Christiaan Huygens

Like some of his contemporaries, Huygens was often slow to commit his results and discoveries to print, preferring to disseminate his work through letters instead.^[42] In his early days, his mentor Frans van Schooten provided technical feedback and was cautious for the sake of his reputation.^[43]

Between 1651 and 1657, Huygens published a number of works that showed his talent for mathematics and his mastery of classical and analytical geometry, increasing his reach and reputation among mathematicians.^[33] Around the same time, Huygens began to question Descartes's laws of collision, which were largely wrong, deriving the correct laws algebraically and later by way of geometry.^[44] He showed that, for any system of bodies, the centre of gravity of the system remains the same in velocity and direction, which Huygens called the conservation of "quantity of movement". While others at the time were studying impact, Huygens's theory of collisions was more general.^[5] These results became the main reference point and the focus for further debates through correspondence and in a short article in Journal des Sçavans but would remain unknown to a larger audience until the publication of De Motu Corporum ex Percussione (Concerning the motion of colliding bodies) in 1703.^[45][44]

In addition to his mathematical and mechanical works, Huygens made important scientific discoveries: he was the first to identify

The

While at the Académie in Paris, Huygens had an important patron and correspondent in Jean-Baptiste Colbert, First Minister to Louis XIV.^[58] However, his relationship with the French Académie was not always easy, and in 1670 Huygens, seriously ill, chose Francis Vernon to carry out a donation of his papers to the Royal Society in London, should he die.^[59] However, the aftermath of the Franco-Dutch War (1672–78), and particularly England's role in it, may have damaged his later relationship with the Royal Society.^[60] Robert Hooke, as a Royal Society representative, lacked the finesse to handle the situation in 1673.^[61]

The physicist and inventor

Huygens moved back to The Hague in 1681 after suffering another bout of serious depressive illness. In 1684, he published Astroscopia Compendiaria on his new tubeless

On his third visit to England, Huygens met Isaac Newton in person on 12 June 1689. They spoke about Iceland spar, and subsequently corresponded about resisted motion.^[68]

Huygens returned to mathematical topics in his last years and observed the acoustical phenomenon now known as

Huygens never married.[71]

Mathematics

Huygens first became internationally known for his work in mathematics, publishing a number of important results that drew the attention of many European geometers.^[72] Huygens's preferred method in his published works was that of Archimedes, though he made use of Descartes's analytic geometry and Fermat's infinitesimal techniques more extensively in his private notebooks.^[17][27]

Published works

Theoremata de Quadratura

Huygens's first publication was Theoremata de Quadratura Hyperboles, Ellipsis et Circuli (Theorems on the quadrature of the hyperbola, ellipse, and circle), published by the Elzeviers in Leiden in 1651.^[42] The first part of the work contained theorems for computing the areas of hyperbolas, ellipses, and circles that paralleled Archimedes's work on conic sections, particularly his Quadrature of the Parabola.^[33] The second part included a refutation to Grégoire de Saint-Vincent's claims on circle quadrature, which he had discussed with Mersenne earlier.

Huygens demonstrated that the centre of gravity of a segment of any hyperbola, ellipse, or circle was directly related to the area of that segment. He was then able to show the relationships between triangles inscribed in conic sections and the centre of gravity for those sections. By generalizing these theorems to cover all conic sections, Huygens extended classical methods to generate new results.^[17]

Quadrature was a live issue in the 1650s and, through Mylon, Huygens intervened in the discussion of the mathematics of Thomas Hobbes. Persisting in trying to explain the errors Hobbes had fallen into, he made an international reputation.^[73]

De Circuli Magnitudine Inventa

Huygens's next publication was De Circuli Magnitudine Inventa (New findings in the measurement of the circle), published in 1654. In this work, Huygens was able to narrow the gap between the circumscribed and inscribed polygons found in Archimedes's Measurement of the Circle, showing that the ratio of the circumference to its diameter or π must lie in the first third of that interval.^[42]

