Joseph Petzval
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Joseph Petzval (6 January 1807 – 17 September 1891) was a
mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...
, inventor, and
physicist A physicist is a scientist who specializes in the field of physics, which encompasses the interactions of matter and energy at all length and time scales in the physical universe. Physicists generally are interested in the root or ultimate cau ...
best known for 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 ...
. He was born in the town of Szepesbéla in the
Kingdom of Hungary The Kingdom of Hungary was a monarchy in Central Europe that existed for nearly a millennium, from the Middle Ages into the 20th century. The Principality of Hungary emerged as a Christian kingdom upon the coronation of the first king Stephen ...
(in German: Zipser Bela, now Spišská Belá in
Slovakia Slovakia (; sk, Slovensko ), officially the Slovak Republic ( sk, Slovenská republika, links=no ), is a landlocked country in Central Europe. It is bordered by Poland to the north, Ukraine to the east, Hungary to the south, Austria to the s ...
). Petzval studied and later lectured at the Institutum Geometricum (currently
Budapest University of Technology and Economics The Budapest University of Technology and Economics ( hu, Budapesti Műszaki és Gazdaságtudományi Egyetem or in short ), official abbreviation BME, is the most significant university of technology in Hungary and is considered the world's olde ...
) in Buda (today part of
Budapest Budapest (, ; ) is the capital and most populous city of Hungary. It is the ninth-largest city in the European Union by population within city limits and the second-largest city on the Danube river; the city has an estimated population ...
). He headed the Institute of Practical Geometry and Hydrology/Architecture between 1841 and 1848. Later in life, he accepted an appointment to a chair of mathematics at the
University of Vienna The University of Vienna (german: Universität Wien) is a public research university located in Vienna, Austria. It was founded by Duke Rudolph IV in 1365 and is the oldest university in the German-speaking world. With its long and rich hist ...
. Petzval became a member of the Hungarian Academy of Sciences in 1873. Petzval is considered to be one of the main founders of
geometrical optics Geometrical optics, or ray optics, is a model of optics that describes light propagation in terms of '' rays''. The ray in geometrical optics is an abstraction useful for approximating the paths along which light propagates under certain circumstan ...
, modern
photography Photography is the art, application, and practice of creating durable images by recording light, either electronically by means of an image sensor, or chemically by means of a light-sensitive material such as photographic film. It is employe ...
and
cinematography Cinematography (from ancient Greek κίνημα, ''kìnema'' "movement" and γράφειν, ''gràphein'' "to write") is the art of motion picture (and more recently, electronic video camera) photography. Cinematographers use a lens to foc ...
. Among his inventions are the Petzval portrait lens and
opera glasses Opera glasses, also known as theater binoculars or Galilean binoculars, are compact, low-power optical magnification devices, usually used at performance events, whose name is derived from traditional use of binoculars at opera performances. Mag ...
, both still in common use today. He is also credited with the discovery of the
Laplace transform In mathematics, the Laplace transform, named after its discoverer Pierre-Simon Laplace (), is an integral transform that converts a function of a real variable (usually t, in the '' time domain'') to a function of a complex variable s (in the ...
and is also known for his extensive work on
aberration in optical systems In optics, aberration is a property of optical systems, such as lenses, that causes light to be spread out over some region of space rather than focused to a point. Aberrations cause the image formed by a lens to be blurred or distorted, with t ...
.


