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Viviani, Vincenzio

1. Dates
Born: Florence, 5 April 1622
Died: Florence, 22 September 1703
Dateinfo: Dates Certain
Lifespan: 81
2. Father
Occupation: Aristocrat
Jacopo di Michelagnolo Viviani was a member of a noble family. The mother was also.
The family was sufficiently endowed financially to be able to care for the education of Vincenzo and his numerous brothers. This certainly implied affluence. Nothing I have seen suggests wealth, though it is stated that the mother's family was rich.
3. Nationality
Birth: Italian
Career: Italian
Death: Italian
4. Education
Schooling: No University
Viviani studied with the Jesuits in Florence, and he studied mathematics with Clemente Settimi of the Scuole Pie. Settimi, who was impressed by Viviani's intelligence and ability, introduced him to Galileo, and Settimi's description of his pupil led to his introduction to the Grand Duke in 1638. The Grand Duke provided 50 scudi per year to the young man to provide him with mathematical books, and he later arranged for Viviani to be Galileo's companion and pupil, an arrangement that began late in 1639 and lasted until Galileo's death.
The years with Galileo took the place of a university education.
5. Religion
Affiliation: Catholic
6. Scientific Disciplines
Primary: Mathematics, Hydraulics, Mechanics
Subordinate: Optics, Physics, Astronomy
Viviani was first of all a student of ancient geometry who, though a leading mathematician, never came to terms with the new analyis. He attempted to restore the fifth book of Euclid's Elements, and to reconstruct the contents of the lost fifth book of Apollonius' Conics, and Aristaeus' De locis solidis. He prepared an Italian version of Archimedes' work on the rectification and squaring of the circle, and he published an Italian translation of the whole of Euclid's Elements.
As an engineer with the Uffiziali dei Fiumi in Florence, he published Discorso intorno al difendersi da' riempimenti e dalle corrosione de' fiumi (1687), completed a work on the nature of fluids (which he did not publish), and left numerous manuscripts on theoretical and practical hydraulics. Two of his compositions were included in the Raccolta del moto dell'acque of the 18th century.
Working as the disciple of Galileo, Viviani nearly completed a work on the resistance of solids, which Grandi did complete and publish after Viviani's death. Viviani left quite a few manuscripts on mechanics.
In the Accademia del Cimento he worked on the compression of air and on optics, and he was responsible for the Accademia's astronomical observations. He also observed some with Cassini.
7. Means of Support
Primary: Government, Patronage, Academia
Secondary: Schoolmastering
As mentioned above, the Grand Duke supplied a sort of pension to Viviani when he was still a boy, and he began to employ him after Galileo's death, first as an inspector of fortifications, and then as an engineer with the Uffiziali dei Fiumi. In 1653, after he had been filling the position for a number of years, he was officially appointed as engineer, and he continued in that position virtually until his death.
After the death of Torricelli (in 1647) Viviani succeeded him as lecturer at the Accademia del Disegno in Florence, a position he held from 1647 until his death in 1703. (I categorize this as Acd.) He also gave lessons at his home.
In 1649 he was appointed lecturer in mathematics to the pages at the court and was thus in charge of the scientific education of the princes.
Beginning in 1664 Viviani, as one of twelve designated leading intellectuals of Europe, received a pension from Louis XIV of 100 doubloons (which seems to mean double scudi, but Milanese rather than Florentine scudi), and to Louis he dedicated his final work in 1702. In 1666 Louis offered Viviani one of the places in the newly organized Académie Royale, and that same year John II Casimir of Poland offered to appoint Viviani as his astronomer. The Grand Duke shifted into gear and appointed Viviani as his mathematician with a stipend of 600 scudi, promising to let him retire as engineer (though Viviani was in fact not allowed to retire as engineer until 1677 and was still at the job in some sense twenty years after that). Manifestly Viviani declined the offers from France and Poland.
8. Patronage
Types: Court Official, Government Official
See various aspects of his relations with the Grand Duke above. The Grand Duke Ferdinando liked to call Viviani in to discuss scientific matters, and to the Grand Duke Viviani dedicated works. He continued in favor with Cosimo III and also dedicated books to him, such as the problem called Viviani's enigma, in 1692.
