Kazimierz Vetulani
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Kazimierz Franciszek Vetulani (3 January 1889 – 4 July 1941) was a Polish
civil engineer A civil engineer is a person who practices civil engineering – the application of planning, designing, constructing, maintaining, and operating infrastructure while protecting the public and environmental health, as well as improving existing i ...
,
professor Professor (commonly abbreviated as Prof.) is an Academy, academic rank at university, universities and other tertiary education, post-secondary education and research institutions in most countries. Literally, ''professor'' derives from Latin ...
at the
Lviv Polytechnic Lviv Polytechnic National University () is a public university in Lviv, Ukraine, founded in 1816. According to the Times Higher Education, as of 2024, it ranks first as a technical institution of higher education and second among all instit ...
, member of the
Polish Mathematical Society The Polish Mathematical Society () is the main professional society of Polish mathematicians and represents Polish mathematics within the European Mathematical Society (EMS) and the International Mathematical Union (IMU). History The society was ...
, author of several dozen papers in the fields of
technology Technology is the application of Conceptual model, conceptual knowledge to achieve practical goals, especially in a reproducible way. The word ''technology'' can also mean the products resulting from such efforts, including both tangible too ...
and
mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...
, as well as in the field of
musical scale In music theory, a scale is "any consecutive series of notes that form a progression between one note and its octave", typically by order of pitch or fundamental frequency. The word "scale" originates from the Latin ''scala'', which literal ...
theory. A participant of
World War I World War I or the First World War (28 July 1914 – 11 November 1918), also known as the Great War, was a World war, global conflict between two coalitions: the Allies of World War I, Allies (or Entente) and the Central Powers. Fighting to ...
in the rank of
lieutenant A lieutenant ( , ; abbreviated Lt., Lt, LT, Lieut and similar) is a Junior officer, junior commissioned officer rank in the armed forces of many nations, as well as fire services, emergency medical services, Security agency, security services ...
of the
Austro-Hungarian Army The Austro-Hungarian Army, also known as the Imperial and Royal Army,; was the principal ground force of Austria-Hungary from 1867 to 1918. It consisted of three organisations: the Common Army (, recruited from all parts of Austria-Hungary), ...
reserve Reserve or reserves may refer to: Places * Reserve, Kansas, a US city * Reserve, Louisiana, a census-designated place in St. John the Baptist Parish * Reserve, Montana, a census-designated place in Sheridan County * Reserve, New Mexico, a US v ...
, he was a
sapper A sapper, also called a combat engineer, is a combatant or soldier who performs a variety of military engineering duties, such as breaching fortifications, demolitions, bridge-building, laying or clearing minefields, preparing field defenses ...
and a
military engineer Military engineering is loosely defined as the art, science, and practice of designing and building military works and maintaining lines of military transport and military communications. Military engineers are also responsible for logistics ...
. He was promoted to the rank of
captain Captain is a title, an appellative for the commanding officer of a military unit; the supreme leader or highest rank officer of a navy ship, merchant ship, aeroplane, spacecraft, or other vessel; or the commander of a port, fire or police depa ...
in the
Polish Army The Land Forces () are the Army, land forces of the Polish Armed Forces. They currently contain some 110,000 active personnel and form many components of the European Union and NATO deployments around the world. Poland's recorded military histor ...
reserve and participated in the
Polish–Ukrainian War The Polish–Ukrainian War, from November 1918 to July 1919, was a conflict between the Second Polish Republic and Ukrainian forces (both the West Ukrainian People's Republic and the Ukrainian People's Republic). The conflict had its roots in ...
. In 1935 he obtained
Ph.D. A Doctor of Philosophy (PhD, DPhil; or ) is a terminal degree that usually denotes the highest level of academic achievement in a given discipline and is awarded following a course of graduate study and original research. The name of the deg ...
at the Lviv Polytechnic. In 1938 he was appointed a deputy professor of general
mechanics Mechanics () is the area of physics concerned with the relationships between force, matter, and motion among Physical object, physical objects. Forces applied to objects may result in Displacement (vector), displacements, which are changes of ...
, and in 1940 he was appointed full professor. Shortly after the Germans seized Lviv during
World War II World War II or the Second World War (1 September 1939 – 2 September 1945) was a World war, global conflict between two coalitions: the Allies of World War II, Allies and the Axis powers. World War II by country, Nearly all of the wo ...
, on the night of 4 July 1941, he was arrested by
Gestapo The (, ), Syllabic abbreviation, abbreviated Gestapo (), was the official secret police of Nazi Germany and in German-occupied Europe. The force was created by Hermann Göring in 1933 by combining the various political police agencies of F ...
, the German secret police, and murdered among a group of Lviv professors.