Early life

In 1801, Joseph Petzval's father married the Zipser-German Susanne Kreutzmann, who was born in Szepesbéla,
Kingdom of Hungary The Kingdom of Hungary was a monarchy in Central Europe that existed for nearly a millennium, from the Middle Ages into the 20th century. The Principality of Hungary emerged as a Christian kingdom upon the coronation of the first king Stephen ...
, a daughter of the previous teacher at the same school in Szepesbéla. The couple brought up six children: Gustáv Adolf (1800–1803), who died prematurely; Nestor Aemilianus (1804–1806); Joseph Maximilián (1807 - 1891); Petrol Baltazár (1809–1889); and three daughters. In 1810, the family moved to Késmárk (in German: Käsmark, today Kežmarok, Slovakia) and in 1819 to Lőcse (in German: Leutschau, today Levoča, Slovakia). The entire family shared an aptitude for technology. Joseph's father worked as a teacher at the evangelical school in Szepesbéla, as well as an
organist An organist is a musician who plays any type of organ. An organist may play solo organ works, play with an ensemble or orchestra, or accompany one or more singers or instrumental soloists. In addition, an organist may accompany congregational h ...
in Szepesbéla and later in Késmárk. He was also a conductor and a
geodesist Geodesy ( ) is the Earth science of accurately measuring and understanding Earth's figure (geometric shape and size), orientation in space, and gravity. The field also incorporates studies of how these properties change over time and equival ...
in Lőcse. He had a reputation as an outstanding musician and composer, who was also gifted mechanically. In 1824, he was awarded two patents: one for improvements to the
pendulum clock A pendulum clock is a clock that uses a pendulum, a swinging weight, as its timekeeping element. The advantage of a pendulum for timekeeping is that it is a harmonic oscillator: It swings back and forth in a precise time interval dependent on i ...
and the other for a "polygraph" (
typewriter A typewriter is a mechanical or electromechanical machine for typing characters. Typically, a typewriter has an array of keys, and each one causes a different single character to be produced on paper by striking an inked ribbon selectivel ...
). Petzval's brother, Petrol Baltazár Petzval, was a well-respected mathematician, engineer and
astronomer An astronomer is a scientist in the field of astronomy who focuses their studies on a specific question or field outside the scope of Earth. They observe astronomical objects such as stars, planets, moons, comets and galaxies – in either ...
.


Education

Joseph Petzval attended elementary school in Késmárk, and began his secondary school studies in Késmárk and Podolin (in German: Pudlein, now Podolínec, Slovakia). On 1 October 1819 he returned to his family in Lőcse, and entered high school. Both in elementary school and high school he ranked among the best in his class in the subjects of
Latin Latin (, or , ) is a classical language belonging to the Italic branch of the Indo-European languages. Latin was originally a dialect spoken in the lower Tiber area (then known as Latium) around present-day Rome, but through the power of the ...
(the official language of the Kingdom of Hungary) and religion; however, he struggled with his Hungarian. Before arriving at Lőcse, he was also very weak in mathematics. In Lőcse, however, he clearly improved in this discipline. One anecdote told about Petzval is as follows: When his family had already decided to make a shoemaker out of Petzval, he read the book ''Analytic Paper on the Elements of Mathematics'' by the German mathematician Hauser over the summer holidays, just after completing his fourth class in elementary school. He was preparing to undergo a repeat class in mathematics. After Petzval finished the book, the child who had been a weak math pupil swiftly became a math genius. After finishing high school, Petzval decided to move to the Institutum Geometricum, the engineering faculty of the Pester University. Before that, he had to complete a two-year
lyceum The lyceum is a category of educational institution defined within the education system of many countries, mainly in Europe. The definition varies among countries; usually it is a type of secondary school. Generally in that type of school the t ...
, which he attended from 1823 to 1825 in Kassa (in German: Kaschau, today Košice,
Slovakia Slovakia (; sk, Slovensko ), officially the Slovak Republic ( sk, Slovenská republika, links=no ), is a landlocked country in Central Europe. It is bordered by Poland to the north, Ukraine to the east, Hungary to the south, Austria to the s ...
). When he arrived there in 1823, Petzval was already well-versed in the subjects of Latin, mathematical analysis, classical literature and stylistics. In addition to his Slovak he was able to speak perfectly in Czech, German and Hungarian. With his father's assistance, he also learned French and English.


