Christiaan Huygens Research Articles

Methodology and Politics in Science: The Fate of Huygens' 1673 Proposal of the Seconds Pendulum as an International Standard of Length and Some Educational Suggestions

This paper is part of a larger work on the history, philosophy and utilisation of pendulum motion studies (Matthews 2000). The paper deals with the fate of Christiaan Huygens 1673 proposal to use the length of a seconds pendulum (effectively one metre) as a universal, natural and objective standard of length. This is something which, if it had been adopted, would have been of inestimable scientific, commercial and cultural benefit. Why it was not originally adopted in the late seventeenth century, and why it was again rejected in the late eighteenth century (1795) when the Revolutionary Assembly in France adopted the metric system with the metre being defined as one ten-millionth of the quarter meridan distance – raise interesting questions about the methodology and politics of science. Given that pendulum motion is a standard component of all science courses throughout the world, and given that most science education reforms, including the US National Science Education Standards and recent Australian state reforms, require that something of the ‘big picture’ of science be conveyed to students (the relationship of science to culture, commerce, history and philosophy) – it is suggested that these educational goals can be advanced by teaching about the fate of Huygens' proposal.

The Huygens entrainment phenomenon and thermoacoustic engines

The earliest known reference to the mode-locking, or entrainment, of two maintained oscillators is Christiaan Huygens' description of two pendulum clocks "falling into synchrony" when hung on the same wall. We describe an analogous phenomenon in acoustics-the mode-locking of two thermoacoustic engines which have their cases rigidly welded together, but which are otherwise uncoupled. This "mass-coupling" might compete with acoustic coupling when the latter is used to enforce antiphase mode-locking in such engines, for vibration cancellation. A simple theory relating the phase difference between the engines in the locked state to the corresponding ratio of their pressure amplitudes is in excellent agreement with theory and numerical simulations. The theory's prediction relating the phase difference to the engines' natural frequency difference is qualitatively confirmed by experiment, despite larger experimental uncertainties. The mass coupling is relatively weak compared to the aforementioned acoustic coupling, and in general occurs in antiphase, so we conclude that mass coupling will not interfere with vibration cancellation by acoustic coupling in most circumstances.

George Graham, visible technician

In December of 1675, in a desperate race with Christiaan Huygens over a patent for a spring-regulated watch, Robert Hooke, FRS (Fellow of the Royal Society of London) characterized the clock maker Thomas Tompion as a ‘Slug’, a ‘Clownish Churlish Dog’ and a ‘Rascall’, because Tompion was making a watch of Hooke's design too slowly for the latter's taste. It was Hooke's watch, not Tompion's; Hooke was the patron and Tompion the client. Fifty years later Tompion's apprentice, George Graham, made watches and clocks and quadrants for other Fellows of the Royal Society, yet these instruments were known as Graham's clocks and Graham's quadrants. Language such as Hooke had used towards Tompion was inconceivable towards Graham; he was a member of the Royal Society's governing body, the Council, and had published several significant papers in the Society's journal, the Philosophical Transactions , in which his testimony on and experiments in astronomy, magnetism, horology and metrology were unquestioned. Yet in the early decades of the eighteenth century one could still go to his shop in London's Strand and buy a watch or a clock from him. Like Tompion, George Graham, FRS was a shopkeeper. Nor was he alone in the eighteenth century, at that supposed bastion of gentlemen, the Royal Society. Nearly two-thirds of the membership had to work for a living in one way or another, some rather grandly as high government officials, senior army officers, clerics with ample livings and physicians and lawyers with large and successful London practices ; others more modestly as sailors, surgeons, apothecaries, schoolteachers, engineers, attorneys and instrument-makers. The latter group included some of the most scientifically eminent members of the Royal Society in the eighteenth century: the sailor James Cook (geography), the printer Benjamin Franklin (electricity), the teacher and preacher Joseph Priestley (chemistry), the instrument-maker and engineer James Watt (chemistry), the musician William Herschel (astronomy), and the silk weaver and optician John Dollond (optics). None of these men were gentlemen (though many of their sons or grandsons became so) yet they made science and were acknowledged to have done so; their papers were published and their best work awarded medals.