Using a technique equivalent to Richardson extrapolation,^[74] Huygens was able to shorten the inequalities used in Archimedes's method; in this case, by using the centre of the gravity of a segment of a parabola, he was able to approximate the centre of gravity of a segment of a circle, resulting in a faster and accurate approximation of the circle quadrature.^[75] From these theorems, Huygens obtained two set of values for π: the first between 3.1415926 and 3.1415927, and the second between 3.1415926533 and 3.1415926538.^[76]

Huygens also showed that, in the case of the hyperbola, the same approximation with parabolic segments produces a quick and simple method to calculate logarithms.^[77] He appended a collection of solutions to classical problems at the end of the work under the title Illustrium Quorundam Problematum Constructiones (Construction of some illustrious problems).^[42]

De Ratiociniis in Ludo Aleae

Huygens became interested in games of chance after he visited Paris in 1655 and encountered the work of Fermat, Blaise Pascal and Girard Desargues years earlier.^[78] He eventually published what was, at the time, the most coherent presentation of a mathematical approach to games of chance in De Ratiociniis in Ludo Aleae (On reasoning in games of chance).^[79][80] Frans van Schooten translated the original Dutch manuscript into Latin and published it in his Exercitationum Mathematicarum (1657).^[81][12]

The work contains early game-theoretic ideas and deals in particular with the problem of points.^[14][12] Huygens took from Pascal the concepts of a "fair game" and equitable contract (i.e., equal division when the chances are equal), and extended the argument to set up a non-standard theory of expected values.^[82] His success in applying algebra to the realm of chance, which hitherto seemed inaccessible to mathematicians, demonstrated the power of combining Euclidean synthetic proofs with the symbolic reasoning found in the works of Viète and Descartes.^[83]

Huygens included five challenging problems at the end of the book that became the standard test for anyone wishing to display their mathematical skill in games of chance for the next sixty years.^[84] People who worked on these problems included Abraham de Moivre, Jacob Bernoulli, Johannes Hudde, Baruch Spinoza, and Leibniz.

Unpublished work

Huygens had earlier completed a manuscript in the manner of Archimedes's On Floating Bodies entitled De Iis quae Liquido Supernatant (About parts floating above liquids). It was written around 1650 and was made up of three books. Although he sent the completed work to Frans van Schooten for feedback, in the end Huygens chose not to publish it, and at one point suggested it be burned.^[33][85] Some of the results found here were not rediscovered until the eighteenth and nineteenth centuries.^[8]

Huygens first re-derives Archimedes's solutions for the stability of the sphere and the paraboloid by a clever application of Torricelli's principle (i.e., that bodies in a system move only if their centre of gravity descends).^[86] He then proves the general theorem that, for a floating body in equilibrium, the distance between its centre of gravity and its submerged portion its at a minimum.^[8] Huygens uses this theorem to arrive at original solutions for the stability of floating cones, parallelepipeds, and cylinders, in some cases through a full cycle of rotation.^[87] His approach was thus equivalent to the principle of virtual work. Huygens was also the first to recognize that, for these homogeneous solids, their specific weight and their aspect ratio are the essentials parameters of hydrostatic stability.^[88][89]

Natural philosophy

Huygens was the leading European natural philosopher between Descartes and Newton.^[17][90] However, unlike many of his contemporaries, Huygens had no taste for grand theoretical or philosophical systems and generally avoided dealing with metaphysical issues (if pressed, he adhered to the Cartesian philosophy of his time).^[7][33] Instead, Huygens excelled in extending the work of his predecessors, such as Galileo, to derive solutions to unsolved physical problems that were amenable to mathematical analysis. In particular, he sought explanations that relied on contact between bodies and avoided action at a distance.^[17][91]

In common with Robert Boyle and Jacques Rohault, Huygens advocated an experimentally oriented, mechanical natural philosophy during his Paris years.^[92] Already in his first visit to England in 1661, Huygens had learnt about Boyle's air pump experiments during a meeting at Gresham College. Shortly afterwards, he reevaluated Boyle's experimental design and developed a series of experiments meant to test a new hypothesis.^[93] It proved a yearslong process that brought to the surface a number of experimental and theoretical issues, and which ended around the time he became a Fellow of the Royal Society.^[94] Despite the replication of results of Boyle's experiments trailing off messily, Huygens came to accept Boyle's view of the void against the Cartesian denial of it.^[95]