Viviani also had a close and continuing relation with Prince Leopoldo. (Leopoldo later became a Cardinal, but I think I should list him solely as part of the court.) Viviani was one of the key members in Leopoldo's Accademia del Cimento. Leopoldo encourage Viviani to publish his work on Apollonius, virtually ordering him to do so, and Viviani dedicated the work to him and to the Grand Duke, who held up the publication by Borelli of his translation of an Arabic manuscript of Apollonius until Viviani's reconstruction of the fifth book was safely out. Viviani dedicated other works to Leopoldo as well. The Medici financed the publication of the work on Apollonius. It appears to me that they financed the publication of all of his works. Viviani did not seem to know how to proceed without them. A letter to a Cardinal, written in 1696, tries to get him to publish three geometrical works that the Medici apparently, for whatever reason, did not publish.
In 1675 Leopoldo instructed him to enter a dispute about some trial problems in geometry published by Cristoforo Sadler, and Leopoldo then pressured him to publish his solutions--the Diporto geometrico attached to some copies of the Quinto libro di Euclide. Viviani also composed his life of Galileo, which took the form of a letter to Leopoldo, at the latter's behest.
Favaro (pp. 103-9) details Viviani's efforts, which began in the mid 50's and continued for at least twenty years, to prepare an edition of Galileo's works. At every early step Leopoldo was involved in the project, which hinged on him. Later, after Viviani began to receive the pension from Louis XIV, he planned to dedicate the edition to him. However, the project languished, and all the more when it became evident that Louis would not take much joy in the works of a man who had been dead for thirty years.
Favaro is explicit in stating that the Medici did not do all that well by a man of Viviani's capacity. It is not wholly clear to me that this is so, but if it is, he seems to me to contrast with Redi who grew wealthy in the service of the Medici. Perhaps Viviani was too useful.
Viviani dedicated a mathematical publication in 1677 to Jean Chapelain, the councillor of Louis XIV who in 1664 had named Viviani was one of the twelve and thus secured for him the patronage of Louis. Chapelain was dead by 1677; the dedication was then a gift of gratitude for past favors.
9. Technological Involvement
Types: Military Engineering, Hydraulics, Instruments, Architecture, Civil Engineering
In the 40's Viviani was sent to inspect the fortifications of Tuscany and to build up those along a threatened frontier.
He was employed by the Grand Duke as an engineer with the Uffiziali dei Fiumi and worked on numerous projects including the channeling of the Chiana. He also worked on roads, pavements, and a bridge, and he did some architectural work. I would be willing to bet my shirt that he also did some cartography, though perhaps only in connection with the hydraulic engineering. At any rate, I did not see any mention of such.
For the Accademia del Cimento he invented numerous instruments--to examine the compression of air, the specific gravity of fluids, the refraction of fluids, and capillary phenomena, as well as an air thermometer, a hygrometer, a hearing trumpet, and a telescope twenty palms long.
10. Scientific Societies
Memberships: Accademia del Cimento, Royal Society, Académie Royal des Sciences
Membership in the Accademia del Cimento from its beginning in 1657.
Fellow of the Royal Society in 1696.
One of the eight foreign members upon the reorganization of the Académie Royale des Sciences in 1699.
Viviani was also in the Arcadia in Rome (elected in 1701 I think) and in the Accademia della Crusca from 1661.
He was Galileo's companion and pupil during the final two years of his life. He became a close friend of Torricelli and is the one who first performed the Torricellian experiment (the barometer), at Torricelli's instructions; Viviani undertook to publish Torricelli's works after his death but did not carry through.
He was a close friend of Redi and Steno.
He corresponded with Ricci, Sluse, degli Angeli, Huygens, Wallis, Leibniz, l'Hopital, the two Bernoullis, Grandi, and others.
The affair over the publication of Apollonius led to a rupture with Borelli that was never healed.
  1. Antonio Favaro, "Amici e correspondenti di Galileo Galilei.
  2. XXIX. Vincenzio Viviani," Atti del Reale Istituto Veneto di scienze, lettere ed arti, 72 (1912-13), pt. 2, 1-155.
  3. M.L. Bonelli, "L'utlimo discepolo: V. Viviani," in Carlo Maccagni, ed. Saggi su Galileo Galilei, 3 vols. (Firenze, 1972), 2, 656-88. Pierfrancesco Tocci, "Vita di Vincenzio Viviani fiorentino, dette Erone Geonio," in G.M. Crescimbeni, Le vite degli Arcadi illustri scritte da diversi autori, 3 vols. (Roma, 1708-14), 1, 119-34.
  4. P. Riccardi, Biblioteca matematica italiana, 1, 625-30; 2, 103.
Not Available and Not Consulted
  1. A. Fabroni, Vitae italiorum doctrina excellentium, (Pisa, 1778), 1, 307-44.
Compiled by:
Richard S. Westfall
Department of History and Philosophy of Science
Indiana University

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©1995 Al Van Helden
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