A Longitude Timekeeper by Isaac Thuret with the Balance Spring Invented by Christiaan Huygens

The recent discovery of an extremely interesting clock signed Thuret A Paris reveals that this clockmaker was much more closely involved in the development of a clock to be used for finding longitudes at sea than has generally been assumed. Isaac Thuret was the clockmaker who made for Christiaan Huygens the first watch with a spiral spring regulating the movements of the balance wheel in 1675. The conflict about his contribution to the invention is usually seen as having ended their cooperation. However, a closer study of Huygens's correspondence strongly suggests that this was not the case. This longitude timekeeper, provided with the pirouette as published by Huygens but abandoned by the makers of pocket watches, supports this view. Its close correspondence in design with the later marine chronometers (no remontoire or fusee) confirms that Huygens and Thuret, apart from the pirouette, were on the right track. However, it would take a century before the reliability and accuracy of the mechanical timekeeper reached the level required for measuring longitudes.

The Lens Production by Christiaan and Constantijn Huygens

Ever since they began to take an interest in lens grinding, the brothers Christiaan and Constantijn Huygens searched for high-quality glass to turn in to lenses. Historical research in combination with optical measurements on preserved lenses has allowed the verificationof the lenses ground by the brothers, and also provided information on who helped them with the necessary knowledge and material.

Shadows and deception: from Borelli's Theoricae to the Saggi of the Cimento

‘Poor Borelli!’ exclaimed Alexandre Koyre at the end of his wonderful and by now classic study of Borelli's ‘celestial mechanics’. Koyre frankly admitted that Borelli lacked Newton's genius and intellectual audacity. However, in his story Borelli deserved a place between Kepler and Newton for his ‘imperfect but decisive’ unification of terrestrial and celestial physics. This framework finds a powerful justification in Borelli's extensive usage of Keplerian astronomy and in Newton's references to Borelli's work on the Medicean planets, Theoricae mediceorum planetarum (Florence, 1666), both in his correspondence with Edmond Halley, with regard to a controversy with Robert Hooke, and in Philosophiae naturalis principia mathematica (London, 1687). Newton's own copy of Borelli's work with signs of his reading – the famous dog-earings – is preserved in the library of Trinity College, Cambridge. The magnitude of Newton's achievement has haunted Borelli's work ever since Principia mathematica appeared in print. For example, although Christiaan Huygens was sent a copy of Borelli's book by Prince Leopold in 1666, his marginal annotations in his own copy of the book were written after he had read Newton's masterpiece, as if Huygens had felt the need to read the book again after 1687. From then onwards Borelli's work has almost inevitably appeared in a new light that has coloured its subsequent readings.My ambition in this paper is to provide a fresh reading of Borelli's work by reconstructing its circumstances of composition, establishing a comparison with a relevant strictly contemporary source, and attending to the immediate reception of Theoricae. Borelli's work was written with an eye to a composite audience including Roman Jesuits, Sicilian intellectual circles and Leopold de' Medici's correspondents across the Alps, such as the Copernican astronomer Ismael Boulliau in Paris. Borelli was aware that his Sicilian readers were likely to have different concerns from those of Roman Jesuits or the Medici. Thus the task of charting the reception of his work is a formidable one. For a variety of reasons, including availability of sources, limitations of space, taste and competence, my analysis of Borelli's work on the Medicean planets is limited to a few themes and is not only no less partial than Koyre's, but in many respects it relies on it. If readers feel stimulated to re-read Koyre's text, one of the aims of this paper will have been fulfilled.

Nonanalytic nonlinear oscillations: Christiaan Huygens, quadratic Schrödinger equations, and solitary waves

An example of an oscillatory system with a time-reversible nonanalytic nonlinearity is shown to be a pendulum with a flexible cord sandwiched between two identical circular disks, in contrast to the analytic case of a pendulum interrupted by a single circular disk. The amplitude-dependent frequencies of both cases are perturbatively calculated, and are compared to numerical simulations over the entire range of amplitudes. The nonanalyticity causes the unusual effect of the frequency to vary linearly with amplitude for small amplitudes, which has also been observed in the resonant frequencies of compressional standing waves in sandstone. A general condition for a nonanalytic nonlinearity to yield this behavior is presented. The amplitude-dependent frequency for the double-interrupted pendulum allows an explanation for Huygens’surprising observation that circular interrupters were as effective as cycloidal interrupters in achieving isochronous motion. A lattice of linearly coupled double-interrupted pendulums is described near the lower and upper cutoff modes by quadratic nonlinear Schrödinger (NLS) equations, in contrast to cubic NLS equations which arise for analytic pendulum lattices as well as typical acoustic and surface waveguides. Solitary breather and kink solutions to the quadratic NLS equations are presented, and are compared to the known soliton solutions of the corresponding cubic NLS equations. Compressional waves in sandstone are shown to be modeled by the inclusion of a nonanalytic quadratic nonlinearity in the stress–strain relationship. Quadratic NLS breathers are predicted to occur in a waveguide of sandstone, and an analysis indicates that such an observation is feasible.