Newton's influence on John Locke was mediated by Huygens, who assured Locke that Newton's mathematics was sound, leading to Locke's acceptance of a corpuscular-mechanical physics.^[96]

Laws of motion, impact, and gravitation

Elastic collisions

The general approach of the mechanical philosophers was to postulate theories of the kind now called "contact action." Huygens adopted this method but not without seeing its limitations,^[97] while Leibniz, his student in Paris, later abandoned it.^[98] Understanding the universe this way made the theory of collisions central to physics, as only explanations that involved matter in motion could be truly intelligible. While Huygens was influenced by the Cartesian approach, he was less doctrinaire.^[99] He studied elastic collisions in the 1650s but delayed publication for over a decade.^[100]

Huygens concluded quite early that

In 1659 Huygens found the constant of gravitational acceleration and stated what is now known as the second of Newton's laws of motion in quadratic form.^[105] He derived geometrically the now standard formula for the centrifugal force, exerted on an object when viewed in a rotating frame of reference, for instance when driving around a curve. In modern notation:

${\displaystyle F_{c}={m\ \omega ^{2}}{r}}$

with m the

In 1657, inspired by earlier research into pendulums as regulating mechanisms, Huygens invented the pendulum clock, which was a breakthrough in timekeeping and became the most accurate timekeeper for almost 300 years until the 1930s.

Part of the incentive for inventing the pendulum clock was to create an accurate marine chronometer that could be used to find longitude by celestial navigation during sea voyages. However, the clock proved unsuccessful as a marine timekeeper because the rocking motion of the ship disturbed the motion of the pendulum. In 1660, Lodewijk Huygens made a trial on a voyage to Spain, and reported that heavy weather made the clock useless. Alexander Bruce entered the field in 1662, and Huygens called in Sir Robert Moray and the Royal Society to mediate and preserve some of his rights.^[121][117] Trials continued into the 1660s, the best news coming from a Royal Navy captain Robert Holmes operating against the Dutch possessions in 1664.^[122] Lisa Jardine doubts that Holmes reported the results of the trial accurately, as Samuel Pepys expressed his doubts at the time.^[123]

A trial for the French Academy on an expedition to Cayenne ended badly. Jean Richer suggested correction for the figure of the Earth. By the time of the Dutch East India Company expedition of 1686 to the Cape of Good Hope, Huygens was able to supply the correction retrospectively.^[124]

Horologium Oscillatorium

Sixteen years after the invention of the pendulum clock, in 1673, Huygens published his major work on horology entitled Horologium Oscillatorium: Sive de Motu Pendulorum ad Horologia Aptato Demonstrationes Geometricae (The Pendulum Clock: or Geometrical demonstrations concerning the motion of pendula as applied to clocks). It is the first modern work on mechanics where a physical problem is idealized by a set of parameters then analysed mathematically.^[6]

Huygens's motivation came from the observation, made by Mersenne and others, that pendulums are not quite

Huygens was the first to derive the formula for the period of an ideal mathematical pendulum (with mass-less rod or cord and length much longer than its swing), in modern notation:

${\displaystyle T=2\pi {\sqrt {\frac {l}{g}}}}$

with T the period, l the length of the pendulum and g the gravitational acceleration. By his study of the oscillation period of compound pendulums Huygens made pivotal contributions to the development of the concept of moment of inertia.^[128]

Huygens also observed

In 1675, while investigating the oscillating properties of the cycloid, Huygens was able to transform a cycloidal pendulum into a vibrating spring through a combination of geometry and higher mathematics.^[131] In the same year, Huygens designed a spiral balance spring and patented a pocket watch. These watches are notable for lacking a fusee for equalizing the mainspring torque. The implication is that Huygens thought his spiral spring would isochronize the balance in the same way that cycloid-shaped suspension curbs on his clocks would isochronize the pendulum.^[132]

