Giordano Riccati

Quick Info

25 February 1709
Castelfranco, Veneto (now Italy)
20 July 1790
Treviso, Veneto (now Italy)

Giordano Riccati made contributions to music, architecture, mechanics and mathematics. He studied and experimented with Young's modulus 25 years before Young.


Giordano Riccati was the fifth son of Jacopo Riccati and Elisabetta dei Conti d'Onigo. Count Jacopo Riccati had inherited the title of Count from his father who died when Jacopo was ten your old. Jacopo and Elisabetta were married on 15 October 1696 and had eighteen children, nine of whom died in childhood and nine survived to adulthood. Jacopo Riccati was of independent means and had a large estate at Castelfranco, Veneto, a small town about 30 km north of Padua and about 40 km north west of Venice. There he cared for his family and also played a major role in the administration of the town, being mayor for nine years between 1698 and 1729. Giordano Riccati was born at Castelfranco; his [14]:-
... birthplace, his family palace, still stands outside the centre of Castelfranco; behind a non-committal façade it houses important frescoes and a superb military Baroque ballroom.
Of Jacopo and Elisabetta Riccati's nine surviving children, the two sons who achieved fame, in addition to Giordano, the subject of this biography, were Vincenzo Riccati and Francesco Riccati (1718-1791). These three all inherited their father's love for the exact sciences and for literature. We know of several other of Giordano's siblings; Giustina (born 1697), Laura (born 1703), and the eldest son Carlo (1705-1789) who inherited the title of Count.

Giordano lived with his family on the estate at Castelfranco until the age of ten. His education up to this time was provided by a private tutor. In 1720 he was sent to the Collegio San Francesco Saverio in Bologna, the same college to which his brothers Carlo and Vincenzo had been sent. This College, run by the Jesuits, is sometimes called Bologna's Collegio dei Nobili, a general term for colleges where boys from aristocratic families were educated by priests. This College in Bologna was situated in the Palazzo Gigli in the Via Cartoleria. There was a policy to reduce the students' contacts with their families which was only allowed through correspondence and short vacations. The syllabus followed the standard Jesuit model: theology, philosophy, physics, mathematics, Latin, Greek, grammar, syntax, humanities, rhetoric, history and geography. We know something of Giordano's teachers at the College. His literature teachers were Massimiliano Gonzaga and Francesco Saverio, he was taught logic and metaphysics by Giuseppe Sbruglio and Bernardino Benzi while Giovanni Battista Regalino and Luigi Marchenti taught him mathematics. Luigi Marchenti was a very competent mathematician who had studied with Pierre Varignon in Paris. Giordano Riccati distinguished himself as the best student in the rhetoric class.

The standard course at the Collegio San Francesco Saverio lasted five years and, in 1725, Riccati went to the Accademia degli Argonauti in Bologna. This Academy, founded in the seventeenth century, provided education in fine literature, liberal arts, drawing, music, dance and in mathematical sciences as well as theology and philosophical sciences. At the Academy, in addition to his academic studies, Riccati learned to play the mandolin and the chitarrone (a large lute) and he followed the drawing course of Carlo Girolamo Niccolini. This broad education influenced Riccati to take an interest in a wide range of subjects but he approached them all in a mathematical way.

After two years at the Accademia degli Argonauti, Riccati returned to Castelfranco in 1727 where his father taught him geometry, trigonometry, infinitesimal calculus, statics and dynamics. In September 1727 Ramiro Rampinelli arrived in Castelfranco, sent there by Eustachio Manfredi and Gabriele Manfredi to deliver a letter and to enquire about Jacopo Riccati's latest research. In addition to teaching his son mathematics, Jacopo Riccati also taught Ramiro Rampinelli who spent several weeks at Castelfranco again in 1728 and in 1729. Ramiro Rampinelli and Giordano Riccati became good friends and, when Riccati went to the University of Padua in 1729 to study law, he met up with Rampinelli and they both attended the hydraulics lectures of Giovanni Poleni, as well as the lectures of the physician and naturalist Antonio Vallisneri (1661-1730), of the classics professor Domenico Lazzarini (1668-1734), and of the theologian Jacopo G Serry.

