Johann Heinrich Lambert (, ''Jean-Henri Lambert'' in
French
French (french: français(e), link=no) may refer to:
* Something of, from, or related to France
** French language, which originated in France, and its various dialects and accents
** French people, a nation and ethnic group identified with Franc ...
; 26 or 28 August 1728 – 25 September 1777) was a
polymath
A polymath ( el, πολυμαθής, , "having learned much"; la, homo universalis, "universal human") is an individual whose knowledge spans a substantial number of subjects, known to draw on complex bodies of knowledge to solve specific pro ...
from the
Republic of Mulhouse, generally referred to as either
Swiss
Swiss may refer to:
* the adjectival form of Switzerland
*Swiss people
Places
* Swiss, Missouri
*Swiss, North Carolina
* Swiss, West Virginia
*Swiss, Wisconsin
Other uses
* Swiss-system tournament, in various games and sports
* Swiss Internation ...
or
French
French (french: français(e), link=no) may refer to:
* Something of, from, or related to France
** French language, which originated in France, and its various dialects and accents
** French people, a nation and ethnic group identified with Franc ...
, who made important contributions to the subjects of
mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...
,
physics
Physics is the natural science that studies matter, its fundamental constituents, its motion and behavior through space and time, and the related entities of energy and force. "Physical science is that department of knowledge which ...
(particularly
optics
Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behaviour of visible, ultrav ...
),
philosophy
Philosophy (from , ) is the systematized study of general and fundamental questions, such as those about existence, reason, knowledge, values, mind, and language. Such questions are often posed as problems to be studied or resolved. ...
,
astronomy
Astronomy () is a natural science that studies celestial objects and phenomena. It uses mathematics, physics, and chemistry in order to explain their origin and evolution. Objects of interest include planets, moons, stars, nebulae, g ...
and
map projections
In cartography, map projection is the term used to describe a broad set of Transformation (function) , transformations employed to represent the two-dimensional curved Surface (mathematics), surface of a globe on a Plane (mathematics), plane. In ...
.
Biography
Lambert was born in 1728 into a
Huguenot
The Huguenots ( , also , ) were a religious group of French Protestants who held to the Reformed, or Calvinist, tradition of Protestantism. The term, which may be derived from the name of a Swiss political leader, the Genevan burgomaster Be ...
family in the city of
Mulhouse
Mulhouse (; Alsatian: or , ; ; meaning '' mill house'') is a city of the Haut-Rhin department, in the Grand Est region, eastern France, close to the Swiss and German borders. It is the largest city in Haut-Rhin and second largest in Alsace a ...
[ (now in ]Alsace
Alsace (, ; ; Low Alemannic German/ gsw-FR, Elsàss ; german: Elsass ; la, Alsatia) is a cultural region and a territorial collectivity in eastern France, on the west bank of the upper Rhine next to Germany and Switzerland. In 2020, it had ...
, France
France (), officially the French Republic ( ), is a country primarily located in Western Europe. It also comprises of Overseas France, overseas regions and territories in the Americas and the Atlantic Ocean, Atlantic, Pacific Ocean, Pac ...
), at that time a city-state allied to Switzerland
). Swiss law does not designate a ''capital'' as such, but the federal parliament and government are installed in Bern, while other federal institutions, such as the federal courts, are in other cities (Bellinzona, Lausanne, Luzern, Neuchâtel ...
. Some sources give 26 August as his birth date and others 28 August.[ Leaving school at 12, he continued to study in his free time while undertaking a series of jobs. These included assistant to his father (a tailor), a clerk at a nearby iron works, a private tutor, secretary to the editor of ''Basler Zeitung'' and, at the age of 20, private tutor to the sons of Count Salis in Chur. Travelling Europe with his charges (1756–1758) allowed him to meet established mathematicians in the German states, The Netherlands, France and the Italian states. On his return to Chur he published his first books (on optics and cosmology) and began to seek an academic post. After a few short posts he was rewarded (1763) by an invitation to a position at the ]Prussian Academy of Sciences
The Royal Prussian Academy of Sciences (german: Königlich-Preußische Akademie der Wissenschaften) was an academy established in Berlin, Germany on 11 July 1700, four years after the Prussian Academy of Arts, or "Arts Academy," to which "Berlin ...
in Berlin, where he gained the sponsorship of Frederick II of Prussia
Frederick II (german: Friedrich II.; 24 January 171217 August 1786) was King in Prussia from 1740 until 1772, and King of Prussia from 1772 until his death in 1786. His most significant accomplishments include his military successes in the S ...
, and became a friend of Euler
Leonhard Euler ( , ; 15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, geographer, logician and engineer who founded the studies of graph theory and topology and made pioneering and influential discoveries in ...
