Della misura dell'acque correnti di don Benedetto Castelli Abbate di S. Benedetto Aloysio, e Matematico di Papa Urbano VIII [...] In questa terza edizione accresciuta del Secondo libro, e di molte curiose Scritture non più stampate [...]

4to (230x168 mm). [10], 184 pp. Collation: †⁶ ††⁴ A-Z⁴. Engraved frontispiece showing a bridge on the Tiber river and, on top, the coat-of-arms of Pope Urban VIII, the dedicatee of the work. At l. H2r opens, with its own title page, the section entitled Demostrazioni geometriche della misura dell'acque correnti di d. Benedetto Castelli (Bologna, presso gli heredi del Dozza, 1659). With some woodcut diagrams and illustrations in text. Contemporary cardboards “alla rustica” (minimal restorations to spine). Some browning, but a very good, genuine copy. Uncut with deckle edges.

Third and definitive greatly enlarged edition, edited posthumously by Carlo Manolessi, who signs the new dedication to abbot Urbano Sacchetti (dated October 15, 1659), of this fundamental work that marks the beginning of modern hydraulics. The first edition had appeared in Rome at the Stamperia Camerale in 1628, while the second one was published in 1639, also in Rome. This third edition contains for the first time the second book, which begins on c. K2v and includes, among other things, the Considerazioni intorno alla laguna di Venezia (c. N2r), two different reports equally entitled Considerazione sopra la bonifica del Bolognese, Ferrarese, e Romagnola (respectively on c. S4r and c. T4v), the Relazione dell'acque del Bolognese, e Ferrarese by Ottavio Corsini, superintendent of reclamations and president of Romagna (c. V2v), and the letter to Monsignor Ferrante Cesarini written by Castelli from Rome on August 12, 1639.

Charged by the Pope with the management of the floods of certain rivers in the Church's state, Castelli observed that when the water flows through a passage, such as the arch of a bridge, it increases in volume and speed. He then determined in mathematical terms the inversely proportional relationship between the area of a river section and the speed of its water. This discovery had major consequences for the control of river floods, irrigation and the distribution of spring water.

Born in or near Brescia, Benedetto Castelli (born Antonio) took the Benedictine habit in 1595 and shortly afterwards moved to Padua, where he continued his mathematical studies and met Galileo Galilei, with whom he would forge a close relationship based on friendship and mutual respect that would last for forty years. When Galileo left for Florence, he asked to be moved to the nearest abbey of his Order in order to be as near as possible to his teacher. During the three years he spent in Florence, he helped Galileo carry out his research on Jupiter's satellites, the phases of Venus, the sunspots and, above all, the floating objects, working on the publication of Delle cose che stanno in su l'acqua (Florence, 1612).

In 1613, thanks to the support of Galileo, Castelli obtained a chair in mathematics at the Studio of Pisa. During his many years of teaching, he also gave private readings on the Compasso and the Saggiatore with great success. Among his pupil in Pisa was Bonaventura Cavalieri, whose fate, like that of his other brilliant pupils Alfonso Borelli and Evangelista Torricelli, was always close to his heart.

After the election of Urban VIII (1623), Castelli was called to Rome, where he held the chair at the Sapienza and was appointed to supervise the waterways in the territory of Ferrara and Bologna. Sent to Brescia in 1633, he was unable to attend Galileo's trial, much to his distress. In 1640, with the aid of newly invented telescopes, he discovered that the two round bodies described by Galileo as being attached to the planet Saturn were actually separate from it. Castelli died in Rome in 1643.

Favaro, 171; Riccardi, I, 290.

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