FERMAT, Pierre de. CASTELLI, Benedetto. TORRICELLI, Evangelista. Traicté.

Traicté de la mesure des eaux courantes [Della misura  dell’acque correnti] … traduit de’italien en françois. Avec un discours de la jonction des mers… Ensemble un traicté du mouvement des eaux d’Evangeliste Torricelli [De motu aquarum] … Traduit du latin en françois [by Pierre Saporta] [– Observation sur Synesius (by Fermat)].

Castres: F. Barcouda, 1664.

First edition in French, very rare, of two works by Castelli and Torricelli which founded the modern science of hydraulics, and including an original contribution by Fermat which is published for the first time in this work – only two other scientific works of Fermat were published in his lifetime, both of extreme rarity. “The translator of Benedetto Castelli’s work on measuring running water inserted into the work brilliant note of Fermat's on a letter of Synesius. The letter itself was so obscure that Père Petau, who wrote a commentary on Synesius, admitted that he could not understand it” (from Fermat’s obituary in the Journal des Sçavans, mathshistory.st-andrews.ac.uk/Obituaries/Fermat_obituary/). Fermat’s contribution, the ‘Observation sur Synesius,’ begins as follows (our translation): “The pages which remain empty in this quire made me think of filling them with the splendid observation which I learned some days ago from the incomparable M. Fermat, who does me the honour of being my friend and of frequently talking with me. It is in the fifteenth letter of Synesius, Bishop of Cyrene, which deals with something not understood by any of his commentators, not even by the learned Father Petau, as he himself avows in his notes on this author. I give this observation even more willingly as it has much in common with the treatises here printed.” The ailing Synesius (378-430 AD) wrote in 402 to his friend and teacher Hypatia asking for an instrument he called a hydroscopium or baryllion, and provided detailed instructions as to its construction. When the works of Synesius were published by the Jesuit theologian Denis Petau (1583-1652) in 1640, Petau confessed that he was unable to understand Synesius’ letter. Castelli asked Fermat for his opinion, and the latter’s response was published as the ‘Observation sur Synesius’. Fermat showed that the instrument described by Synesius was a hydrometer, used to measure the specific gravities of liquids, and he gives a detailed description of its construction, with a diagram. The text of ‘Observation sur Synesius’ was reprinted in the preface of the edition of Diophantus’ Arithmetica edited by Fermat’s son Samuel (1670), in the ‘Erudito lectori’ of Fermat’s Varia opera (1679), and in his Oeuvres (Tome I, Appendix).

The first work is a translation of Dimostrazioni geometriche della misura dell’acque correnti (1628). “Castelli’s work is considered one of the cornerstones of modern hydraulics, and its importance is such that he is often claimed to have been the founder of the Italian hydraulics school. This treatise on the speed of liquids in channels and on the measurement of that speed is the first to enunciate the well-known theorem in hydraulics known by the author’s name. Castelli proposed the first accurate and effective methods for measuring the volume of moving water. This fundamental step in hydraulic mechanics and engineering was accomplished by the geometric method of using the cross-sections of a river to measure the volume. He also discusses the relation of velocity and head-in flow through an orifice. Castelli’s work is quoted by almost every major survey of hydraulics ...” (Roberts & Trent, p. 66).

The present French translation of Castelli’s work has a lengthy preface, ‘a messeigneurs les commissaires… pour la jonction des mers,’ signed by Saporta, on the great scheme (actually carried out under Louis XIV) to join the Mediterranean to the Atlantic by means of a canal joining the Garonne river to the Etang de Thau in the south, the famous Canal du Midi. It exerted a great influence on the French engineer Pierre-Paul Riquet Caraman (1609-80), the architect of the Canal du Midi, who had read Castelli’s work in this first French edition.

The second work is a translation of a set of propositions entitled De motu aquarum, part of Torricelli’s work De motu gravium, which was first published in his Opera geometrica (1644). “The treatise [De motu gravium] also refers to the movement of water in a paragraph so important that Ernst Mach proclaimed Torricelli the founder of hydrodynamics. Torricelli’s aim was to determine the efflux velocity of a jet of liquid spurting from a small orifice in the bottom of a receptacle. Through experiment he had noted that if the liquid was made to spurt upward, the jet reached a height less than the level of the liquid in the receptacle. He supposed, therefore, that if all the resistances to motion were nil, the jet would reach the level of the liquid. From this hypothesis, equivalent to a conservation principle, he deduced the theorem that bears his name: The velocity of the jet at the point of efflux is equal to that which a single drop of the liquid would have if it could fall freely in a vacuum from the level of the top of the liquid to the orifice of efflux. Torricelli also showed that if the hole is made in the wall of the receptacle, the jet of fluid will be parabolic in form; he ended the paragraph with interesting observations on the breaking of the fluid stream into drops and on the effects of air resistance. Torricelli’s skill in hydraulics was so well known to his contemporaries that he was approached for advice on freeing the Val di Chiana from stagnant waters, and he suggested the method of reclamation by filling” (DSB XIII, 437).

Johann Beckmann (A History of Inventions, Discoveries, and Origins, tr. William Johnstone, Vol. 2, 1846) gives the following account of Synesius’ hydrometer.