Biography


Early life and education

He was born on 3 January 1889 in
Sanok Sanok (in full the Royal Free City of Sanok — , , ''Sanok'', , ''Sianok'' or ''Sianik'', , , ''Sūnik'' or ''Sonik'') is a town in the Subcarpathian Voivodeship of southeastern Poland with 38,397 inhabitants, as of June 2016. Located on the San ...
, then within the
Kingdom of Galicia and Lodomeria The Kingdom of Galicia and Lodomeria, also known as Austrian Galicia or colloquially Austrian Poland, was a constituent possession of the Habsburg monarchy in the historical region of Galicia (Eastern Europe), Galicia in Eastern Europe. The Cr ...
; the son of
Roman Vetulani Roman Vetulani (8 August 1849 – 12 August 1908) was a Polish high school professor, secretary of the Polish Sokol movement, "Sokół" gymnastics organization chapter in Sanok, honorary member of Macierz Ziemi Cieszyńskiej since 1898. Biograp ...
, a high school professor, and Matylda
née The birth name is the name of the person given upon their birth. The term may be applied to the surname, the given name or to the entire name. Where births are required to be officially registered, the entire name entered onto a births registe ...
Pisz (1861–1891). His mother died on 15 December 1891, when Kazimierz Vetulani was less than three years old. He was raised by his father and his second wife, Elżbieta née Kunachowicz. He had five younger, half-siblings: brothers
Zygmunt Zygmunt, Zigmunt, Zigmund and spelling variations thereof are masculine given names and occasionally surnames. It has the same etymology as the Germanic name Zigmund. People so named include: Given name Medieval period * Sigismund I the Old (1467 ...
(1894–1942), Tadeusz (1897–1952) and
Adam Adam is the name given in Genesis 1–5 to the first human. Adam is the first human-being aware of God, and features as such in various belief systems (including Judaism, Christianity, Gnosticism and Islam). According to Christianity, Adam ...
(1901–1976), and sisters Maria (master of economics, clerk of the Agricultural Bank in Kraków, 1895–1945) and Elżbieta (1903–1921, died of tuberculosis). The family lived in Sanok, in the house at Floriańska Street (later renamed Ignacy Daszyński Street) and in the villa of the Zaleski family at Świętego Jana Square. In 1906, Roman Vetulani died of a heart attack, chanting six children, including the then-seventeen-year-old Kazimierz. The mother, Elżbieta Vetulani, received a pension from her deceased husband, yet she remained the only breadwinner and faced material difficulties. In 1907, Kazimierz Vetulani passed the
matriculation examination A matriculation examination or matriculation exam is a university entrance examination, which is typically held towards the end of secondary school. After passing the examination, a student receives a School leaving qualification, school leaving ce ...
with distinction at the Queen Sophia High School in Sanok. On the matriculation certificate of 15 June 1907, he had an excellent degree in mathematics and Polish language with a notion of a particular passion for those subjects. In the years 1907–1913 he studied
civil engineering Civil engineering is a regulation and licensure in engineering, professional engineering discipline that deals with the design, construction, and maintenance of the physical and naturally built environment, including public works such as roads ...
at the
Lviv Polytechnic Lviv Polytechnic National University () is a public university in Lviv, Ukraine, founded in 1816. According to the Times Higher Education, as of 2024, it ranks first as a technical institution of higher education and second among all instit ...
, but he did not obtain a diploma. During the studies, he earned his living by giving tutoring and writing theses. He also made scientific and technical travels to
Italy Italy, officially the Italian Republic, is a country in Southern Europe, Southern and Western Europe, Western Europe. It consists of Italian Peninsula, a peninsula that extends into the Mediterranean Sea, with the Alps on its northern land b ...
,
Austria Austria, formally the Republic of Austria, is a landlocked country in Central Europe, lying in the Eastern Alps. It is a federation of nine Federal states of Austria, states, of which the capital Vienna is the List of largest cities in Aust ...
, the
Czech Republic The Czech Republic, also known as Czechia, and historically known as Bohemia, is a landlocked country in Central Europe. The country is bordered by Austria to the south, Germany to the west, Poland to the northeast, and Slovakia to the south ...
and
Germany Germany, officially the Federal Republic of Germany, is a country in Central Europe. It lies between the Baltic Sea and the North Sea to the north and the Alps to the south. Its sixteen States of Germany, constituent states have a total popu ...
, where he visited the construction sites of large partitions of valleys, large bridges, boulevards and river regulations.


