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).

The treatise Risposta alle opposizioni, it is important to underline, however, that the text was written almost entirely by Galileo, and Castelli only wrote some parts of the work. However, it was decided to publish the treatise under Castelli's name. This decision was taken by Galileo himself. He was advised by some friends and consultors not to publish the treatise in his name, so as not to link it to that of his opponents. For this reason, in the title page of the work there is no name and the dedicatory letter to Enea Piccolomini, secret valet of Cosimo II de 'Medici (1590 – 1621) is signed Don Benedetto Castelli.

The Risposta alle opposizioni highlights the crucial role of mathematical analysis in the search for physical causes. This book conveyed disruptive ideas in relation to Aristotelian theories of buoyancy supported by Peripatetics. The Aristotelians were convinced that the cause for the phenomenon of buoyancy was the geometric form of the body. Following Archimedes, Galileo, and Castelli too, affirmed that it depended on the difference between the weight of the body and that of the liquid in which it was immersed.

One of the main supporters of the Aristotelian thesis was the Italian philosopher Ludovico delle Colombe (1565 – 1616), who by the end of 1612 published a treatise entitled Discorso apologetico d'intorno al Discorso di Galileo Galilei. Moreover, the philosopher and theologian Vincenzo di Grazia also advocated the Aristotelian thesis in Considerazioni sopra 'l discorso di Galileo Galilei, published in 1613. The work Risposta alle opposizioni was published by Cosimo Giunti in 1615, in response to the treatises of L. delle Colombe and V. di Grazia as this long and complex treatise is divided into two main sections: the first contains the issues to reply to the work of L. delle Colombe (Considerazioni intorno al discorso apologetico di Ludovico delle Colombe); while the second entitled Considerazioni appartenenti al libro del sig. Vincenzo di Grazia, addresses the problems posed by Vincenzo di Grazia.

The treatise is written in Italian and the edition of 1615 is present in the National Library of Spain (BNE). It is also included in a multi-volume present in the National Library of Portugal: Opera di Galileo, In questa nuova editione insieme raccolte, e di varii trattati dell’istesso autore non più stampati accresciute. This is an edition printed in Bologna between 1655- 1656.