He later used spiral springs in more conventional watches, made for him by

Huygens's design came around the same time as, though independently of, Robert Hooke's. Controversy over the priority of the balance spring persisted for centuries. In February 2006, a long-lost copy of Hooke's handwritten notes from several decades of Royal Society meetings was discovered in a cupboard in Hampshire, England, presumably tipping the evidence in Hooke's favour.^[134][135]

Optics

Dioptrics

Huygens had a long-term interest in the study of light refraction and lenses or dioptrics.^[136] From 1652 date the first drafts of a Latin treatise on the theory of dioptrics, known as the Tractatus, which contained a comprehensive and rigorous theory of the telescope. Huygens was one of the few to raise theoretical questions regarding the properties and working of the telescope, and almost the only one to direct his mathematical proficiency towards the actual instruments used in astronomy.^[137]

Huygens repeatedly announced its publication to his colleagues but ultimately postponed it in favor of a much more comprehensive treatment, now under the name of the Dioptrica.^[23] It consisted of three parts. The first part focused on the general principles of refraction, the second dealt with spherical and chromatic aberration, while the third covered all aspects of the construction of telescopes and microscopes. In contrast to Descartes' dioptrics which treated only ideal (elliptical and hyperbolical) lenses, Huygens dealt exclusively with spherical lenses, which were the only kind that could really be made and incorporated in devices such as microscopes and telescopes.^[138]

Huygens also worked out practical ways to minimize the effects of spherical and chromatic aberration, such as long focal distances for the objective of a telescope, internal stops to reduce the aperture, and a new kind of ocular known as the

Huygens is especially remembered in optics for his wave theory of light, which he first communicated in 1678 to the Académie des sciences in Paris. Originally a preliminary chapter of his Dioptrica, Huygens's theory was published in 1690 under the title Traité de la Lumière^[146] (Treatise on light), and contains the first fully mathematized, mechanistic explanation of an unobservable physical phenomenon (i.e., light propagation).^[7][147] Huygens refers to Ignace-Gaston Pardies, whose manuscript on optics helped him on his wave theory.^[148]

The challenge at the time was to explain

In 1655, Huygens discovered the first of Saturn's moons, Titan, and observed and sketched the Orion Nebula using a refracting telescope with a 43x magnification of his own design.^[11][10] Huygens succeeded in subdividing the nebula into different stars (the brighter interior now bears the name of the Huygenian region in his honour), and discovered several interstellar nebulae and some double stars.^[153] He was also the first to propose that the appearance of Saturn, which have baffled astronomers, was due to "a thin, flat ring, nowhere touching, and inclined to the ecliptic”.^[154]

More than three years later, in 1659, Huygens published his theory and findings in Systema Saturnium. It is considered the most important work on telescopic astronomy since Galileo's Sidereus Nuncius fifty years earlier.^[155] Much more than a report on Saturn, Huygens provided measurements for the relative distances of the planets from the Sun, introduced the concept of the micrometer, and showed a method to measure angular diameters of planets, which finally allowed the telescope to be used as an instrument to measure (rather than just sighting) astronomical objects.^[156] He was also the first to question the authority of Galileo in telescopic matters, a sentiment that was to be common in the years following its publication.

In the same year, Huygens was able to observe Syrtis Major, a volcanic plain on Mars. He used repeated observations of the movement of this feature over the course of a number of days to estimate the length of day on Mars, which he did quite accurately to 24 1/2 hours. This figure is only a few minutes off of the actual length of the Martian day of 24 hours, 37 minutes.^[157]

Planetarium

At the instigation of Jean-Baptiste Colbert, Huygens undertook the task of constructing a mechanical planetarium that could display all the planets and their moons then known circling around the Sun. Huygens completed his design in 1680 and had his clockmaker Johannes van Ceulen built it the following year. However, Colbert passed away in the interim and Huygens never got to deliver his planetarium to the French Academy of Sciences as the new minister, François-Michel le Tellier, decided not to renew Huygens's contract.^[158][159]

In his design, Huygens made an ingenious use of continued fractions to find the best rational approximations by which he could choose the gears with the correct number of teeth. The ratio between two gears determined the orbital periods of two planets. To move the planets around the Sun, Huygens used a clock-mechanism that could go forwards and backwards in time. Huygens claimed his planetarium was more accurate that a similar device constructed by Ole Rømer around the same time, but his planetarium design was not published until after his death in the Opuscula Posthuma (1703).^[158]

Cosmotheoros

Shortly before his death in 1695, Huygens completed his most speculative work entitled Cosmotheoros. At his direction, it was to be published only posthumously by his brother, which Constantijn Jr. did in 1698.