Leibniz and the Two Clocks

Leibniz and the Two Clocks David Scott Anyone familiar with Leibniz’s philosophy in general and with his critique of occasionalism in particular is likely familiar with his example of two clocks. Generally speaking, the example illustrates a range of hypotheses that, according to Leibniz, might possibly explain the connections between substances in the world. The most important of these hypotheses are Leibniz’s own doctrine of the preestablished harmony and the occasionalist—for present purposes, Malebranche’s—doctrine of causation. In Leibniz’s mind at least, the two clocks example (so-called because substances are represented by two clocks) illustrates the superiority of the hypothesis of the preestablished harmony over occasionalism. Whether the example in fact succeeds in this regard is the primary question of this paper. Given the times, Leibniz’s choice of example is understandable. A clock is ideally suited to represent a mechanism, of course; and in view of the general “mechanization of the world view” of that time, the example seems to have been in the air.1 Spring-driven clocks had appeared at the outset of the sixteenth century, and the kind of clock Leibniz seems to have in mind in his example, namely, one driven by a pendulum, was the invention, in about 1656, of Christian Huygens, who was a significant influence on Leibniz. Huygens’s invention in fact provided the impetus for a broadening of the importance and extent of horology.2 Although Leibniz’s choice of example was understandable, it was not a happy one, and the general importunity of his use of this example was [End Page 445] recognized by both his contemporary critics and his subsequent commentators.3 In fact his choice of the example becomes almost ironic when it is recalled that Geulincx, who is most commonly associated with the example, was an occasionalist. The operations of two clocks, between which there is a constant and fixed relation, say, of keeping the same time, cannot normally be said to be “related.” The example is more intuitively taken to indicate the random, accidental, unnecessary, and unconnected nature of the otherwise constant and regular relation between the clocks; and so one would think the example more suited to an occasionalist’s position than to that of Leibniz. In what follows I aim to judge the effectiveness—in Leibniz’s own terms—of the two clocks example. In gauging the effectiveness of Leibniz’s use of the example, I expect that a few things can be learned about Leibniz’s system in general and about his critique of occasionalism in particular. My procedure will be to examine separately what I take to be four significant occasions in which Leibniz compares things or substances in the world and clocks. The passages in question date from a period spanning ten years, and in each instance the example is put to service in Leibniz’s attempt to better occasionalism. Beyond this, although the comparison is employed or appraised in slightly different ways each time, the uses to which it is put are basically two. In the first two instances examined below, it is employed primarily to distinguish the preestablished harmony from occasionalism. I will be arguing that, to the extent that it fails to illustrate his point, Leibniz fails adequately to distinguish these two doctrines. This was Arnauld’s criticism.4 In the third and fourth instances, however, the example is employed solely to illustrate certain features of the preestablished harmony. On my analysis, it does not appear to fulfill this role either. [End Page 446] First Use of the Example One of the more well known statements of the two clocks example is from an explanation Leibniz gives to Basnage de Beauval in 1696 of his “New System” (1695): Imagine two clocks or watches which are in perfect agreement. Now this can happen in three ways. The first is that of a natural influence.... The second way of making two clocks, even poor ones, agree is always to assign a skilled craftsman to them who adjusts them and constantly sets them in agreement. The third way is to construct these two timepieces at the beginning with such skill and accuracy that one can...

Nonanalytic nonlinear oscillations: Christiaan Huygens, quadratic Schrödinger equations, and solitary waves

An example of an oscillatory system with a time-reversible nonanalytic nonlinearity is shown to be a pendulum with a flexible cord sandwiched between two identical circular disks, in contrast to the analytic case of a pendulum interrupted by a single circular disk. The amplitude-dependent frequencies of both cases are perturbatively calculated, and are compared to numerical simulations. The nonanalyticity causes the unusual effect of the frequency to vary linearly with amplitude for small amplitudes, which has also been observed in compressional standing waves in sandstone. The general condition for a nonanalytic nonlinearity to yield this behavior is presented. The amplitude-dependent frequency for the double-interrupted pendulum allows an explanation for Huygens’ observation that circular interrupters were as effective as cycloidal interrupters in achieving isochronous motion. A lattice of linearly coupled double-interrupted pendulums is described near the lower and upper cutoff modes by quadratic nonlinear Schrödinger (NLS) equations, in contrast to cubic NLS equations which arise for analytic pendulum lattices as well as typical acoustic and surface wave guides. Solitary breather and kink solutions to the quadratic NLS equations are presented, and the quadratic NLS breather is predicted to occur in a bar of sandstone. [Work supported by ONR.]