. In this stimulating and financially stable environment, he worked prodigiously until his death in 1777.[ W. W. Rouse Ball (1908]
Johann Heinrich Lambert (1728–1777)
via Trinity College, Dublin
, name_Latin = Collegium Sanctae et Individuae Trinitatis Reginae Elizabethae juxta Dublin
, motto = ''Perpetuis futuris temporibus duraturam'' (Latin)
, motto_lang = la
, motto_English = It will last i ...
Work
Mathematics
Lambert was the first to introduce hyperbolic function
In mathematics, hyperbolic functions are analogues of the ordinary trigonometric functions, but defined using the hyperbola rather than the circle. Just as the points form a circle with a unit radius, the points form the right half of the u ...
s into trigonometry
Trigonometry () is a branch of mathematics that studies relationships between side lengths and angles of triangles. The field emerged in the Hellenistic world during the 3rd century BC from applications of geometry to astronomical studies. ...
. Also, he made conjectures about non-Euclidean space. Lambert is credited with the first proof that π is irrational using a generalized continued fraction for the function tan x. Euler
Leonhard Euler ( , ; 15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, geographer, logician and engineer who founded the studies of graph theory and topology and made pioneering and influential discoveries in ...
believed the conjecture but could not prove that π was irrational, and it is speculated that Aryabhata also believed this, in 500 CE. Lambert also devised theorems about conic section
In mathematics, a conic section, quadratic curve or conic is a curve obtained as the intersection of the surface of a cone with a plane. The three types of conic section are the hyperbola, the parabola, and the ellipse; the circle is a ...
s that made the calculation of the orbit
In celestial mechanics, an orbit is the curved trajectory of an object such as the trajectory of a planet around a star, or of a natural satellite around a planet, or of an artificial satellite around an object or position in space such as ...
s of comet
A comet is an icy, small Solar System body that, when passing close to the Sun, warms and begins to release gases, a process that is called outgassing. This produces a visible atmosphere or coma, and sometimes also a tail. These phenomena ...
s simpler.
Lambert devised a formula for the relationship between the angles and the area of hyperbolic triangles. These are triangles drawn on a concave surface, as on a saddle
The saddle is a supportive structure for a rider of an animal, fastened to an animal's back by a girth. The most common type is equestrian. However, specialized saddles have been created for oxen, camels and other animals. It is not kno ...
, instead of the usual flat Euclidean surface. Lambert showed that the angles added up to less than π (radian
The radian, denoted by the symbol rad, is the unit of angle in the International System of Units (SI) and is the standard unit of angular measure used in many areas of mathematics. The unit was formerly an SI supplementary unit (before that ...
s), or 180°. The amount of shortfall, called the defect, increases with the area. The larger the triangle's area, the smaller the sum of the angles and hence the larger the defect C△ = π — (α + β + γ). That is, the area of a hyperbolic triangle (multiplied by a constant C) is equal to π (in radians), or 180°, minus the sum of the angles α, β, and γ. Here C denotes, in the present sense, the negative of the curvature
In mathematics, curvature is any of several strongly related concepts in geometry. Intuitively, the curvature is the amount by which a curve deviates from being a straight line, or a surface deviates from being a plane.
For curves, the can ...
of the surface (taking the negative is necessary as the curvature of a saddle surface is defined to be negative in the first place). As the triangle gets larger or smaller, the angles change in a way that forbids the existence of similar hyperbolic triangles, as only triangles that have the same angles will have the same area. Hence, instead of the area of the triangle's being expressed in terms of the lengths of its sides, as in Euclidean geometry, the area of Lambert's hyperbolic triangle can be expressed in terms of its angles.
Map projection
Lambert was the first mathematician to address the general properties of map projection
In cartography, map projection is the term used to describe a broad set of transformations employed to represent the two-dimensional curved surface of a globe on a plane. In a map projection, coordinates, often expressed as latitude and l ...
s (of a spherical Earth). In particular he was the first to discuss the properties of conformality and equal area
preservation and to point out that they were mutually exclusive.
(Snyder 1993[.] p77). In 1772, Lambert published[Lambert, Johann Heinrich. 1772. ''Ammerkungen und Zusatze zurder Land und Himmelscharten Entwerfung''. In Beitrage zum Gebrauche der Mathematik in deren Anwendung, part 3, section 6).][
]
seven new map projections under the title ''Anmerkungen und Zusätze zur Entwerfung der Land- und Himmelscharten'', (translated as ''Notes and Comments on the Composition of Terrestrial and Celestial Maps'' by Waldo Tobler (1972)[Tobler, Waldo R, ''Notes and Comments on the Composition of Terrestrial and Celestial Maps'', 1972. (University of Michigan Press), reprinted (2010) by Esri]
).