Huygens wrote that availability of water in liquid form was essential for life and that the properties of water must vary from planet to planet to suit the temperature range. He took his observations of dark and bright spots on the surfaces of Mars and Jupiter to be evidence of water and ice on those planets.[165] He argued that extraterrestrial life is neither confirmed nor denied by the Bible, and questioned why God would create the other planets if they were not to serve a greater purpose than that of being admired from Earth. Huygens postulated that the great distance between the planets signified that God had not intended for beings on one to know about the beings on the others, and had not foreseen how much humans would advance in scientific knowledge.^[166]

It was also in this book that Huygens published his estimates for the relative sizes of the

Huygens has been called the first theoretical physicist and a founder of modern mathematical physics.^[168][169] Although his influence was considerable during his lifetime, it began to fade shortly after his death. His skills as a geometer and mechanical ingenuity elicited the admiration of many of his contemporaries, including Newton, Leibniz, l'Hôpital, and the Bernoullis.^[42] For his work in physics, Huygens has been deemed one of the greatest scientists in the Scientific Revolution, rivaled only by Newton in both depth of insight and the number of results obtained.^[4][170] Huygens also helped develop the institutional frameworks for scientific research on the European continent, making him a leading actor in the establishment of modern science.^[171]

Mathematics and physics

In mathematics, Huygens mastered the methods of ancient Greek geometry, particularly the work of Archimedes, and was an adept user of the analytic geometry and infinitesimal techniques of Descartes and Fermat.^[85] His mathematical style can be best described as geometrical infinitesimal analysis of curves and of motion. Drawing inspiration and imagery from mechanics, it remained pure mathematics in form.^[72] Huygens brought this type of geometrical analysis to a close, as more mathematicians turned away from classical geometry to the calculus for handling infinitesimals, limit processes, and motion.^[38]

Huygens was moreover able to fully employ mathematics to answer questions of physics. Often this entailed introducing a simple model for describing a complicated situation, then analyzing it starting from simple arguments to their logical consequences, developing the necessary mathematics along the way. As he wrote at the end of a draft of De vi Centrifuga:^[33]

Whatever you will have supposed not impossible either concerning gravity or motion or any other matter, if then you prove something concerning the magnitude of a line, surface, or body, it will be true; as for instance, Archimedes on the

quadrature of the parabola

, where the tendency of heavy objects has been assumed to act through parallel lines.

Huygens favoured axiomatic presentations of his results, which require rigorous methods of geometric demonstration: although he allowed levels of uncertainty in the selection of primary axioms and hypotheses, the proofs of theorems derived from these could never be in doubt.^[33] Huygens's style of publication exerted an influence in Newton's presentation of his own major works.^[172][173]

Besides the application of mathematics to physics and physics to mathematics, Huygens relied on mathematics as methodology, specifically its ability to generate new knowledge about the world.^[174] Unlike Galileo, who used mathematics primarily as rhetoric or synthesis, Huygens consistently employed mathematics as a way to discover and develop theories covering various phenomena and insisted that the reduction of the physical to the geometrical satisfy exacting standards of fit between the real and the ideal.^[125] In demanding such mathematical tractability and precision, Huygens set an example for eighteenth-century scientists such as Johann Bernoulli, Jean le Rond d'Alembert, and Charles-Augustin de Coulomb.^[33][168]

Although never intended for publication, Huygens made use of algebraic expressions to represent physical entities in a handful of his manuscripts on collisions.^[44] This would make him one of the first to employ mathematical formulae to describe relationships in physics, as it is done today.^[5] Huygens also came close to the modern idea of limit while working on his Dioptrica, though he never used the notion outside geometrical optics.^[175]