Giordano Riccati and Ramiro Rampinelli remained good friends and, from 1730 to 1758 when Rampinelli suffered a stroke, the two exchanged over 200 letters discussing their common scientific interests. The correspondence begins on 28 April 1730, when Rampinelli, turned to his friend Giordano Riccati to discuss architectural issues in which both were very interested, taking advantage of their friendship to seek explanations on certain matters from Jacopo Riccati. Silvia Mazzone writes [17]:-
The direct correspondence between Giordano Riccati and Rampinelli consists of 207 letters preserved partly in the Riccati archive at the Biblioteca Civica Joppi in Udine, and partly in a collection of papers belonging to Rampinelli at the Library del Seminario Vescovile di Padova. It is available in critical edition edited by Silvia Mazzone and Clara Silvia Roero, with the collaboration of Erika Luciano, in 'L'epistolario di Jacopo, Vincenzo e Giordano Riccati con Ramiro Rampinelli e Maria Gaetana Agnesi 1727-1758' (2010). ... Most of the letters were found in the original, three letters are autograph copies, only one is a copy. In addition, many important attachments have been identified in Padua that substantially supplement the correspondence. Of this material 62 letters and 4 attachments are the work of Giordano Riccati. ... At the centre of the intense debate that develops throughout the correspondence are the scientific interests of the two correspondents, ranging from architecture to acoustics, from the mechanics of solids to that of fluids, from analysis to geometry and geometric optics. Generally it is Rampinelli who asks for information and materials to continue his studies and proposes complex questions and problems to his friend that he cannot solve. Rampinelli submits to Giordano's judgment the handouts he draws up for his students ...
Music motivated Giordano Riccati's interest in strings and pipes which he approached in a mathematical way. As early as 1740 he was working on the elastic strings and fibres which led eventually to his book Delle corde ovvero fibre elastiche (1767). He writes in the Preface:-
The pleasure of music has drawn me to devote a fair amount of thought to those solid and fluid strings of which most musical instruments are made, and having at various times written eight chapters on this subject, I have recently gone through them page by page and revised them here and there so that with less embarrassment they can [now] be presented to the public.
Riccati applied much mathematics to this study which is highly technical. We give, to illustrate the work, a non-technical passage on the harpsichord (quoted from [6]):-
In all the harpsichords and spinets that I have examined, when I have compared the lower strings with the higher ones I have found them to be somewhat shorter than the ratio of the vibration frequencies would require. From this it follows that the lower strings, on account of their thickness, are a little less tense than the higher strings. I believe that the practitioners do this because the hole through which the strings are passed [in the process of drawing them] compresses and strengthens thin strings more than [it does] thick ones, so the latter cannot bear the tension of a force quite proportional to their [greater] thickness. There is also the danger that the lower strings might be broken in the process of wrapping them around the pin, which flattens them. On the other hand, when they are protected from these risks and strung to the proper tension, they last a long time without breaking. The higher strings on the contrary do not last very well and break easily. ... Experience together with theory has taught practitioners the suitable thicknesses for the lower and higher strings, and these may be, within certain discrete limits, done by approximation rather than exactly. When two strings of congruent thicknesses are put on an instrument, there remains another means - the force of the quills - of equalising the strength of the sounds. When tuners play two strings at once, they understand exactly which quill should be increased or diminished in force in order that the two lower and higher sounds may make an equal impression on the ear.
He also studied organ pipes and violin strings [14]:-
For his consideration of organ pipes, Riccati measured those of the instrument at Treviso Cathedral, 'a very perfect work by Urbano of Venice in the year 1420'. ... Riccati's equally precise observations of violin strings confirm that through the influence of Giuseppe Tartini (with whom he corresponded) violin strings in the Veneto had been thickened into 'regular ropes' for greater sound.
Giuseppe Tartini (1692-1770), mentioned in this quote, was a composer and violinist who formulated principles of musical harmony [5]:-
Relations between the great violinist [Tartini] and Giordano Riccati were not always serene; in this regard, the relations between Tartini and the cultured Venetian patrician [Giordano Riccati] began in a rather stormy way, due to some criticisms expressed by the Treviso scholar on Tartini's musical theories. In a letter to the Marquis Angelo Gabrielli (dated 6 February 1760), who had been asked by Riccati to be an arbitrator between him and Tartini ... Tartini vigorously refutes the objections formulated by Riccati in the dissertation ... But after those warlike signs followed a peace heralding a long friendship.
As an architect, Riccati did not simply study the subject theoretically but rather he also designed and built many buildings [4]:-
... for example, we can admire the façade of the church of San Teonisto, the church of Sant'Andrea, the imposing, airy interior of the Cathedral, the staircase Palazzo Ca' Spineda (the Capitular Library was unfortunately destroyed in the tragic bombing of 7 April 1944); the churches of Santa Maria della Pieve in Castelfranco Veneto, of Caerano and of Venegazzù are also works of the Treviso scholar.
Riccati sent Rampinelli several manuscripts on architecture making up the Compendio di architettura . He did not publish this but his brother Francesco Riccati incorporated many of Giordano's themes in his own work Dissertazione intorno l'Architettura civile (1761).