Lambert did not give names to any of his projections but they are now known as:
# Lambert conformal conic projection, Lambert conformal conic
# Transverse Mercator
# Lambert azimuthal equal area
# Lagrange projection
# Lambert cylindrical equal area
# Transverse cylindrical equal area
# Lambert conical equal area
The first three of these are of great importance.[ Further details may be found at ]map projections
In cartography, map projection is the term used to describe a broad set of Transformation (function) , transformations employed to represent the two-dimensional curved Surface (mathematics), surface of a globe on a Plane (mathematics), plane. In ...
and in several texts.[This paper can be downloaded fro]
USGS pages.
Physics
Lambert invented the first practical hygrometer
A hair tension dial hygrometer with a nonlinear scale.
A hygrometer is an instrument used to measure the amount of water vapor in air, in soil, or in confined spaces. Humidity measurement instruments usually rely on measurements of some other q ...
. In 1760, he published a book on photometry, the '' Photometria''. From the assumption that light travels in straight lines, he showed that illumination was proportional to the strength of the source, inversely proportional to the square of the distance of the illuminated surface and the sine of the angle of inclination of the light's direction to that of the surface. These results were supported by experiments involving the visual comparison of illuminations and used for the calculation of illumination. In ''Photometria'' Lambert also cited a law of light absorption, formulated earlier by Pierre Bouguer
Pierre Bouguer () (16 February 1698, Croisic – 15 August 1758, Paris) was a French mathematician, geophysicist, geodesist, and astronomer. He is also known as "the father of naval architecture".
Career
Bouguer's father, Jean Bouguer, one ...
he is mistakenly credited for (the Beer–Lambert law) and introduced the term ''albedo
Albedo (; ) is the measure of the diffuse reflection of solar radiation out of the total solar radiation and measured on a scale from 0, corresponding to a black body that absorbs all incident radiation, to 1, corresponding to a body that refle ...
''. Lambertian reflectance is named after him. He wrote a classic work on perspective and contributed to geometrical optics.
The non- SI unit of luminance, Lambert, is named in recognition of his work in establishing the study of photometry Photometry can refer to:
* Photometry (optics), the science of measurement of visible light in terms of its perceived brightness to human vision
* Photometry (astronomy), the measurement of the flux or intensity of an astronomical object's electro ...
. Lambert was also a pioneer in the development of three-dimensional colour models. Late in life, he published a description of a triangular colour pyramid (''Farbenpyramide''), which shows a total of 107 colours on six different levels, variously combining red, yellow and blue pigments, and with an increasing amount of white to provide the vertical component. His investigations were built on the earlier theoretical proposals of Tobias Mayer, greatly extending these early ideas. Lambert was assisted in this project by the court painter Benjamin Calau.
Logic and philosophy
In his main philosophical work, ''Neues Organon'' (''New Organon'', 1764, named after Aristotle
Aristotle (; grc-gre, Ἀριστοτέλης ''Aristotélēs'', ; 384–322 BC) was a Greek philosopher and polymath during the Classical period in Ancient Greece. Taught by Plato, he was the founder of the Peripatetic school of ...
's '' Organon''), Lambert studied the rules for distinguishing subjective from objective appearances, connecting with his work in optics
Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behaviour of visible, ultrav ...
. The ''Neues Organon'' contains one of the first appearances of the term ''phenomenology'', and it includes a presentation of the various kinds of syllogism. According to John Stuart Mill
John Stuart Mill (20 May 1806 – 7 May 1873) was an English philosopher, political economist, Member of Parliament (MP) and civil servant. One of the most influential thinkers in the history of classical liberalism, he contributed widely to ...
,
A modern edition of the ''Neues Organon'' was published in 1990 by the Akademie-Verlag of Berlin.
In 1765 Lambert began corresponding with Immanuel Kant
Immanuel Kant (, , ; 22 April 1724 – 12 February 1804) was a German philosopher and one of the central Enlightenment thinkers. Born in Königsberg, Kant's comprehensive and systematic works in epistemology, metaphysics, ethics, and ...