Later influence

Huygens's standing as the greatest scientist in Europe was eclipsed by Newton's at the end of the seventeenth century, despite the fact that, as Hugh Aldersey-Williams notes, "Huygens's achievement exceeds that of Newton in some important respects".^[176] Although his journal publications anticipated the form of the modern scientific article,^[93] his persistent classicism and reluctance to publish his work did much to diminish his influence in the aftermath of the Scientific Revolution, as adherents of Leibniz’ calculus and Newton's physics took centre stage.^[38][85]

Huygens's analyses of curves that satisfy certain physical properties, such as the cycloid, led to later studies of many other such curves like the caustic, the brachistochrone, the sail curve, and the catenary.^[24][35] His application of mathematics to physics, such as in his studies of impact and birefringence, would inspire new developments in mathematical physics and rational mechanics in the following centuries (albeit in the new language of the calculus).^[7] Additionally, Huygens developed the oscillating timekeeping mechanisms, the pendulum and the balance spring, that have been used ever since in mechanical watches and clocks. These were the first reliable timekeepers fit for scientific use (e.g., to make accurate measurements of the inequality of the solar day, which was not possible before).^[6][125] His work in this area foreshadowed the union of applied mathematics with mechanical engineering in the centuries that followed.^[132]

Portraits

During his lifetime, Huygens and his father had a number of portraits commissioned. These included:

• 1639 – Constantijn Huygens in the midst of his five children by Adriaen Hanneman, painting with medallions, Mauritshuis, The Hague^[177]
• 1671 – Portrait by Caspar Netscher, Museum Boerhaave, Leiden, loan from Haags Historisch Museum^[177]
• c.1675 – Depiction of Huygens in Établissement de l'Académie des Sciences et fondation de l'observatoire, 1666 by
  Versailles^[178]
• 1679 – Medaillon portrait in relief by the French sculptor Jean-Jacques Clérion^[177]
• 1686 – Portrait in pastel by Bernard Vaillant, Museum Hofwijck, Voorburg^[177]
• 1684 to 1687 – Engravings by
  G. Edelinck after the painting by Caspar Netscher^[177]
• 1688 – Portrait by Pierre Bourguignon (painter), Royal Netherlands Academy of Arts and Sciences, Amsterdam^[177]

Commemorations

The European Space Agency spacecraft that landed on Titan, Saturn's largest moon, in 2005 was named after him.^[179]

A number of monuments to Christiaan Huygens can be found across important cities in the Netherlands, including Rotterdam, Delft, and Leiden.

• 
  Rotterdam
• 
  Delft
• 
  Leiden
• 
  Haarlem
• 
  Voorburg

Works

Source(s):^[17]