The young Huygens solves the problem of elastic collisions

Christiaan Huygens was probably the first person to solve the problem of elastic collisions. He did this in the 1650s when he was only in his early twenties. The first formal publication of his general rule for the outcome of a head-on hard collision was in March 1669 in the Journal des Sçavans. Our present paper describes in detail Huygens’ work on elastic collisions. We focus particularly on how Huygens’ instinct for symmetry led him to a solution in the center-of-gravity reference frame. He readily transformed this solution to other frames using what we now call the Galilean velocity transformation. Huygens’ symmetry approach is quite different from the modern description of collisions using Newtonian action and reaction forces.

Christiaan Huygens’ discovery of the center of oscillation formula

Christiaan Huygens was the first person to discover the general formula for the center of oscillation length of a physical pendulum. He was motivated to do this work by his interest in constructing accurate pendulum clocks. It is remarkable that Huygens arrived at his brilliant solution about a quarter of a century before the publication of the first edition of Newton’s Principia. This paper analyzes Huygens’ little-known derivation in detail. We take particular note of Huygens’ ingenious idea of having the moving physical pendulum ‘‘theoretically explode’’ into constituent pieces which then rise until their kinetic energy is exhausted.

A New Minimization Proof for the Brachistochrone

The other two names are the tautochrone and the brachistochrone. In order to talk about the properties of the cycloid that gave it these names, we need to turn the curve upside-down, so that it is concave upward. Thus, throughout this paper, a rolling circle will always be rolling the ceiling. The word tautochrone means same time. In the 1600's Christian Huygens discovered a pendulum whose period is independent of how high the bob swings; this is only approximately true for a regular pendulum. Huygens found that if obstructions in the shape of half cycloids are placed so that the string of a pendulum wraps around them as it swings (see Figure 2), then the bob also traces out a cycloid. Further, the period of motion is independent of whether the bob makes the full swing or swings only part of the way back and forth. This is equivalent to saying that if we build a ramp in the shape of a cycloid and let a marble roll down it, the time it takes to reach the lowest point is independent of where on the cycloid we started the marble. See Section 8.

Mutual clock synchronization in global digital communication networks

AbstractThere are numerous synchronization methodologies available for consideration in solving the problem of network synchronization in digital communication networks [1, 2]. They include: independent clocks, pulse stuffing, elastic stores, master‐slave hierarchical, time reference distribution, mutual synchronization, etc. This paper considers the network synchronization performance achievable using the method of mutual clock synchronization observed first by Christiaan Huygens in 1665 [3]. Network synchronization performance metrics studied include: nodal timing accuracy, timing jitter, slip rate, time interval between slips, probability of loss of synchronization. These metrics are shown to depend upon the distance (range) between clocks, ranging error, clock stability, nodal phase error processing bandwidth, data rate, signal‐to‐noise ratio and network connectivity. In this regard, the mutual synchronization performance achievable with long wavelength biological rhythms and electric power system rhythms is compared with the performance achievable using short wavelength rhythms required in wideband and broadband digital communications networks. The results are further applied to the problem of synchronizing a satellite communications network. When intrasatellite communication crosslinks (links between satellites in the same orbital plane) are used in a constellation of communication satellites, it is shown that the maximum data rate, the network connectivity and the constellation altitude drive the achievable network synchronization performance; the latter is set by technological limitations due to clock frequency stability, the maximum range between satellites and the minimum ranging error achievable by the ranging system. In this sense, low Earth orbits (LEO) are preferred over geosynchronous (GEO)Earth orbits. The theory is also applied to the Teledesic and Iridium networks.

Christiaan Huygens and the foundations of optics

On the occasion of the tercentenary of the death of Christiaan Huygens, his contributions to optics, more particularly to the wave theory of light, are critically reviewed against the background of the work of Kepler, Descartes and Newton. Recent historiography has shown that Huygens' work was overshadowed by Newton's and Euler's during the 18th century. In the beginning of the 19th century however, 'Huygens' principle' and its foremost application, the analysis of double refraction, were rediscovered by Thomas Young and Augustin Fresnel. Huygens' principle indeed appeared to be easily adaptable to the new theory of transversal light waves. Up to the present day, Fresnel's transversal interpretation of Huygens' principle has been a precious aid in understanding the foundations of optics.

