Giordano Riccati - Delle corde ovvero fibre elastiche schediasmi fisico-matematici - 1767

Giordano Riccati — On Strings or Elastic Fibres. Physico-Mathematical Sketches
Bologna, Stamperia di San Tommaso d’Aquino, 1767

The copy presented here belongs to the first edition, published in Bologna in 1767, of one of the most significant works of Italian science in the eighteenth century dedicated to the mechanics of strings, vibrations, and acoustics. The volume, in quarto format and with 246 pages, is accompanied by illustrative plates with geometric and physico-mathematical diagrams intended to make visible phenomena that Riccati subjects to rigorous mathematical analysis.

The author: Giordano Riccati

Giordano Riccati (Castelfranco Veneto, 1709 – Treviso, 1790) belonged to one of the most important scientific families of eighteenth-century Italy. Son of the mathematician Jacopo Riccati and brother of Vincenzo Riccati, he was educated with the Jesuits in Bologna and earned in 1731 a law degree in Padua, while dedicating most of his intellectual activity to mathematics, physics, theoretical music, and architecture.

His figure is particularly interesting because he embodies perfectly that eighteenth-century tendency to connect different disciplines. For Riccati, mathematics was not an abstract science detached from experience: it could be applied to music, mechanics, acoustics, architecture, and the study of materials.

His interest in vibrations also arose from music. Reflections on the strings of musical instruments gradually led him toward more general problems concerning elasticity, oscillations, and sound propagation. His research on elastic strings began around 1740 and would culminate after years of elaboration in the 1767 volume.

Riccati also had intellectual connections with important figures of Italian musical and scientific culture, including Antonio Vallotti, Giovenale Sacchi, and Giuseppe Tartini.

The work and its content

The full title, ** On Strings or Elastic Fibres. Physico-Mathematical Sketches by the Count Giordano Riccati, Treviso nobleman **, already reveals the author’s ambition.

The term “schediasmi,” derived from Greek and used in the erudite tradition to indicate discussions or essays composed on specific topics, introduces a collection in which Riccati progressively tackles different problems related to the physical properties of strings and the production and propagation of sound.

The work comprises eight Sketches and five Dissertations. The first ones primarily address the behavior of elastic strings, their tension and vibrations; the subsequent dissertations develop the study of sound propagation.

Riccati thus seeks to establish mathematically the relationships among elements such as:

- length of the string;
- tension;
- density;
- mass;
- elasticity;
- frequency of vibrations;
- pitch of the sound;
- propagation of the sound wave.

The seemingly simple problem of a vibrating string thus becomes a laboratory in which general laws of nature can be observed.

And this is one of the most important aspects of the work: music is used as a measurable physical phenomenon.

The scientific plates

The plates in the volume, such as the one visible in your copy, are particularly meaningful.

They are not mere decorative illustrations: the diagrams visually translate the mathematical constructions through which Riccati seeks to describe the behavior of vibrating systems.

The plate you photographed, indicated as “Plate I,” presents several numbered figures, Fig. 1–Fig. 8, with bodies, strings, geometric points, curves, and proportional constructions.

The graphical language is that typical of eighteenth-century mathematical science: letters and segments do not simply represent objects, but constitute true elements of the reasoning.

The presence of these plates thus greatly increases the historical-scientific interest of the copy.

From the musical string to the physics of sound

The meaning of the work goes beyond the study of musical instruments.

In the eighteenth century the nature of sound was one of the most fertile meeting points between mathematics, physics, and musical theory.

Riccati fits into a tradition that goes back at least to Galileo Galilei and had crossed the scientific revolution of the Seventeenth Century.

Galileo studied the relation between the length of strings, tension, and pitch, contributing to the transformation of musical theory into a quantitative problem.

In the following century, figures such as Marin Mersenne further explored the relationship between strings and sound phenomena.

Riccati inherits this tradition and brings it into the scientific climate of the Enlightenment, characterized by growing confidence in the possibility of mathematically describing natural phenomena.

The relation with Euler and the mathematization of nature

The work must also be placed in the broader context of European mathematics dominated by figures such as Leonhard Euler.

In the eighteenth century Euler, Bernoulli, and other great mathematicians were developing the analytical tools needed to address problems of oscillation, elasticity, fluids, and vibrating bodies.

It is significant that this copy contains references to Eulero: Riccati’s research belongs to that great European process by which problems once belonging to natural philosophy were progressively transformed into mathematical problems.

A vibrating string is no longer just a phenomenon observed by a musician: it becomes a system governed by quantitative relationships.

The link with Tartini and the Italian musical tradition

Another particularly suggestive connection is with Giuseppe Tartini, one of the major figures of Italian music in the eighteenth century.

