Jurij Vega
Encyclopedia
Baron
Baron
Baron is a title of nobility. The word baron comes from Old French baron, itself from Old High German and Latin baro meaning " man, warrior"; it merged with cognate Old English beorn meaning "nobleman"...

 Jurij Bartolomej Vega (also correct Veha; official ; ) (March 23, 1754 – September 26, 1802) was a Slovene mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....

, physicist
Physicist
A physicist is a scientist who studies or practices physics. Physicists study a wide range of physical phenomena in many branches of physics spanning all length scales: from sub-atomic particles of which all ordinary matter is made to the behavior of the material Universe as a whole...

 and artillery
Artillery
Originally applied to any group of infantry primarily armed with projectile weapons, artillery has over time become limited in meaning to refer only to those engines of war that operate by projection of munitions far beyond the range of effect of personal weapons...

 officer.

Early life

Born to a farmers family in the small village of Zagorica
Zagorica pri Dolskem
Zagorica pri Dolskem is a dispersed settlement in the hills northeast of Dolsko in the Dol pri Ljubljani Municipality in the Upper Carniola region of Slovenia.Zagorica was the birthplace of the Slovene mathematician Jurij Vega.-External links:*...

 east of Ljubljana
Ljubljana
Ljubljana is the capital of Slovenia and its largest city. It is the centre of the City Municipality of Ljubljana. It is located in the centre of the country in the Ljubljana Basin, and is a mid-sized city of some 270,000 inhabitants...

 in Slovenia
Slovenia
Slovenia , officially the Republic of Slovenia , is a country in Central and Southeastern Europe touching the Alps and bordering the Mediterranean. Slovenia borders Italy to the west, Croatia to the south and east, Hungary to the northeast, and Austria to the north, and also has a small portion of...

, Jurij was 6 years old when his father Jernej Veha died. Jurij (or George in English
English language
English is a West Germanic language that arose in the Anglo-Saxon kingdoms of England and spread into what was to become south-east Scotland under the influence of the Anglian medieval kingdom of Northumbria...

) was educated first in Moravče and later in 1767 attended high school for six years in Ljubljana, studying Latin, Greek
Greek language
Greek is an independent branch of the Indo-European family of languages. Native to the southern Balkans, it has the longest documented history of any Indo-European language, spanning 34 centuries of written records. Its writing system has been the Greek alphabet for the majority of its history;...

, religion
Religion
Religion is a collection of cultural systems, belief systems, and worldviews that establishes symbols that relate humanity to spirituality and, sometimes, to moral values. Many religions have narratives, symbols, traditions and sacred histories that are intended to give meaning to life or to...

, German, history
History
History is the discovery, collection, organization, and presentation of information about past events. History can also mean the period of time after writing was invented. Scholars who write about history are called historians...

, geography
Geography
Geography is the science that studies the lands, features, inhabitants, and phenomena of Earth. A literal translation would be "to describe or write about the Earth". The first person to use the word "geography" was Eratosthenes...

, science
Science
Science is a systematic enterprise that builds and organizes knowledge in the form of testable explanations and predictions about the universe...

, and mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

. At that time there were about 500 students there. He was a schoolfellow of Anton Tomaž Linhart
Anton Tomaž Linhart
Anton Tomaž Linhart was a Slovene playwright and historian, best known as the author of the first comedy in Slovene, Županova Micka...

, a Slovenian writer and historian. Jurij completed high school when he was 19, in 1773. After completing Lyceum
Lyceum
The lyceum is a category of educational institution defined within the education system of many countries, mainly in Europe. The definition varies between countries; usually it is a type of secondary school.-History:...

 in Ljubljana he became a navigational engineer. Tentamen philosophicum, a list of questions for his comprehensive examination, was preserved and is available in the Mathematical Library in Ljubljana. The problems cover logic
Logic
In philosophy, Logic is the formal systematic study of the principles of valid inference and correct reasoning. Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy, mathematics, semantics, and computer science...

, algebra
Algebra
Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures...