Muskets and Pendulums: Benjamin Robins, Leonhard Euler, and the Ballistics Revolution

Muskets and Pendulums: Benjamin Robins, Leonhard Euler, and the Ballistics Revolution BRETT D. STEELE Ballistics was revolutionized between 1742 and 1753 by Benjamin Robins (1707-51) and Leonhard Euler (1707-83). As one artillery officer wrote in 1789, “Before Robins, who was in gunnery what the immortal Newton was in philosophy, the founder of a new system deduced from experiment and nature, the service of artillery was a mere matter of chance, founded on no principles, or at best, but erroneous ones.”1 John Pringle, a president of the Royal Society, put it more simply in 1783 by stating that Robins created a “new science.”2John Nef wrote in 1950 that Robins’s work “provides a landmark in the interrelations between knowledge and war.”3 Two engineers more recently described him as being “one of the fathers of aerodynamics,” while Thomas P. Hughes referred to him as “a founder of modern gunnery.”4 What did Mr. Sti ei.e is in the Program for the History of Science and Technology at the University of Minnesota, writing his dissertation on 18th-century ballistics and gunnery and working on an economic theory of technological products. His research was supported by fellowships from the Smithsonian Institution’s National Museum ofAmerican History and the Deutsches Museum and by the assistance of I. S. Weissbrodt. He thanks Ed Layton, Roger Hahn, Michael Segre, Mark Levinson, Maarten Heyboer,John Jackson, Don Opitz, and the Technology and Culture referees for their helpful comments and criticisms. 'Papacino D’Antoni, A Treatise on Gunpowder; a Treatise on Fire-Arms; and a Treatise on the Service of Artillery in the Time of War, trans. Captain Thomson of the Royal Regiment of Artillery (London, 1789), p. xvii. John Pringle, Six Discourses . . . on occasion ofSix Annual Assignments ofSir Godfrey Copleys Medal (London, 1783), p. 273. John Nef, War and Human Progress: An Essay on the Rise of Industrial Civilization (Cambridge, Mass., 1950), p. 194. 4H. M. Barkla and L.J. Auchterlonie, “The Magnus or Robins Effect on Rotating Spheres,”Journal ofFluid Mechanics A7 (1971): 437. See Thomas P. Hughes’s commentary after David D. Bien’s article, “Military Education in 18th Century France: Technical and Non-technical Determinants,” in Science, Technology and Warfare: Proceedings of the 3rd Military History Symposium, USAFA, 8-9 May 1969, ed. Monte D. Wright and LawrenceJ. Paszek (Washington, D.C., 1971), p. 73. No books devoted to the history of ballistics in the 18th century exist in English at present. In other languages, however, there are some useful intellectual histories that include the subject. See M. P. Charbonnier, Essais sur© 1994 by the Society for the History of Technology. All rights reserved. 0040-165X/94/3502-0002$01.00 348 The Ballistics Revolution 349 such a seemingly obscure British mathematician and engineer do to generate such acclaim? Charles Hutton, the 18th-century artillery professor at Woolwich, said that Robins’s research represents “the first work that can be considered as attempting to establish a practical system of gunnery, and projectiles, on good experiments, on the force of gunpowder, on the resistance of the air, and on the effects of different pieces of artillery.”” More specifically, Robins invented new instruments which he used to discover and quantify the enormous magnitude of air-resistance force acting on high-speed projectiles and to make the first observations of the sound barrier. He also conducted a theoretical and experimental thermodynamic analysis of interior ballistics, discov­ ered the Magnus (or Robins) effect of fluid mechanics, and established a rational understanding of the rifling phenomenon. Of all his aerody­ namic discoveries, the enormous and complex function of air-resistance force encountered by high-speed projectiles caused the greatest sensa­ tion in the 18th century. This discovery quantitatively showed the inadequacy of Galileo’s projectile theory, which neglected air resistance, and the oversimplification ofSir Isaac Newton’s and Christian Huygens’s air-resistance theory for projectile motion. Furthermore, Robins’s airresistance experiments made the practical mathematical analysis of high-speed ballistic motion possible. Robins summarized his initial discoveries in New Principles of Gunnery, a short book that was first published in 1742?’ Euler translated this work into German and added an extensive mathematical analysis...