Further studies and career

After completing the Lyceum, Petzval worked for a year as an educator for Count Almássy in the
Heves county Heves county ( hu, Heves megye, ) lies in northern Hungary, between the right bank of the river Tisza and the Mátra and Bükk mountains. It shares borders with the Hungarian counties Pest, Nógrád, Borsod-Abaúj-Zemplén and Jász-Nagykun ...
. In addition to bringing in some urgently needed money, this experience also provided him with important social contacts. From 1826 to 1828, Petzval studied at the Institutum Geometricum in Buda, and earned an engineering diploma in 1828. In the same year, he joined the graduate degree program of the university, and became the self-appointed adjunct chair for the Physics Department (in 1831). From 1828 to 1835, Petzval simultaneously worked as an urban engineer for the city of Buda—particularly as a specialist in flood abatement and sewers—and studied mathematics, mechanics and practical geometry. He authored an unrealized plan to build a navigation channel around Buda. In 1830, his dam computations saved the city from an inundation caused by the flooding of the
Danube The Danube ( ; ) is a river that was once a long-standing frontier of the Roman Empire and today connects 10 European countries, running through their territories or being a border. Originating in Germany, the Danube flows southeast for , p ...
. After he received his Ph.D. in 1832, he taught as an associate professor at the university. During this period, he also received a degree in mathematics. In 1835, he was appointed a university professor in higher mathematics. After being invited to the University of Vienna in 1836, Petzval accepted a position of the chair of mathematics there in 1837, and worked until 1877 as a professor of mathematics. Apart from mathematics, he was also concerned with mechanics, ballistics, optics, and acoustics. His lectures on the theory of algebraic equations, which integrated linear and differential equations with constant and variable coefficients, ballistics, acoustic theory, and other areas were high quality and became well attended. Petzval moved into a rented abandoned monastery at
Kahlenberg The Kahlenberg () is a mountain () located in the 19th District of Vienna, Austria (Döbling). General The Kahlenberg lies in the Vienna Woods and is one of the most popular destinations for day-trips from Vienna, offering a view over the entire ...
mountain. He founded his own glass-sharpening workshop there. His lenses became world-famous because Petzval was also a skillful lens sharpener and precision mechanic. In 1840, he designed his famous portrait lens. 1845 brought disputes with the entrepreneur Peter Wilhelm Friedrich von Voigtländer (1812–1878) over who had the right to produce Petzval's lenses. In 1859, Petzval's home was broken into, and his manuscripts — a result of many years of research — were destroyed. Petzval never managed to reconstruct the lost documents. His most refined technical book on optics, lost with his manuscripts, would never appear in print. From then on, he primarily concerned himself with acoustics and began to withdraw from society. His enterprise with Carl Dietzler failed in 1862 (see further below); Dietzler died in 1872. In 1869, at the age of 62, Petzval married his housekeeper, but she died four years later. In 1877, he stopped lecturing, withdrew to a monastery on Kahlenberg, and became a
hermit A hermit, also known as an eremite (adjectival form: hermitic or eremitic) or solitary, is a person who lives in seclusion. Eremitism plays a role in a variety of religions. Description In Christianity, the term was originally applied to a Ch ...
. Petzval died in Vienna in 1891, nearly forgotten, embittered, and destitute. His grave is in the Viennese central cemetery. His bitterness at the end of his life can probably be traced, on the one hand, to his continuing controversy with Voigtländer, the loss of his manuscripts, and his business failure; and on the other hand, to the fact that he was never really acknowledged for his lifelong work in the field of optics. Just before his death, Petzval was reported to have said: :"''I defeated the light, I have it firmly in hand, because there is much darkness in the world too.''"