 “The oldest mention of the hydrometer occurs in the fifth century, and may be found in the letters of Synesius to Hypatia (d. 415 AD) … Synesius, of a noble pagan family, who cultivated philosophy and the mathematics with the utmost ardour, had been one of her most intimate friends and followers. On account of his learning, talents, and open disposition, he was universally esteemed, and he had been employed with great success on public occasions of importance. The church at Ptolemais at length wished to have him for their bishop. After much reluctance he accepted the office, but on condition that they should not require him to acknowledge the resurrection of the dead, which he doubted. The people having consented to allow him this indulgence, he suffered himself to be baptized, and became their bishop. He was confirmed by the orthodox patriarch Theophilus, the predecessor of Cyril, to whose jurisdiction Ptolemais belonged; and he afterwards renounced his errors, and declared himself convinced of the truth of the resurrection. This learned man showed his gratitude to Hypatia, by the honourable mention which he made of her in some letters that are still preserved among his writings.

“In his fifteenth letter, he tells Hypatia that he was so unfortunate, or found himself so ill, that he wished to use a hydroscopium, and he requests that she would cause one to be constructed for him. ‘It is a cylindrical tube,’ adds he, ‘of the size of a reed or pipe. A line is drawn upon it lengthwise, which is intersected by others, and these point out the weight of water. At the end of the tube is a cone, the base of which is joined to that of the tube, so that they have both only one base. This part of the instrument is called baryllion. If it be placed in water, it remains in a perpendicular direction, so that one can discover by it the weight of the fluid.’

“Petavius, who published the works of Synesius in the year 1640, acknowledges in his annotations, that this passage he did not understand. An old scholiast, he says, who had added some illegible words, seemed to think that it referred to a water-clock; but this he considers improbable, as a clepsydra was not immersed in water, but filled with it. He conjectures, therefore, that it may allude to some such instrument as that which Vitruvius calls chorobates. The latter however was employed for leveling; and it appears that Synesius, who complains of the bad state of his health, could not think of leveling. Besides, no part of the description in Vitruvius agrees with that which is given in so clear a manner by Synesius.

“Petau published his edition of the works of this philosopher in the time of Pierre de Fermat, conseiller au parlement de Toulouse, a man of great learning, who was an excellent mathematician, and well-acquainted with antiquities and the works of the ancients … As Fermat was often consulted respecting difficult passages of the ancients, he could not be unacquainted with that in the new edition of Synesius. He drew up an explanation of it, and gave it to a friend who was then about to publish a French translation of Bened[etto] Castelli’s book, Della Misura dell’ Acque Correnti, and who caused it to be printed along with that work. Fermat died in the year 1665. After his death his son published some of his writings under the title of Varia Opera Mathematica; and in this collection is inserted his short treatise on the hydroscopium, from which I have extracted the following explanation.

“It is impossible, says he, that the hydroscopium could be the level or chorobates of Vitruvius, for the lines on the latter were perpendicular to the horizon, whereas the lines on the former were parallel to it. The hydroscopium was undoubtedly a hydrometer of the simplest construction. The tube may be made of copper, and open at the top; but at the other end, which, when used, is the lowest, it must terminate with a cone, the base of which is soldered to that of the tube. Lengthwise, along the tube, are drawn two lines, which are intersected by others, and the more numerous these divisions are, the instrument will be so much more correct. When placed in water, it sinks to a certain depth, which will be marked by the cross lines, and which will be greater in proportion to the lightness of the water. A figure, which is added, illustrates this explanation more than was necessary. When a common friend of Fermat and Petavius showed it to the latter, he considered it to be so just, that he wished to have an opportunity of introducing it in a new edition.

“Mersenne, on the other hand, entertains some doubt respecting this instrument, though he does not mention Fermat, with whom he was well-acquainted; for in the dispute which the latter had with Descartes, Mersenne was the bearer of the letters that passed between them, as we learn from the Life of Descartes, by Baillet. His objections however are of little weight. Why should Synesius, asks Mersenne, consider himself unfortunate, because he had not a hydrometer? It may be here replied, that he was in an infirm state, and that the physicians seem to have ordered him to drink no water but what was pure and light. We know that in former times, when so many artificial liquors were not in use, people were accustomed, more than at present, to good water. We read in the works of the ancient physicians, such as Galen and Celsus, directions how to examine the lightness and purity of water. He might have tried it, says Mersenne, with a common balance. He indeed might, but not so conveniently … Mersenne thinks further, that the cone, added to the end of the tube, would have been unnecessary in a hydrometer; but it serves to keep the instrument with more ease in a perpendicular direction in the water. Such is the opinion of H. Klügel …

“For the explanation of Fermat one may produce a still stronger testimony, with which he seems not to have been acquainted. It can be proved that this instrument was used in the next, or at least in the sixth century. Of that period, we have a Latin poem on weights and measures, which contains a very just description of a hydrometer. The author, in manuscripts, is called sometimes Priscianus … With much more probability may we consider as the author the well-known grammarian Priscian, who died about the year 528 … Be the author who he may, this much is evident, that he was acquainted with the hydrometer of Synesius, and has described it in a very clear manner.”

The translator, Pierre Saporta (1613-85), a Montpellier lawyer, was a correspondent of Henry Oldenburg. Fermat, normally associated with Toulouse, where he was conseiller du roi, had for many years close links with Castres, a strongly Huguenot town on the banks of the river Agout. In fact, he died and was buried there in 1665. In 1648 a protestant Academy was founded at Castres amongst whose members were Pierre Bayle, Pierre Borel, the physician and writer on alchemy, de Ranchin and Pierre Saporta. It was thus that Fermat and Saporta became acquainted and eventually close friends. The second work has a preface by Saporta addressed to Fermat, whom he terms ‘le souverain legislateur de tous les scavans’. Fermat had prompted Saporta to undertake the translation as a sequel to that of Castelli.

4to (199 x 140 mm), pp. [x], 87, woodcut diagrams in text (light browning to first and last leaves). Contemporary calf (spine ends worn).

Item #5780

Price: $12,500.00