, metaphysics
Metaphysics
Metaphysics is a branch of philosophy concerned with explaining the fundamental nature of being and the world, although the term is not easily defined. Traditionally, metaphysics attempts to answer two basic questions in the broadest possible terms:...

, geometry
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....

, trigonometry
Trigonometry
Trigonometry is a branch of mathematics that studies triangles and the relationships between their sides and the angles between these sides. Trigonometry defines the trigonometric functions, which describe those relationships and have applicability to cyclical phenomena, such as waves...

, geodesy
Geodesy
Geodesy , also named geodetics, a branch of earth sciences, is the scientific discipline that deals with the measurement and representation of the Earth, including its gravitational field, in a three-dimensional time-varying space. Geodesists also study geodynamical phenomena such as crustal...

, stereometry, geometry
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....

 of curve
Curve
In mathematics, a curve is, generally speaking, an object similar to a line but which is not required to be straight...

s, ballistics
Ballistics
Ballistics is the science of mechanics that deals with the flight, behavior, and effects of projectiles, especially bullets, gravity bombs, rockets, or the like; the science or art of designing and accelerating projectiles so as to achieve a desired performance.A ballistic body is a body which is...

, and general and special physics
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...

.

Military service

Jurij left Ljubljana five years after graduation and entered military service in 1780 as Professor of Mathematics at the Artillery School in Vienna. At that time he started to sign his last name as Vega and no longer Veha. When Jurij was 33 he married Josefa Svoboda (Jožefa Swoboda) (1771–1800), a Czech
Czech Republic
The Czech Republic is a landlocked country in Central Europe. The country is bordered by Poland to the northeast, Slovakia to the east, Austria to the south, and Germany to the west and northwest....

 noble from České Budějovice
Ceské Budejovice
České Budějovice is a city in the Czech Republic. It is the largest city in the South Bohemian Region and is the political and commercial capital of the region and centre of the Roman Catholic Diocese of České Budějovice and of the University of South Bohemia and the Academy of Sciences...

 who was 16 at that time.

Vega participated in several wars. In 1788 he served under Austrian Imperial Field-Marshal Ernst Gideon von Laudon (1717–1790) in a campaign against the Turks
Ottoman Empire
The Ottoman EmpireIt was usually referred to as the "Ottoman Empire", the "Turkish Empire", the "Ottoman Caliphate" or more commonly "Turkey" by its contemporaries...

 at Belgrade
Belgrade
Belgrade is the capital and largest city of Serbia. It is located at the confluence of the Sava and Danube rivers, where the Pannonian Plain meets the Balkans. According to official results of Census 2011, the city has a population of 1,639,121. It is one of the 15 largest cities in Europe...

. His command of several mortar
Mortar (weapon)
A mortar is an indirect fire weapon that fires explosive projectiles known as bombs at low velocities, short ranges, and high-arcing ballistic trajectories. It is typically muzzle-loading and has a barrel length less than 15 times its caliber....

 batteries contributed considerably to the fall of the Belgrade fortress. Between 1793 and 1797 he fought French Revolution
French Revolution
The French Revolution , sometimes distinguished as the 'Great French Revolution' , was a period of radical social and political upheaval in France and Europe. The absolute monarchy that had ruled France for centuries collapsed in three years...

aries under the command of Austrian General Dagobert-Sigismond de Wurmser (1724–1797) with the European coalition on the Austrian side. He fought at Fort Louis
Fort-Louis
Fort-Louis is a commune in the Bas-Rhin department in Alsace in north-eastern France.It acquired its name and its principal raison d'être from a 17th century fort...

, Mannheim
Mannheim
Mannheim is a city in southwestern Germany. With about 315,000 inhabitants, Mannheim is the second-largest city in the Bundesland of Baden-Württemberg, following the capital city of Stuttgart....

, Mainz
Mainz
Mainz under the Holy Roman Empire, and previously was a Roman fort city which commanded the west bank of the Rhine and formed part of the northernmost frontier of the Roman Empire...