Private life and hobbies

Petzval was a good sportsman and rider. As a young child, he often traveled with his family to the
High Tatras The High Tatras or High Tatra Mountains ( Slovak: Vysoké Tatry; pl, Tatry Wysokie; rue, Высокі Татри,'' Vysoki Tatry''; hu, Magas-Tátra; german: Hohe Tatra; french: Hautes Tatras), are a mountain range along the border of norther ...
, and was also a dedicated athlete. In Vienna, he was for a long time the best fencer and ring fighter in the city. He also inherited an excellent talent for music from his father. Allegedly, while he was a lecturer in Vienna, he always rode to his lectures on a black Arabian horse. Petzval never wanted to communicate anything about his private life, and was therefore relatively inscrutable to others during his lifetime. As Dr. Ermenyi described in his book, ''Dr. Josef Petzval's Life'' :"''. . . he went so far as to always insert a bare point, for example, use the appearing annual yearbook of the Imperial Academy of Sciences, in whatever apart from the names of the members the date and the place appear aforementioned to the birth for itself into this column.''" At the end of his life he lived in increasingly greater isolation in his "castle" on Kahlenberg, with only his horse for company, although several academies and scholarly societies appointed him a member (member of the Academy of Sciences in Vienna (1846/1849), external member of the Hungarian Academy of Sciences (1873), honorary member of the Union of the Czech mathematicians and physicists (1881), carriers of the French Charles Chevalier Platinmedaille, and others).


Disputes

Petzval placed very high requirements on himself and others. That was probably connected with his critical, contentious and sarcastic nature, which brought him many conflicts, particularly in the field of mathematics. Petzval had a controversy with
Christian Doppler Christian Andreas Doppler ( (); 29 November 1803 – 17 March 1853) was an Austrian mathematician and physicist. He is celebrated for his principle – known as the Doppler effect – that the observed frequency of a wave depends on the relative ...
over problems of acoustics, and Doppler responded in 1852 with a book entitled "Remarks Over the Objections Stated by Professor Petzval Against the Correctness of My Theory". In particular he was involved in lengthy disputes with the entrepreneur Voigtländer. These began in 1845, when Petzval raised the issue of fraud for the first time. Because Petzval only held a patent in Austria, Voigtländer shifted his production to
Braunschweig Braunschweig () or Brunswick ( , from Low German ''Brunswiek'' , Braunschweig dialect: ''Bronswiek'') is a city in Lower Saxony, Germany, north of the Harz Mountains at the farthest navigable point of the river Oker, which connects it to the ...
in
Germany Germany,, officially the Federal Republic of Germany, is a country in Central Europe. It is the second most populous country in Europe after Russia, and the most populous member state of the European Union. Germany is situated betwe ...
, where he produced about 60,000 Petzval lenses in the following 20 years. Petzval for his part co-operated since 1854 with the Austrian optics producer Dietzler. The latter's lenses were marketed in Austria as the "photographic Dialyt", while Voigtländer marketed the lenses in Germany and Austria as the "Voightländer Orthoskop". After further interference by Voigtländer, Dietzler went bankrupt in 1862. When Petzval threatened legal action, Voigtländer closed his Austrian plant in 1866. Petzval could have then transferred the marketing, but he had renounced working with optics after his home was robbed in 1859 and worked instead on acoustics. In 1862, he also stopped lecturing on optics.