Giordano Riccati was much involved with giving advice to Maria Gaetana Agnesi who was being taught by Rampinelli. On 21 July 1745 Rampinelli sent Giordano Riccati Agnesi's manuscript on Cartesian Algebra asking him to "encourage, correct, remove and supplement [where needed and] to examine everything with the utmost rigour." Giordano Riccati replied to Rampinelli on 19 August (see, for example, [21]):-
We read the most learned writings with great avidity and found many reasons to admire the Lady's great intelligence, the accuracy of her method and the clarity of her explanations ... In substance, I ask you to humbly defer to Her Ladyship and assure her, with utmost sincerity, that, having received the permission she so graciously bestowed upon my esteemed father and I, we will soon give her our respectful opinion.
On 12 May 1746 he wrote [21]:-
I can assure you in all sincerity that my esteemed father's sentiment and my own is that the manuscripts are more than worthy of seeing the light of publication, as throughout the work are found truth, method and admirable clarity. My excellent father examined the work on Integral Calculus, and he will very shortly finish drafting some notes he deems necessary ... As I was unable to meditate on the contents of your letter ... I sent it to my brother, Father Vincenzo, who, upon thinking it over, found that the issue was much more complicated than he first thought.
In June 1746 Agnesi's manuscript on the differential calculus was sent to Giordano Riccati. He replied on 15 July 1746 [21]:-
I shall make sure to forward Cartesian Analysis to you with all haste, together with a number of notes of little import dictated not by any real necessity but simply for your and the Lady's service. Thus may Her Ladyship go ahead with publication and do credit to her sex through a work that will show her wonderful talent.
Again on 4 August Giordano Riccati wrote [21]:-
As soon I had the opportunity, I cast my eye over the geometric foundations upon which my esteemed patron the Countess has established the differential calculus. These could be neither more correct nor more precise. I find all the writings of the praiseworthy Lady overflowing with the same characteristics and it would be well for her not to deprive the public of a work that would do credit to our Italy.
At the beginning of December 1746 Giordano Riccati sent Agnesi the annotations that he and his father had made on Agnesi's manuscript. Agnesi replied to Giordano Riccati on 12 December [21]:-
In consideration of the kind indulgence and all too fine expressions his Lordship Count Jacopo and your good self have made on my feeble efforts, I am now making so bold as to have the book printed, sure that the work will be well received after its being granted the honour of being scrutinised by your sharp eye ... I am with great pleasure looking over the notes that are truly worthy of your great knowledge and shall make all possible use of them, bearing in mind the order of these comments as some of them cannot be inserted in the places mentioned because the reader cannot be supposed to be informed of the methods that your Lordship's great learning allows you to use in such circumstances.
After Agnesi's Instituzioni analitiche was published, Giordano Riccati wrote on 6 October 1752 [21]:-
Her 'Instituzioni analitiche' is now found in the hands of everyone, and the young now learn Algebra by studying the work of Her Ladyship Countess Agnesi.
In 1771 Riccati published his most complete text on architecture, the Letter to Roberto Zuccareda, in which he presented six general rules on structures and their relationships with statics [22]:-
There followed mathematical essays on the figure and the flattening of the arches (1780, 1788), on the elliptical curves in the vaults (1790) and on specific themes. He edited the edition of Francesco Maria Preti's 'Elementi di architettura' (1780) and declared that he had addressed those theories with fatherly assistance.
In 1782 Riccati published Delle vibrazioni sonore dei cilindri in which he computed what, in the language of today, would be the ratio of Young's modulus for steel to that of brass, obtaining the remarkably accurate value of 2.06. Of course since Thomas Young did not undertake his work until 25 years after Riccati's work was published, the statement we have just made is not in the form in which Riccati expressed this result. To suggest that the modulus should be named after Riccati and not Thomas Young would not be entirely fair, however, since the concept appears in Leonard Euler's work in 1727.