Near field measurements and the synthesis of linear arrays with prescribed radiation patterns: a survey of some early work at Christiaan Huygens Laboratory

An analog complex series analyzer that performs discrete Fourier transform and also solves for the complex roots of the array polynomial equation is described. A planar near-field scan facility, covering the frequency bands from 1.5-40 GHz and featuring a mechanical accuracy of 0.03 mm deviation from a perfect straight line, is also described. Some applications that provide a check on the theory of the analyzer and scanner are discussed. The pros and cons of various near-field measurement methods are compared. It is concluded that, with respect to ease of measurement and correction of the near-field distribution, the planar scan is to be preferred, whereas for overall performance checking, the compact antenna range is useful, although it carries an appreciable cost penalty.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

An unpublished autograph by Christiaan Huygens: His letter to David Gregory of 19 January 1694

Summary A letter written by Christiaan Huygens to David Gregory (19 January 1694) is published here for the first time. After an introduction about the contacts between the two correspondents, an annotated English translation of the letter is given. The letter forms part of the wider correspondence about the ‘new calculus’, in which L'Hospital and Leibniz also participated, and gives some new evidence about Huygens's ambivalent attitude towards the new developments. Therefore, two mathematical passages in the letter are discussed separately. An appendix contains the original Latin text.

Representing the Earth's Shape: The Polemics Surrounding Maupertuis's Expedition to Lapland

HISTORICAL ACCOUNTS OF QUANTIFICATION in the physical sciences in the eighteenth century have often been described as a straightforward series of steps in a process of maturation, as instruments and standards advanced in precision.' This paper calls into question the self-evident nature of precision by investigating the production and uses of measurements. In the case of the dispute over the shape of the earth, centered in Paris in the 1730s, the precision of measurements was a matter to be interpreted, attacked, defended, and represented. The whole messy business, undertaken by the participants to win consensus from their contemporaries, took place in the context of academic politics and the intellectual fashions of the salons and the court. All parties to the dispute claimed to be drawing on precision measurements; evaluating precision turned out to require the use of a range of intellectual, mathematical, instrumental, political, and textual resources. The alleged precision was then used to construct and defend rival scientific programs and practices. The origins of the eighteenth-century dispute go back to Isaac Newton and Christiaan Huygens, both of whom calculated the earth to be slightly flattened at the poles, though they were working from different theories of gravity. The only empirical support available to them came from pendulum measurements taken near the equator that showed the effect of gravity to be less there than at higher latitudes. By the early eighteenth century French astronomers had produced another set of data: measurements of celestial arcs and terrestrial distances made in the course of an ambitious project to map the kingdom of France. In 1718 Jacques Cassini announced that these measurements implied an elongated rather than a flattened earth. Virtually uncontested for fifteen years, his claim attracted renewed attention in the early 1730s, when a contingent of Paris Academy mathematicians questioned the adequacy of local measures for settling the matter.2 As a result, the royal treasury financed two expeditions, one to the equator and one to the arctic circle, to make measurements for a more definitive comparison.

A 17th-century debate on the consequentia mirabilis

In modern times the so‐called consequentia mirabilis (if not-P, then P). then P) was first enthusiastically applied and commented upon by Cardano (1570) and Clavius (1574). Of later passages where it occurs Saccheri’s use (1697) has drawn a good deal of attention. It is less known that about the middle of the 17th century this remarkable mode of arguing became the subject of an interesting debate, in which the Belgian mathematician Andreas Tacquet and Christiaan Huygens were the main representatives of opposite views concerning its probative force. In this article the several phases and moves of that debate are delineated

Unrolling Time: Christiaan Huygens and the Mathematization of Nature. Joella G. Yoder

Previous articleNext article No AccessBook ReviewsUnrolling Time: Christiaan Huygens and the Mathematization of Nature. Joella G. Yoder Michael S. MahoneyMichael S. Mahoney Search for more articles by this author PDFPDF PLUS Add to favoritesDownload CitationTrack CitationsPermissionsReprints Share onFacebookTwitterLinkedInRedditEmail SectionsMoreDetailsFiguresReferencesCited by Isis Volume 81, Number 3Sep., 1990 Publication of the History of Science Society Article DOIhttps://doi.org/10.1086/355494 Views: 5Total views on this site Copyright 1990 History of Science Society, Inc.PDF download Crossref reports no articles citing this article.