Discoveries and inventions


Optics

Petzval's greatest achievements lie in his work with
geometric optics Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is ca ...
. In 1839,
Louis Daguerre Louis-Jacques-Mandé Daguerre ( , ; 18 November 1787 – 10 July 1851) was a French artist and photographer, recognized for his invention of the eponymous daguerreotype process of photography. He became known as one of the fathers of photog ...
presented the Daguerreotype, the first commercially successful photographic process.
Fox Talbot William Henry Fox Talbot FRS FRSE FRAS (; 11 February 180017 September 1877) was an English scientist, inventor, and photography pioneer who invented the salted paper and calotype processes, precursors to photographic processes of the later ...
's calotype was discovered earlier but did not enjoy commercial success. Petzval learned of the invention from his friend, Viennese professor Andreas von Ettingshausen. The daguerreotype was problematic in that it required exposure times as long as 30 minutes to create a portrait. With Ettingshausen's urging, Petzval set up a workshop and laboratory at
Kahlenberg The Kahlenberg () is a mountain () located in the 19th District of Vienna, Austria (Döbling). General The Kahlenberg lies in the Vienna Woods and is one of the most popular destinations for day-trips from Vienna, offering a view over the entire ...
in
Vienna en, Viennese , iso_code = AT-9 , registration_plate = W , postal_code_type = Postal code , postal_code = , timezone = CET , utc_offset = +1 , timezone_DST ...
and, after six months of complex computations, produced designs for improved objective lenses for both portraiture and landscape photography. Because the
artillery Artillery is a class of heavy military ranged weapons that launch munitions far beyond the range and power of infantry firearms. Early artillery development focused on the ability to breach defensive walls and fortifications during siege ...
was one of the few occupations that used advanced mathematical computations at the time, Archduke Ludwig lent eight artillery cannoneers and three corporals to the computational efforts. The calculations these men carried out in tandem with each other have been regarded as an early (albeit human) example of a
parallel computer Parallel computing is a type of computation in which many calculations or processes are carried out simultaneously. Large problems can often be divided into smaller ones, which can then be solved at the same time. There are several different fo ...
. Petzval's portrait objective lens ('' Petzval Porträtobjektiv'') was an almost distortionless ''Anachromatischer vierlinser'' (double achromatic objective lens, with four lenses in three groups). The luminous intensity of this flat "portrait lens" was substantially higher than the daguerre standard of 1839, the Wollaston Chevalier lens (). The screen with a focal length of 160 mm made crucially shorter exposure times possible — using exposures of only about 15 to 30 seconds compared to the 10 minutes previously. Thus, snapshots became possible for the first time. The portrait objective lens consisted of a cemented double lens in front () and a double lens with a gap in the back. The rear double lens was necessary for the correction of spherical and coma errors. The Chevalier lens used two cemented double lenses, but was immediately replaced by the Petzval lens, so that the Petzval ''Porträtlinse'' was the first cemented lens in widespread use. The first portrait objective lenses were rather small and had a diameter of 2.6 cm. The 1856 Petzval lenses produced by Dietzler had a diameter of 15 cm and a weight of 15 kg, with which one could make portraits measuring 33 by 42 cm