, Wiesbaden
Wiesbaden
Wiesbaden is a city in southwest Germany and the capital of the federal state of Hesse. It has about 275,400 inhabitants, plus approximately 10,000 United States citizens...

, Kehl
Kehl
Kehl is a town in southwestern Germany in the Ortenaukreis, Baden-Württemberg. It is located on the river Rhine, directly opposite the French city of Strasbourg.-History:...

, and Dietz
Dietz
Dietz is a surname, and may refer to:* August Dietz , a philatelist, editor and publisher* Cyrus E. Dietz , Illinois Supreme Court Justice* Danny Dietz , United States Navy SEAL and recipient of the Navy Cross...

. In 1795 he had two 30-pound (14 kilogram) mortars cast, with conically drilled bases and a greater charge, for a firing range up to 3000 metres (3300 yards). The old 60 lb (27 kg) mortars had a range of only 1800 m (2000 yd).

In September 1802 Jurij Vega was reported missing. After a few days' search his body was found. The police report concluded that it was an accident. However, the true cause of his death remains a mystery, but it is believed that he died on 1802-09-26 in Nußdorf
Nußdorf, Vienna
Nußdorf was a separate municipality until 1892 and is today a suburb of Vienna in the 19th district of Döbling.- Location :Nußdorf lies on both banks of the Nußbach , where the brook meets the Danube Canal...

 on the Danube
Danube
The Danube is a river in the Central Europe and the Europe's second longest river after the Volga. It is classified as an international waterway....

, near the Austria
Austria
Austria , officially the Republic of Austria , is a landlocked country of roughly 8.4 million people in Central Europe. It is bordered by the Czech Republic and Germany to the north, Slovakia and Hungary to the east, Slovenia and Italy to the south, and Switzerland and Liechtenstein to the...

n capital, Vienna
Vienna
Vienna is the capital and largest city of the Republic of Austria and one of the nine states of Austria. Vienna is Austria's primary city, with a population of about 1.723 million , and is by far the largest city in Austria, as well as its cultural, economic, and political centre...

. There is a well-backed theory about his death: he loved horses, and apparently he found out a miller owned a magnificent one. When he went to the miller to negotiate about the price, the miller, upon seeing his Lord and military insignia, took interest in the money he was carrying with him, murdered him; one of Jurij's tools (compass) was found in the mill one year after his disappearance and it had "J V" initials on it.

Mathematical accomplishments

Vega published a series of books of logarithm
Logarithm
The logarithm of a number is the exponent by which another fixed value, the base, has to be raised to produce that number. For example, the logarithm of 1000 to base 10 is 3, because 1000 is 10 to the power 3: More generally, if x = by, then y is the logarithm of x to base b, and is written...

 tables. The first one appeared in 1783. Much later, in 1797 it was followed by a second volume that contained a collection of integrals and other useful formulae. His Handbook, which was originally published in 1793, was later translated into several languages and appeared in over 100 issues. His major work was Thesaurus Logarithmorum Completus
Thesaurus Logarithmorum Completus
Thesaurus Logarithmorum Completus, a large logarithm table handbook, was the main work of Slovenian mathematician Jurij Vega. It was first published in 1794 in Leipzig. Its 90th edition was published in 1924....

(Treasury of all Logarithms) that was first published 1794 in Leipzig
Leipzig
Leipzig Leipzig has always been a trade city, situated during the time of the Holy Roman Empire at the intersection of the Via Regia and Via Imperii, two important trade routes. At one time, Leipzig was one of the major European centres of learning and culture in fields such as music and publishing...

. This table was actually based on Adriaan Vlacq
Adriaan Vlacq
Adriaan Vlacq was a Dutch book publisher and author of mathematical tables. Born in Gouda, Vlacq published a table of logarithms from 1 to 100,000 to 10 decimal places in 1628 in his Arithmetica logarithmica. This table extended Henry Briggs' original tables which only covered the values...