Riccati was deeply interested in musical theory and the mathematical problems of harmony. His relations with the Padua musical environment, including Tartini and Vallotti, helped maintain a close link between mathematical research and practical music.

This makes Delle corde a book ideally placed between the laboratory of the scientist and the workshop of the luthier.

The string that Riccati studies mathematically is indeed the same string that, mounted on a violin, a cello, or another instrument, becomes the origin of the musical phenomenon.

A book that anticipates the modern science of acoustics

The historical importance of On Strings lies above all in its attempt to transform acoustics into a discipline founded on observation, experiment, and mathematics.

A bibliographic antiquarian source defines the first edition as an important work in the history of mathematical acoustics and emphasizes its study of string vibration and sound propagation.

Riccati’s research thus belongs to that intellectual transformation that would lead in the nineteenth century to the modern mathematical physics of vibrations and waves.

In this sense, the 1767 volume sits at a particularly interesting historical point: behind it lies Galileo’s scientific revolution, in front of it lies the great nineteenth-century era of wave theory and mathematical acoustics.

Stamperia di San Tommaso d'Aquino

The volume was printed in Bologna, at the Stamperia di San Tommaso d'Aquino, an important type-founding workshop active in the city during the eighteenth century.

The workshop appears in bibliographic catalogs with numerous variants of the name, including Typographia Sancti Thomae Aquinatis, Tipografia di S. Tommaso d'Aquino, and Stamperia del Santo Ufficio a S. Tommaso d'Aquino.

The fact that a mathematically and physically complex treatise was produced in Bologna is not casual.

In the eighteenth century Bologna was one of the main Italian centers for scientific, mathematical, and university studies. The city possessed a long academic tradition tied to the Bologna Studio, while local typography served an intellectually active community.

The choice of Stamperia di San Tommaso d'Aquino thus places the work within that particular cultural environment where erudite tradition, religious institutions, universities, and the new science coexisted.

A connection with Maria Gaetana Agnesi

Another very interesting connection concerns Maria Gaetana Agnesi, one of the most important Italian mathematicians of the eighteenth century.

Riccati and his family were directly involved in the revision of the Instituzioni analitiche for the use of Italian youth by Agnesi: between 1745 and 1748 Giordano collaborated with his father on revising certain parts of the work, devoted to algebra and Cartesian geometry.

This episode is particularly significant because it shows the level of the intellectual network in which Riccati moved.

Thus, his On Strings did not arise in isolation, but within an Italian mathematical milieu in which ideas, treatises, problems, and correspondences among scholars circulated.

A work between music, mathematics, and natural philosophy

The true bibliographic charm of the volume probably lies in its interdisciplinary nature.

It is simultaneously:
- a book of mathematics, because it repeatedly uses proportions, formulas, and demonstrations;
- a book of physics, because it studies the material properties of strings and air;
- a book of acoustics, because it investigates the production and propagation of sound;
- a book of musical theory, because it applies these principles to instruments and musical phenomena;
- a document of the history of science, because it testifies to the transition from natural philosophy to modern mathematical physics.

The same plate we see in your copy visually summarizes this character: geometry becomes the instrument through which a physical phenomenon is made intelligible.

Impact and reception

Interest in Riccati’s researches did not remain confined to the year of publication.
Already in the second half of the eighteenth century, studies on string vibration became a stable part of the debate on mechanics and acoustics. A significant testimony is Girolamo Barbarigo, who in 1780, addressing the resistance of strings, explicitly invoked Riccati’s Sketches published in Bologna in 1767.

The work also continued to be remembered in later scientific and musical literature. Its presence in bibliographies dedicated to the history of musical strings testifies to the continuity of its fortune as a historical source for the study of acoustics and instrument making.

Conclusion

On Strings or Elastic Fibres of 1767 is much more than an ancient treatise devoted to musical strings.

It is the document of an era in which sound began to be wrested from the exclusive domain of musical theory to become an object of measurement, experiment, and calculation. In its pages, Giordano Riccati observes a string and, through it, seeks to understand a more general law of nature.

In this sense, the work places itself in an extraordinary line that unites Galileo, Mersenne, Tartini, and Euler and leads toward the nineteenth-century mathematical physics of vibrations and waves. The vibrating string thus becomes a small laboratory of the scientific revolution: a simple, almost everyday object transformed by mathematics into a gateway to understanding the world.

Collation and state of preservation:
xxiv; 246pp 1 plate in the text between pages 26 and 27; 7 folded plates outside the text COMPLETE
Excellent state of preservation, pages marginated and fresh as the plates, perfect preservation state

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