In 1840, Petzval allowed the Viennese entrepreneur Peter Wilhelm Friedrich von
Voigtländer Voigtländer () was a significant long-established company within the optics and photographic industry, headquartered in Braunschweig, Germany, and today continues as a trademark for a range of photographic products. History Voigtländer was f ...
to produce the lens for a one-time payment of 2,000 guldens, without a patent or a contract, which led later to a lasting controversy between Petzval and Voigtländer. Voigtländer, who had confirmed the process through his own calculations, produced a prototype in May 1840 and began production of the lens for the daguerrotype cameras in 1841, making a fortune in the process. The thermionic cameras were made from brass, using round daguerreotype plates which exposed a diameter of 8 cm. In 1841, 600 of these cameras were manufactured and sold at a price of 120 guldens. Voigtländer received a medal at the world exhibition in Paris for this achievement. These first metal-body cameras were prototypes of today's modern cameras. It took another 50 years until an improved camera became available. Petzval's portrait objective lens was used into the 1920s (often under other names) in cameras and is used today in projectors. The lens played an important role in the development of photography and cinematography. Even with all its apparent improvements, Petzval was dissatisfied with the lens and, after some improvements, left it for others to produce and patent. The camera with the new landscape objective, produced by Dietzler, possessed a light foldable chamber with double bellows. Petzval never made a commercial profit from the lens. Among Petzval's other works are the invention of opera glasses, lens system calculations that led to the perfection of a telescope and microscope (1843), computations for efficient binoculars, and construction of new floodlights (1847). His plan for the construction of lighting systems for ships on the
Danube The Danube ( ; ) is a river that was once a long-standing frontier of the Roman Empire and today connects 10 European countries, running through their territories or being a border. Originating in Germany, the Danube flows southeast for , p ...
could not be carried out, however. His special mirror lamp (Petzval lamp), which made possible a maximum utilization of light energy, was used particularly for the bright projectors developed by Petzval. Petzval can also be regarded as the inventor of the modern unastigmatic lens system, based on records from his estate. Around 1860, Petzval conducted photogrammetric measurements using equipment he had designed. He also proved scientifically that glowing solid compounds emit more light than burning gases. Carl Freiherr Auer von Welsbach later applied this principle to the gas lamp he designed. Petzval's achievements are used today in cinematography,
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 meteorology. The ''Astro-Petzval-Objektiv'' lens is used in astronomy. This objective made a distortion-free illustration of a large part of the sky, as well as permitting photographing of galaxies and star fields. German optics companies (Töpfer, Voigtländerkorrigie, Zeiss) produced the Petzval objective lens until the 1940s. Petzval's largest contributions to optics are his theoretical bases for the construction and correction of optical lens systems. He carried out fundamental work for the theory of aberration in optical systems. A few central terms of this field were later named after Petzval: * The ''Petzval surface'' is the generally curved image plane of an unadjusted optical system. * In the case of adherence to the Petzval condition the Petzval surface is even. To the regret of physicists, Petzval never released a prepared multi-volume optical work.


Mathematics

In mathematics, Petzval stressed practical applicability. He said, "Mankind does not exist for science's sake, but science should be used to improve the conditions of mankind." He worked on applications of the Laplace transformation. His work was very thorough, but not completely satisfying, since he could not use an edge integration in order to invert the transformation. Petzval wrote a paper in two volumes as well as a long work on this subject. A controversy with the student Simon Spritzer, who accused Petzval of plagiarism of
Pierre-Simon Laplace Pierre-Simon, marquis de Laplace (; ; 23 March 1749 – 5 March 1827) was a French scholar and polymath whose work was important to the development of engineering, mathematics, statistics, physics, astronomy, and philosophy. He summarized ...
, led the Spritzer-influenced mathematicians
George Boole George Boole (; 2 November 1815 – 8 December 1864) was a largely self-taught English mathematician, philosopher, and logician, most of whose short career was spent as the first professor of mathematics at Queen's College, Cork in ...
and Jules Henri Poincaré to later name the transformation after Laplace. Petzval tried to represent practically everything in his environment mathematically. Thus he tried to mathematically model fencing or the course of the horse. His obsession with mathematics finally led to the discovery of the portrait objective.


Acoustics

In the study of acoustics, Petzval was particularly concerned with string
oscillation Oscillation is the repetitive or periodic variation, typically in time, of some measure about a central value (often a point of equilibrium) or between two or more different states. Familiar examples of oscillation include a swinging pendulum ...
s, differential equations of the string oscillations, and the mathematical theory of musical instruments. He designed a piano with three key sequences. Petzval developed a theory of the oscillations of strained strings as well as his own theory of tone systems.


Memorials

The Jozef Maximilián Petzval Museum of the History of Photography and Cinematography, part of the Slovak Technical Museum of Košice, is located in Spišská Belá, in the house where Petzval was born. The crater Petzval on the
far side of the Moon The far side of the Moon is the lunar hemisphere that always faces away from Earth, opposite to the near side, because of synchronous rotation in the Moon's orbit. Compared to the near side, the far side's terrain is rugged, with a multitu ...
is named after him, as are roads and statues in modern Slovakia,
Austria Austria, , bar, Östareich officially the Republic of Austria, is a country in the southern part of Central Europe, lying in the Eastern Alps. It is a federation of nine states, one of which is the capital, Vienna, the most populous ...
, and Hungary. In 1980 a planetoid (3716 Petzval, 1980 TG) was named after Petzval upon the request of the astronomical institute in Tatranská Lomnica and Czech scientists; Petzval's portrait objective lens made possible the discovery of many planetoids at the end of the 19th century. The Austrian Board of Education has bestowed the "Petzval Medal" for special achievements in the area of scientific photography since 1928.