Giordano Riccati's contributions were so varied that in many ways he has not, until comparatively recently, received the recognition that he deserves. He was, however, honoured in many ways during his lifetime [22]:-
He held various positions: he was hydraulic commissioner for the layout of rivers, perpetual censor in the Venetian Senate, a member of the college of nobles and of the Agricultural Academy of Treviso. He was also a member of the Academy of Sciences, Letters and Arts of Padua, of the Institute of Sciences of Bologna, of the Literary Society of Modena, and of the National Academy of Sciences of Italy (the Academy of XL).
Carlo, Giordano and Francesco Riccati all died in the space of two years between 1789 and 1791. Vincenzo Riccati had died in 1775. Domenico Maria Federici, an important figure in the Venetian culture of the eighteenth century, knew Giordano Riccati well and wrote his obituary which included the oration which Federici delivered at Riccati's funeral. He made much of his belief that Riccati's scientific work and his Christian beliefs were not in contradiction to each other [13]:-
Free thinkers, indiscreet and too severe zealots of our century, do not think, therefore, that perfect philosophy cannot be united with true piety, social services with Christian duties: let your censures, your vain sophisms cease, and your excessive severity is confused. Philosophy can optimally link with piety, civil society with the Gospel, moral virtues with science.
He also described Riccati's character and appearance [13]:-
By his natural character he tended not to rigour, but to gentleness, as, in literary controversies, and in domestic circumstances, and in homeland revolutions, he proved incessantly. [...] Tall of stature, healthy and resistant complexion, and nothing less than delicate texture, of noble appearance, grave and majestic, candid and well coloured in the cheeks, so that for some praise or surprise in public office for not grateful words, it often increased the reddening: this easy blushing lasted until the last days.

References (show)