's tables, but corrected a number of errors and extended the logarithms of trigonometric functions for the small angles. An engineer, Franc Allmer, honourable senator of the Technical university of Graz
Graz
The more recent population figures do not give the whole picture as only people with principal residence status are counted and people with secondary residence status are not. Most of the people with secondary residence status in Graz are students...

, has found Vega's logarithmic tables with 10 decimal
Decimal
The decimal numeral system has ten as its base. It is the numerical base most widely used by modern civilizations....

 places in the Museum of Carl Friedrich Gauss in Göttingen
Göttingen
Göttingen is a university town in Lower Saxony, Germany. It is the capital of the district of Göttingen. The Leine river runs through the town. In 2006 the population was 129,686.-General information:...

. Gauss
Carl Friedrich Gauss
Johann Carl Friedrich Gauss was a German mathematician and scientist who contributed significantly to many fields, including number theory, statistics, analysis, differential geometry, geodesy, geophysics, electrostatics, astronomy and optics.Sometimes referred to as the Princeps mathematicorum...

 used this work frequently and he has written in it several calculations. Gauss has also found some of Vega's errors in the calculations in the range of numbers, of which there are more than a million. A copy of Vega's Thesaurus belonging to the private collection of the British mathematician and computing pioneer Charles Babbage
Charles Babbage
Charles Babbage, FRS was an English mathematician, philosopher, inventor and mechanical engineer who originated the concept of a programmable computer...

 (1791–1871) is preserved at the Royal Observatory, Edinburgh
Royal Observatory, Edinburgh
The Royal Observatory, Edinburgh is an astronomical institution located on Blackford Hill in Edinburgh, Scotland. The site is owned by the Science and Technology Facilities Council...

.

Over the years Vega wrote a four volume textbook Vorlesungen über die Mathematik (Lectures about Mathematics). Volume I appeared in 1782 when he was 28 years old, Volume II in 1784, Volume III in 1788 and Volume IV in 1800. His textbooks also contain interesting tables: for instance, in Volume II one can find closed form expressions for sines of multiples of 3 degrees
Exact trigonometric constants
Exact constant expressions for trigonometric values are sometimes useful, mainly for simplifying solutions into radical forms which allow further simplification....

, written in a form easy to work with.

Vega wrote at least six scientific papers. On August 20, 1789 Vega achieved a world record when he calculated pi
Pi
' is a mathematical constant that is the ratio of any circle's circumference to its diameter. is approximately equal to 3.14. Many formulae in mathematics, science, and engineering involve , which makes it one of the most important mathematical constants...

 to 140 places, of which the first 126 were correct.http://www.southernct.edu/~sandifer/Ed/History/Preprints/Talks/Jurij%20Vega/Vega%20math%20script.pdf This calculation he proposed to the Russian Academy of Sciences
Russian Academy of Sciences
The Russian Academy of Sciences consists of the national academy of Russia and a network of scientific research institutes from across the Russian Federation as well as auxiliary scientific and social units like libraries, publishers and hospitals....

 in Saint Petersburg
Saint Petersburg
Saint Petersburg is a city and a federal subject of Russia located on the Neva River at the head of the Gulf of Finland on the Baltic Sea...

 (Санкт Петербург) in the booklet V. razprava (The fifth discussion), where he had found with his calculating method an error on the 113th place from the estimation of Thomas Fantet de Lagny (1660–1734) from 1719 of 127 places. Vega retained his record 52 years until 1841 and his method is mentioned still today. His article was not published by the Academy until six years later, in 1795. Vega had improved John Machin
John Machin
John Machin, , a professor of astronomy at Gresham College, London, is best known for developing a quickly converging series for Pi in 1706 and using it to compute Pi to 100 decimal places.Machin's formula is:...

's formula from 1706:


with his formula, which is equal to Euler's
Leonhard Euler
Leonhard Euler was a pioneering Swiss mathematician and physicist. He made important discoveries in fields as diverse as infinitesimal calculus and graph theory. He also introduced much of the modern mathematical terminology and notation, particularly for mathematical analysis, such as the notion...

 formula from 1755:


and which converges faster than Machin's formula. He had checked his result with the similar Hutton's formula:


He had developed the second term in the series only once.