• 1650 – De Iis Quae Liquido Supernatant (About parts floating above liquids), unpublished.^[180]
• 1651 – Theoremata de Quadratura Hyperboles, Ellipsis et Circuli, republished in Oeuvres Complètes, Tome XI.^[42]
• 1651 – Epistola, qua diluuntur ea quibus 'Εξέτασις [Exetasis] Cyclometriae Gregori à Sto. Vincentio impugnata fuit, supplement.^[181]
• 1654 – De Circuli Magnitudine Inventa.^[33]
• 1654 – Illustrium Quorundam Problematum Constructiones, supplement.^[181]
• 1655 – Horologium (The clock), short pamphlet on the pendulum clock.^[6]
• 1656 – De Saturni Luna Observatio Nova (About the new observation of the moon of Saturn), describes the discovery of Titan.^[182]
• 1656 – De Motu Corporum ex Percussione, published posthumously in 1703.^[183]
• 1657 – De Ratiociniis in Ludo Aleae (Van reeckening in spelen van geluck), translated into Latin by Frans van Schooten.^[12]
• 1659 – Systema Saturnium (System of Saturn).^[181]
• 1659 – De vi Centrifuga (Concerning the centrifugal force), published posthumously in 1703.^[184]
• 1673 – Horologium Oscillatorium Sive de Motu Pendulorum ad Horologia Aptato Demonstrationes Geometricae, includes a theory of evolutes and designs of pendulum clocks, dedicated to Louis XIV of France.^[126]
• 1684 – Astroscopia Compendiaria Tubi Optici Molimine Liberata (Compound telescopes without a tube).^[42]
• 1685 – Memoriën aengaende het slijpen van glasen tot verrekijckers, dealing with the grinding of lenses.^[7]
• 1686 – Kort onderwijs aengaende het gebruijck der horologiën tot het vinden der lenghten van Oost en West (in Old Dutch), instructions on how to use clocks to establish the longitude at sea.^[185]
• 1690 – Traité de la Lumière, dealing with the nature of light propagation.^[23]
• 1690 – Discours de la Cause de la Pesanteur (Discourse about gravity), supplement.^[42]
• 1691 – Lettre Touchant le Cycle Harmonique, short tract concerning the 31-tone system.^[37]
• 1698 – Cosmotheoros, deals with the solar system, cosmology, and extraterrestrial life.^[166]
• 1703 – Opuscula Posthuma including:^[42]
  • De Motu Corporum ex Percussione (Concerning the motions of colliding bodies), contains the first correct laws for collision, dating from 1656.
  • Descriptio Automati Planetarii, provides a description and design of a planetarium.
• 1724 – Novus Cyclus Harmonicus, a treatise on music published in Leiden after Huygens's death.^[37]
• 1728 – Christiani Hugenii Zuilichemii, dum viveret Zelhemii Toparchae, Opuscula Posthuma (alternate title: Opera Reliqua), includes works in optics and physics.^[184]
• 1888–1950 – Huygens, Christiaan. Oeuvres complètes. Complete works, 22 volumes. Editors
  D.J. Korteweg (11–15), A.A. Nijland (15), J.A. Vollgraf (16–22). The Hague:^[181]
  • Tome I: Correspondance 1638–1656 (1888).
  • Tome II: Correspondance 1657–1659 (1889).
  • Tome III: Correspondance 1660–1661 (1890).
  • Tome IV: Correspondance 1662–1663 (1891).
  • Tome V: Correspondance 1664–1665 (1893).
  • Tome VI: Correspondance 1666–1669 (1895).
  • Tome VII: Correspondance 1670–1675 (1897).
  • Tome VIII: Correspondance 1676–1684 (1899).
  • Tome IX: Correspondance 1685–1690 (1901).
  • Tome X: Correspondance 1691–1695 (1905).
  • Tome XI: Travaux mathématiques 1645–1651 (1908).
  • Tome XII: Travaux mathématiques pures 1652–1656 (1910).
  • Tome XIII, Fasc. I: Dioptrique 1653, 1666 (1916).
  • Tome XIII, Fasc. II: Dioptrique 1685–1692 (1916).
  • Tome XIV: Calcul des probabilités. Travaux de mathématiques pures 1655–1666 (1920).
  • Tome XV: Observations astronomiques. Système de Saturne. Travaux astronomiques 1658–1666 (1925).
  • Tome XVI: Mécanique jusqu’à 1666. Percussion. Question de l'existence et de la perceptibilité du mouvement absolu. Force centrifuge (1929).
  • Tome XVII: L’horloge à pendule de 1651 à 1666. Travaux divers de physique, de mécanique et de technique de 1650 à 1666. Traité des couronnes et des parhélies (1662 ou 1663) (1932).
  • Tome XVIII: L'horloge à pendule ou à balancier de 1666 à 1695. Anecdota (1934).
  • Tome XIX: Mécanique théorique et physique de 1666 à 1695. Huygens à l'Académie royale des sciences (1937).
  • Tome XX: Musique et mathématique. Musique. Mathématiques de 1666 à 1695 (1940).
  • Tome XXI: Cosmologie (1944).
  • Tome XXII: Supplément à la correspondance. Varia. Biographie de Chr. Huygens. Catalogue de la vente des livres de Chr. Huygens (1950).