Military service and stay in Kraków

In the first half of 1914 he lectured on
explosives engineering Explosives engineering is the field of science and engineering which is related to examining the behavior and usage of explosive materials. Topics Some of the topics that explosives engineers study, research, and work on include: * Developmen ...
, including
blowing up In mathematics, blowing up or blowup is a type of geometric transformation which replaces a subspace of a given space with the space of all directions pointing out of that subspace. For example, the blowup of a point in a plane replaces the poin ...
bridges and railroads, at the officer training courses of the
Polish Rifle Squads The Polish Rifle Squads () was a Polish pro-independence paramilitary organization, founded in 1911 by the Youth Independence Organization in the Austro-Hungarian sector of partitioned Poland. Among its founders were Norwid Neugebauer, Marian J ...
in
Vienna Vienna ( ; ; ) is the capital city, capital, List of largest cities in Austria, most populous city, and one of Federal states of Austria, nine federal states of Austria. It is Austria's primate city, with just over two million inhabitants. ...
. During
World War I World War I or the First World War (28 July 1914 – 11 November 1918), also known as the Great War, was a World war, global conflict between two coalitions: the Allies of World War I, Allies (or Entente) and the Central Powers. Fighting to ...
he was called to serve in the
Austro-Hungarian Army The Austro-Hungarian Army, also known as the Imperial and Royal Army,; was the principal ground force of Austria-Hungary from 1867 to 1918. It consisted of three organisations: the Common Army (, recruited from all parts of Austria-Hungary), ...
and infantry
reserve Reserve or reserves may refer to: Places * Reserve, Kansas, a US city * Reserve, Louisiana, a census-designated place in St. John the Baptist Parish * Reserve, Montana, a census-designated place in Sheridan County * Reserve, New Mexico, a US v ...
. He was promoted to the rank of second lieutenant on 1 September 1915, and then to the rank of
lieutenant A lieutenant ( , ; abbreviated Lt., Lt, LT, Lieut and similar) is a Junior officer, junior commissioned officer rank in the armed forces of many nations, as well as fire services, emergency medical services, Security agency, security services ...
on 1 November 1917. Around 1916–1918 he was assigned to the Imperial-Royal railway regiment. In the 1917/1918 academic year, he studied again at the Lviv Polytechnic. As the war ended and Poland regained independence, he was admitted to the
Polish Army The Land Forces () are the Army, land forces of the Polish Armed Forces. They currently contain some 110,000 active personnel and form many components of the European Union and NATO deployments around the world. Poland's recorded military histor ...
as a lieutenant. In 1918 he built
armoured train An armoured train (Commonwealth English) or armored train (American English) is a railway train protected with heavy metal plating and which often includes railway wagons armed with artillery, machine guns, and autocannons. Some have also h ...
s in
Nowy Sącz Nowy Sącz (; ; ; ; ) is a city in the Lesser Poland Voivodeship of southern Poland. It is the district capital of Nowy Sącz County as a separate administrative unit. With a population of 83,116 as of 2021, it is the largest city in the Beskid S ...
and
Przemyśl Przemyśl () is a city in southeastern Poland with 56,466 inhabitants, as of December 2023. Data for territorial unit 1862000. In 1999, it became part of the Podkarpackie Voivodeship, Subcarpathian Voivodeship. It was previously the capital of Prz ...
and traveled to the besieged Lviv. He was promoted to the rank of
captain Captain is a title, an appellative for the commanding officer of a military unit; the supreme leader or highest rank officer of a navy ship, merchant ship, aeroplane, spacecraft, or other vessel; or the commander of a port, fire or police depa ...
