 296 314 doi 10 1016 j hm 2014 12 001 hdl 2318 1514382 Bibliography EditMichieli Adriano Augusto 1943 44 Una famiglia di matematici e poligrafi trevigiani i Riccati II Vincenzo Riccati Atti del R Istituto Veneto di Scienze Lettere ed Arti 103 2 69 109 Indorato Luigi Nastasi Pietro 1991 Riccati s proof of the parallelogram of forces in the context of the vis viva controversy Physis 28 751 767 Vincenzo Riccati Science and Its Times Understanding the Social Significance of Scientific Discovery Vol 4 Gale Group 2000 p 264 ISBN 9780787639365 Retrieved 14 August 2023 Capecchi Danilo 2012 History of Virtual Work Laws A History of Mechanics Prospective Springer ISBN 9788847020566 Tournes Dominique 2004 Vincenzo Riccati s treatise on integration of differential equations by tractional motion 1752 Oberwolfach Reports 1 2739 2741 External links Edit nbsp Wikimedia Commons has media related to Vincenzo Riccati Natucci A 1984 Riccati Vincenzo Dictionary of Scientific Biography Vol XI New York Charles Scribner s Sons pp 401 402 O Connor John J Robertson Edmund F Vincenzo Riccati MacTutor History of Mathematics Archive University of St Andrews Retrieved from https en wikipedia org w index php title Vincenzo Riccati amp oldid 1173680766, wikipedia, wiki, book, books, library,