Although he worked in the subjects of ballistics, physics and astronomy
Astronomy
Astronomy is a natural science that deals with the study of celestial objects and phenomena that originate outside the atmosphere of Earth...

, his major contributions are to the mathematics of the second half of the 18th century.

In 1781 Vega tried to push further his idea in the Austrian Habsburg monarchy
Habsburg
The House of Habsburg , also found as Hapsburg, and also known as House of Austria is one of the most important royal houses of Europe and is best known for being an origin of all of the formally elected Holy Roman Emperors between 1438 and 1740, as well as rulers of the Austrian Empire and...

 about the usage of the decimal metric system
Metric system
The metric system is an international decimalised system of measurement. France was first to adopt a metric system, in 1799, and a metric system is now the official system of measurement, used in almost every country in the world...

 of units. His idea was not accepted, but it was introduced later under the emperor Franz Josef I in 1871.

Jurij Vega was a member of the Academy of Practical Sciences in Mainz, the Physical and Mathematical Society of Erfurt
Erfurt
Erfurt is the capital city of Thuringia and the main city nearest to the geographical centre of Germany, located 100 km SW of Leipzig, 150 km N of Nuremberg and 180 km SE of Hannover. Erfurt Airport can be reached by plane via Munich. It lies in the southern part of the Thuringian...

, the Bohemian Scientific Society in Prague
Prague
Prague is the capital and largest city of the Czech Republic. Situated in the north-west of the country on the Vltava river, the city is home to about 1.3 million people, while its metropolitan area is estimated to have a population of over 2.3 million...

, and the Prussian Academy of Sciences in Berlin
Berlin
Berlin is the capital city of Germany and is one of the 16 states of Germany. With a population of 3.45 million people, Berlin is Germany's largest city. It is the second most populous city proper and the seventh most populous urban area in the European Union...

. He was also an associate member of the British Scientific Society in Göttingen
Göttingen
Göttingen is a university town in Lower Saxony, Germany. It is the capital of the district of Göttingen. The Leine river runs through the town. In 2006 the population was 129,686.-General information:...

. He was awarded the Order of Maria Theresa
Maria Theresa of Austria
Maria Theresa Walburga Amalia Christina was the only female ruler of the Habsburg dominions and the last of the House of Habsburg. She was the sovereign of Austria, Hungary, Croatia, Bohemia, Mantua, Milan, Lodomeria and Galicia, the Austrian Netherlands and Parma...

 on May 11, 1796. In 1800 Jurij Vega obtained a title of hereditary baron including the right to his own coat of arms.

Post of Slovenia has issued a stamp honouring Jurij Vega and the National Bank of Slovenia has issued a 50 tolar
Slovenian tolar
The tolar was the currency of Slovenia from 1991 until the introduction of the euro on 1 January 2007. It was subdivided into 100 stotins...

 banknote in his honour.

An asteroid
Asteroid
Asteroids are a class of small Solar System bodies in orbit around the Sun. They have also been called planetoids, especially the larger ones...

 14966 Jurijvega
14966 Jurijvega
14966 Jurijvega is a main-belt asteroid discovered on July 30, 1997 by Herman Mikuž at the Črni Vrh Observatory in Slovenia.On May 9, 2001 it was named after baron Jurij Vega, a late 18th-century Slovene mathematician and physicist....

, discovered on July 30, 1997, is named after him.

External links

  • Jurij Vega on the Slovenian 50 Tolars banknote.
  • University of St Andrews
    University of St Andrews
    The University of St Andrews, informally referred to as "St Andrews", is the oldest university in Scotland and the third oldest in the English-speaking world after Oxford and Cambridge. The university is situated in the town of St Andrews, Fife, on the east coast of Scotland. It was founded between...

    ' page on Vega: http://www-groups.dcs.st-and.ac.uk/~history/Mathematicians/Vega.html
  • Vega and his time
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