Ethnicity and name

The Magyar Tudományos Akadémia ''Acta technica, Volume 25, 1959'' notes a dispute over the ethnicity of Petzval. According to the Hungarian Academy of Sciences: The same publication also cites Petzval's expressed claim to being Hungarian and a ''"...loyal son of the fatherland"'' As mentioned earlier, he struggled with Hungarian language while at school, since it was not his mother tongue. Petzvals contemporaries widely accepted that he was Hungarian, as Petzval always proclaimed. "He lived 54 years of his life in Vienna, but could not become, and did not become a Viennese - devotedly to his native country, he remained a Hungarian." - told Lueger, mayor of Vienna, at Petzval's burial. Petzval József, Mai Manó Ház Photography Museum, Budapest
/ref>


Works

* ''Bericht über die Ergebnisse einiger dioptrischen Untersuchungen'' ( Pest, 1843) * ''Eigenschaften einer guten Camera-Obscura'' (
Wien en, Viennese , iso_code = AT-9 , registration_plate = W , postal_code_type = Postal code , postal_code = , timezone = CET , utc_offset = +1 , timezone_DST ...
, 1847) * ''Integration der linearen Differenzialgleichungen mit Constanten und veränderlichen Coefficienten, I–II.'' (
Wien en, Viennese , iso_code = AT-9 , registration_plate = W , postal_code_type = Postal code , postal_code = , timezone = CET , utc_offset = +1 , timezone_DST ...
, 1853–1859) * ''Berichte über optische Untersuchungen'' (
Wien en, Viennese , iso_code = AT-9 , registration_plate = W , postal_code_type = Postal code , postal_code = , timezone = CET , utc_offset = +1 , timezone_DST ...
, 1857) * ''Über das neue Landschaft – als Fernobjektiv'' (
Wien en, Viennese , iso_code = AT-9 , registration_plate = W , postal_code_type = Postal code , postal_code = , timezone = CET , utc_offset = +1 , timezone_DST ...
, 1858) * ''Theorie der Störungen der Stützlinien (bei Gewölben und Hängebrücken)'' (
Leipzig Leipzig ( , ; Upper Saxon: ) is the most populous city in the German state of Saxony. Leipzig's population of 605,407 inhabitants (1.1 million in the larger urban zone) as of 2021 places the city as Germany's eighth most populous, as ...
, 1904–1905) * ''Theorie der Tonsysteme'' (
Leipzig Leipzig ( , ; Upper Saxon: ) is the most populous city in the German state of Saxony. Leipzig's population of 605,407 inhabitants (1.1 million in the larger urban zone) as of 2021 places the city as Germany's eighth most populous, as ...
, 1904–1905) * ''Aus den Vorlesungen über Ballistik. Ein Beitr. zur Geschichte der Ballistik'' (
Leipzig Leipzig ( , ; Upper Saxon: ) is the most populous city in the German state of Saxony. Leipzig's population of 605,407 inhabitants (1.1 million in the larger urban zone) as of 2021 places the city as Germany's eighth most populous, as ...
, 1908)


References


External links


Article on Petzval Lenses









Joseph Petzval at Monoskop.org
{{DEFAULTSORT:Petzval, Joseph 1807 births 1891 deaths People from Spišská Belá People from the Kingdom of Hungary Carpathian German people Hungarian-German people Hungarian engineers Ballistics experts Hungarian inventors 19th-century Hungarian physicists Lens designers 19th-century Hungarian mathematicians