Della misura dell’acque correnti

Benedetto Castelli, 1628

Benedetto Castelli (ca 1578 – 1643) is considered the father of modern hydraulics. He was one of the most famous students of Galileo Galilei (1564 – 1642). He was born Antonio Castelli between 1577 and 1578 in northern Italy, probably in Trenzano or Botticino. However, at the age of eighteen, he joined the Benedictine order of Cassino and became known as Benedetto Castelli. Around 1600, he moved to the Monastery of Santa Giustina in Padua, where he met Galileo Galilei, establishing a master-disciple relationship that lasted for more than forty years. Castelli studied the works of the ancient Greeks: the geometry of Euclid and the astronomy of Tolomeo, and the hydrostatics of Archimedes. In 1607, Castelli was in Cava de' Tirreni, in southern Italy, along with other Benedictine monks. From here, he sent a letter to Galilei, the first of an impressive correspondence.

Castelli was collaborating with Galileo and contributed for the printing of Galileo's work Discorso intorno alle cose che stanno in su l'acqua, o che in essa si muovono (1612). As thou, he took an active part in the dispute of floats in the 1610s. Following this dispute, Castelli published the long compendium Risposta alle opposizioni (1615).

Toward the end of 1624, Castelli was in Rome. The newly elected Pope Urban VIII called him to collaborate in the solution of the problem concerning the course of the Rhine River. As the Pope's trusted mathematician, Castelli accompanied Cardinal Ottavio Corsini (1588 – 1641) on a visit to the area of Bologna and Ferrara, where the absence of significant slopes made it difficult for the waters of the Po to drain into the adjacent countryside, resulting in large expanses of marshland. From a political and diplomatic point of view, this issue opposed the legations of the Papal State and the Republic of Venice and the duchies of Mantua and Ferrara. Castelli's solution, proposed to Corsini, was the canalization of the Reno into the Po, an idea accepted by the Pope, who had the works started by the end of 1628. In that same year, Castelli published his treatise Della misura dell'acque correnti, printed at the Stamperia Camerale Apostolica.

Around the figure of Castelli was born a real school: some of his students were the distinguished scientists, mathematicians and experts on hydraulics: Evangelista Torricelli (1608 – 1647), Bonaventura Cavalieri (1598 – 1647)and Alfonso Borelli (1608 – 1679).

Castelli’s treatise Della misura dell'acque correnti is a work that contains remarkable scientific insights. The main novelty lies in the concept of a river’s flow. The work is dedicated by Castelli to the Pope and begins with a brief introduction where the history and structure of the treatise is explained. The treatise is divided into two parts: the first - Della misura dell'acque correnti - is more accessible and less technical, while the second - Dimostrazioni geometriche della misura dell'acque correnti - has a highly technical and geometric-mathematical content. The first part of the book sets out sixteen corollaries and thirteen appendices, dealing with the problem of incompressibility and measurement of running water. The second part enunciates three definitions that form the basis of the following mathematical treatment, consisting of axioms and propositions. The second part of the book was published posthumously in 1660, in the treatise’s third edition, always under the same title.

Castelli's work was translated into English and French. The English translation dates from 1661 and is based on the third edition of Castelli's treatise. It was published in London by Thomas Salusbury and then reprinted in 1667 in the second volume of the Mathematical collections and translations. The first French translation was edited by Pierre Saporta and published in 1664.

Castelli's work can be found in the University Library of Valencia and the Spanish National Library (BNE), and in the Library of the Compultense University.

Editions & translations

  • The book was first published in 1628.

  • In 1639 was published the second Italian edition, always in Rome by Francesco Cavalli. In addition, in this version appeared two appendices.

  • The third Italian edition appeared posthumously in 1660. It was published in Bologna and edited by Carlo Manolessi (ca 1600 – ca 1661). In 1667 was republished the English edition of 1661. It appeared in the second volume of Mathematical collections and translations in two parts: from the original copies, of Galileus, and other famous modern authores. It was printed by W.Leybourn in London.

  • The treatise in Italian was reprinted in the various editions of the Raccolta d’autori italiani che trattano del moto delle acque (Firenze 1723; Parma 1766-1768; Firenze 1768; Bologna 1821-1823).

  • There is a recent critical edition published in 2016. The title: Benedetto Castelli, Della misura dell’acque correnti. Alcuni opuscoli filosofici. It is edited by Salvatore Ricciardoand published by Editrice Morcelliana. Salvatore Ricciardo works at the University of Bergamo and is author of several studies about history of science.


[1] BALDINI U., Saggi sulla cultura della compagnia di Gesù (secoli XVI-XVIII), CLEUP Editrice, Padova 2000.

[2] MAFFIOLI C., «Acqua premuta». Benedetto Castelli and the incompressibility of water, in Bollettino di storia delle scienze matematiche, 2008, vol. 28, n. 1, pp. 9-50.

[3] RICCIARDO S., Introduzione, in Della misura dell’acque correnti. Alcuni opuscoli filosofici, Editrice Morcelliana, Brescia 2018.