. Kant intended to dedicate the '' Critique of Pure Reason'' to Lambert, but the work was delayed, appearing after Lambert's death.[O'Leary M., ''Revolutions of Geometry'', London:Wiley, 2010, p.385]
Astronomy
Lambert also developed a theory of the generation of the universe
The universe is all of space and time and their contents, including planets, stars, galaxies, and all other forms of matter and energy. The Big Bang theory is the prevailing cosmological description of the development of the univers ...
that was similar to the nebular hypothesis that Thomas Wright and Immanuel Kant
Immanuel Kant (, , ; 22 April 1724 – 12 February 1804) was a German philosopher and one of the central Enlightenment thinkers. Born in Königsberg, Kant's comprehensive and systematic works in epistemology, metaphysics, ethics, and ...
had (independently) developed. Wright published his account in ''An Original Theory or New Hypothesis of the Universe'' (1750), Kant in ''Allgemeine Naturgeschichte und Theorie des Himmels'', published anonymously in 1755. Shortly afterward, Lambert published his own version of the nebular hypothesis of the origin of the Solar System
The Solar System Capitalization of the name varies. The International Astronomical Union, the authoritative body regarding astronomical nomenclature, specifies capitalizing the names of all individual astronomical objects but uses mixed "Solar ...
in ''Cosmologische Briefe über die Einrichtung des Weltbaues'' (1761). Lambert hypothesized that the stars near the Sun were part of a group which travelled together through the Milky Way
The Milky Way is the galaxy that includes our Solar System, with the name describing the galaxy's appearance from Earth: a hazy band of light seen in the night sky formed from stars that cannot be individually distinguished by the naked eye. ...
, and that there were many such groupings (star system
A star system or stellar system is a small number of stars that orbit each other, bound by gravitational attraction. A large group of stars bound by gravitation is generally called a '' star cluster'' or ''galaxy'', although, broadly speaking ...
s) throughout the galaxy
A galaxy is a system of stars, stellar remnants, interstellar gas, dust, dark matter, bound together by gravity. The word is derived from the Greek ' (), literally 'milky', a reference to the Milky Way galaxy that contains the Solar System ...
. The former was later confirmed by Sir William Herschel. In astrodynamics
Orbital mechanics or astrodynamics is the application of ballistics and celestial mechanics to the practical problems concerning the motion of rockets and other spacecraft. The motion of these objects is usually calculated from Newton's laws of ...
he also solved the problem of determination of time of flight along a section of orbit, known now as Lambert's problem.
His work in this area is commemorated by the Asteroid
An asteroid is a minor planet of the inner Solar System. Sizes and shapes of asteroids vary significantly, ranging from 1-meter rocks to a dwarf planet almost 1000 km in diameter; they are rocky, metallic or icy bodies with no atmosphere. ...
187 Lamberta named in his honour.
Meteorology
Lambert propounded the ideology of observing periodic phenomena first, try to derive their rules and then gradually expand the theory. He expressed his purpose in meteorology as follows:
To obtain more and better data of meteorology, Lambert proposed to establish a network of weather stations around the world, in which the various weather configurations (rain, clouds, dry ...) would be recorded – the methods that are still used nowadays. He also devoted himself to the improvement of the measuring instruments and accurate concepts for the advancement of meteorology. This results in his published works in 1769 and 1771 on hygrometry and hygrometers.
Published works
Lambert, Johann Heinrich. "Pyrometrie; oder, Vom maasse des feuers und der wȧrme. Mit acht kupfertafeln." Berlin, Bey Haude und Spener, 1779.
File:Lambert-1.jpg, 1779 copy of "Pyrometrie oder vom Maasse des Feuers und der Wärme"
File:Lambert-2-1.jpg, Title page to "Pyrometrie oder vom Maasse des Feuers und der Wärme"
File:Lambert-5.jpg, First page of "Pyrometrie oder vom Maasse des Feuers und der Wärme"
See also
* List of things named after Johann Lambert
* Asteroid 187 Lamberta
* Lambert (Martian crater)
Notes
References
*
*
*
External links
Johann Heinrich Lambert (1728-1777): Collected Works - Sämtliche Werke Online
*
Britannica
Digitized works
at Université de Strasbourg
The University of Strasbourg (french: Université de Strasbourg, Unistra) is a public research university located in Strasbourg, Alsace, France, with over 52,000 students and 3,300 researchers.
The French university traces its history to the e ...
* "Mémoire sur quelques propriétés remarquables..." (1761), demonstration of irrationality of π, online and analyzed
BibNum
' (PDF).
{{DEFAULTSORT:Lambert, Johann Heinrich
18th-century Swiss philosophers
1728 births
1777 deaths
18th-century Swiss astronomers
Swiss male writers
Swiss non-fiction writers
Members of the Prussian Academy of Sciences
Alsatian-German people
Scientists from Mulhouse
Swiss people of Walloon descent
Pi-related people
18th-century German astronomers
18th-century German philosophers
German male writers
18th-century German mathematicians
18th-century Swiss mathematicians
18th-century Swiss writers
Male non-fiction writers