  1. G T Bagni, La matematica nella Marca: Vincenzo, Giordano e Francesco Riccati (Teorema, Treviso, 1993).
  2. P Barbieri, Acustica, accordatura e temperamento nell'illuminismo veneto: con scritti inediti di Alessandro Barca, Giordano Riccati e altri autori (Istituto di paleografia musicale, Rome, 1987).
  3. D M Federici, Commentario opra la vita e gli studii del Conte Giordano Riccati: nobile trevigiano (Vinegia, 1790).
  4. G T Bagni, Il trevigiano Giordano Riccati (1709-1790) e la Matematica del Settecento, Cassamarca 17 XI (2) (1997), 60-64.
  5. G T Bagni, Scienza e musica nella Marca del Settecento: Giordano Riccati e Giuseppe Tartini, Cassamarca 12 XII (1) (1997), 68-72.
  6. P Barbieri, Giordano Riccati on the Diameters of Strings and Pipes, The Galpin Society Journal 38 (1985), 20-34.
  7. P Barbieri and L Tronchin, L'acustica teatrale nel neoclassicismo italiano : con una ricostruzione virtuale del teatro ideale di Francesco Milizia (1773), in Davide Bonsi (ed.), Giordano Riccati, illuminista veneto ed europeo (Leo S Olschki, 2012), 133-164.
  8. D Bonsi and P Ruggeri, Simulazione acustica dell'abbassamento della cantoria dell'organo nel duomo di Chioggia, in Davide Bonsi (ed.), Giordano Riccati, illuminista veneto ed europeo (Leo S Olschki, 2012), 165-180.
  9. C Caffagni, L'architettura ben temperata nel pensiero di Giordano Riccati, in Davide Bonsi (ed.), Giordano Riccati, illuminista veneto ed europeo (Leo S Olschki, 2012), 103-122.
  10. A De Piero, Della maniera di perfezionare la musica : due lettere di Giordano Riccati a Giovenale Sacchi sui duetti da camera di Händel e di Bononcini, in Davide Bonsi (ed.), Giordano Riccati, illuminista veneto ed europeo (Leo S Olschki, 2012), 181-194.
  11. L Del Fra, L'esperienza uditiva: Giordano Riccati e il fondamento della musica, in Davide Bonsi (ed.), Giordano Riccati, illuminista veneto ed europeo (Leo S Olschki, 2012), 195-210.
  12. V Farinati, Tipologie e costruzione delle sale teatrali nell'opera di Giordano Riccati, in Davide Bonsi (ed.), Giordano Riccati, illuminista veneto ed europeo (Leo S Olschki, 2012), 89-102.
  13. Giordano Riccati Visto da un Suo Contemporaneo, Cultura Veneto.
  14. F Hammond, Review: Acustica, accordatura e temperamento nell'illuminismo veneto: con scritti inediti di Alessandro Barca, Giordano Riccati e altri autori, by Patrizio Barbieri, Music & Letters 71 (3) (1990), 383-384.
  15. M G Lugaresi, Oltre i confini della Serenissima : il carteggio scientifico tra Giordano Riccati e Gian Francesco Malfatti, in Davide Bonsi (ed.), Giordano Riccati, illuminista veneto ed europeo (Leo S Olschki, 2012), 53-70.
  16. G Mambella, Spirito sistematico e attitudine sperimentale nelle teorie musicali di Giordano Riccati, in Davide Bonsi (ed.), Giordano Riccati, illuminista veneto ed europeo (Leo S Olschki, 2012), 211-224.
  17. S Mazzone, La formazione matematica di Giordano Riccati nella corrispondenza con Ramiro Rampinelli, in Davide Bonsi (ed.), Giordano Riccati, illuminista veneto ed europeo (Leo S Olschki, 2012), 3-22.
  18. E Molteni, Gli scritti di Giordano Riccati sull'architettura : proporzioni, matematica, giudizio e buon gusto, in Davide Bonsi (ed.), Giordano Riccati, illuminista veneto ed europeo (Leo S Olschki, 2012), 71-88.
  19. L Moretti, Le chiese di Giordano Riccati, in Davide Bonsi (ed.), Giordano Riccati, illuminista veneto ed europeo (Leo S Olschki, 2012), 123-132.
  20. E Patergnani, Giordano Riccati e le enciclopedie del Settecento, in Davide Bonsi (ed.), Giordano Riccati, illuminista veneto ed europeo (Leo S Olschki, 2012), 35-52.
  21. C S Roero, M G Agnesi, R Rampinelli and the Riccati family: a cultural fellowship formed for an important scientific purpose, the 'Instituzioni analitiche', in Historia mathematica 42 (2015), 296-314.
  22. C S Roero, Riccati, Giordano, in Dizionario Biografico degli Italiani 87 (2016).
  23. G Sandra, Gabriele Manfredi e l'ambiente scientifico bolognese nella prima metà del Settecento, in Davide Bonsi (ed.), Giordano Riccati, illuminista veneto ed europeo (Leo S Olschki, 2012), 23-34.
  24. I Szabó, Die Familie der Mathematiker Riccati, Humanismus und Technik 18 (1974), 57-75; 109-131.

Additional Resources (show)

Other websites about Giordano Riccati:

  1. MathSciNet Author profile
  2. zbMATH entry

Written by J J O'Connor and E F Robertson
Last Update November 2020