• History of the internal combustion engine
• List of largest optical telescopes historically
• Fokker Organ
• Seconds pendulum

References

Further reading

• Andriesse, C.D. (2005). Huygens: The Man Behind the Principle. Foreword by Sally Miedema. Cambridge University Press.
• Aldersey-Williams, Hugh. (2020). Dutch Light: Christiaan Huygens and the Making of Science in Europe. London: Picador.
• Bell, A. E. (1947). Christian Huygens and the Development of Science in the Seventeenth Century
• Boyer, C.B. (1968). A History of Mathematics, New York.
• Dijksterhuis, E. J. (1961). The Mechanization of the World Picture: Pythagoras to Newton
• Hooijmaijers, H. (2005). Telling time – Devices for time measurement in Museum Boerhaave – A Descriptive Catalogue, Leiden, Museum Boerhaave.
• Struik, D.J. (1948). A Concise History of Mathematics
• Van den Ende, H. et al. (2004). Huygens's Legacy, The golden age of the pendulum clock, Fromanteel Ltd, Castle Town, Isle of Man.
• Yoder, J G. (2005). "Book on the pendulum clock" in Ivor Grattan-Guinness, ed., Landmark Writings in Western Mathematics. Elsevier: 33–45.

External links

Wikimedia Commons has media related to Christiaan Huygens.

Wikiquote has quotations related to Christiaan Huygens.

Primary sources, translations

• Works by Christiaan Huygens at Project Gutenberg:
  • C. Huygens (translated by Silvanus P. Thompson, 1912), Treatise on Light; Errata.
• Works by or about Christiaan Huygens at Internet Archive
• Works by Christiaan Huygens at LibriVox (public domain audiobooks)
• Clerke, Agnes Mary (1911). "Huygens, Christiaan" . Encyclopædia Britannica. Vol. 14 (11th ed.). pp. 21–22.
• Correspondence of Christiaan Huygens at Early Modern Letters Online
• De Ratiociniis in Ludo Aleae or The Value of all Chances in Games of Fortune, 1657 Christiaan Huygens's book on probability theory. An English translation published in 1714. Text pdf file.
• Horologium oscillatorium (German translation, pub. 1913) or Horologium oscillatorium (English translation by Ian Bruce) on the pendulum clock
• ΚΟΣΜΟΘΕΩΡΟΣ (Cosmotheoros). (English translation of Latin, pub. 1698; subtitled The celestial worlds discover'd: or, Conjectures concerning the inhabitants, plants and productions of the worlds in the planets.)
• C. Huygens (translated by Silvanus P. Thompson), Traité de la lumière or Treatise on light, London: Macmillan, 1912, archive.org/details/treatiseonlight031310mbp; New York: Dover, 1962; Project Gutenberg, 2005, gutenberg.org/ebooks/14725; Errata
• Systema Saturnium 1659 text a digital edition of Smithsonian Libraries
• On Centrifugal Force (1703)
• Huygens's work at WorldCat Archived 23 October 2020 at the Wayback Machine
• The Correspondence of Christiaan Huygens in EMLO
• Christiaan Huygens biography and achievements
• Portraits of Christiaan Huygens
• Huygens's books, in digital facsimile from the Linda Hall Library:
  • (1659) Systema Saturnium (Latin)
  • (1684) Astroscopia compendiaria (Latin)
  • (1690) Traité de la lumiére (French)
  • (1698) ΚΟΣΜΟΘΕΩΡΟΣ, sive De terris cœlestibus (Latin)

Museums

• Huygensmuseum Hofwijck in Voorburg, Netherlands, where Huygens lived and worked.
• Huygens Clocks exhibition from the Science Museum, London
• Online exhibition on Huygens in Leiden University Library (in Dutch)

Other

• O'Connor, John J.; Robertson, Edmund F., "Christiaan Huygens", MacTutor History of Mathematics Archive, University of St Andrews
• Huygens and music theory
  Huygens–Fokker Foundation —on Huygens's 31 equal temperament
  and how it has been used
• Christiaan Huygens on the 25 Dutch Guilder banknote of the 1950s.
• Christiaan Huygens at the Mathematics Genealogy Project
• How to pronounce "Huygens"