in the corps of railway officers on 1 June 1919. After completing his military service, he settled in
Kraków , officially the Royal Capital City of Kraków, is the List of cities and towns in Poland, second-largest and one of the oldest cities in Poland. Situated on the Vistula River in Lesser Poland Voivodeship, the city has a population of 804,237 ...
and started work in a construction company. After the
Peace of Riga The Treaty of Riga was signed in Riga, Latvia, on between Poland on one side and Soviet Russia (acting also on behalf of Soviet Belarus) and Soviet Ukraine on the other, ending the Polish–Soviet War (1919–1921). The chief negotiators o ...
of March 1921, he lectured at the Technical College of Railway Forces and at the courses of professional and reserve officers in Kraków. He made contact with professors of the
Jagiellonian University The Jagiellonian University (, UJ) is a public research university in Kraków, Poland. Founded in 1364 by Casimir III the Great, King Casimir III the Great, it is the oldest university in Poland and one of the List of oldest universities in con ...
. In the years 1924–1939 he was a member of the
Polish Mathematical Society The Polish Mathematical Society () is the main professional society of Polish mathematicians and represents Polish mathematics within the European Mathematical Society (EMS) and the International Mathematical Union (IMU). History The society was ...
. Thanks to the kindness of Kraków's mathematicians, he could use the collections of the Mathematical Institute. In the documents of the Polish Mathematical Society, the following address of Vetulani was noted (until 1938): Kraków, Smoleńsk Street 14. In the 1921/1922 academic year, Kazimierz Vetulani was employed as an assistant at the Mining Academy in Kraków, where he lectured in
strength of materials Strength may refer to: Personal trait *Physical strength, as in people or animals *Character strengths like those listed in the Values in Action Inventory *The exercise of willpower Physics * Mechanical strength, the ability to withstand ...
. Then he worked as a technical advisor to a number of large companies, enterprises and central and local government institutions as well as private clients. In 1923 he was assigned as a reserve officer in the 1st Railway Regiment of the Polish Army. In 1924 he was verified on the list of railway sapper officers in the rank of captain and assigned as a reserve officer to the 1st Railway Sapper Regiment. In 1934, as a reserve captain of the engineering corps and sappers, he was included in a group of
militia A militia ( ) is a military or paramilitary force that comprises civilian members, as opposed to a professional standing army of regular, full-time military personnel. Militias may be raised in times of need to support regular troops or se ...
officers. He was assigned to the District Officers' Staff No. V and was then on the records of the Poviat Supplementary Command of the City of Kraków.


Work at the Lviv Polytechnic

Throughout 1920s and 1930s, Kazimierz Vetulani published a number of scientific papers. He actively participated in the scientific life, presenting the results of his research, among others, at the Second Congress of Romanian Mathematicians in
Turnu-Severin Drobeta-Turnu Severin (), colloquially Severin, is a city in Mehedinți County, Oltenia, Romania, on the northern bank of the Danube, close to the Iron Gates. It is one of six Romanian county seats lying on the river Danube. "Drobeta" is the name ...
on 5–9 May 1932. He obtained the academic degree of road and bridge
engineer Engineers, as practitioners of engineering, are professionals who Invention, invent, design, build, maintain and test machines, complex systems, structures, gadgets and materials. They aim to fulfill functional objectives and requirements while ...
at the Faculty of Civil and Water Engineering of the Lviv Polytechnic in April 1935. In the same year, he obtained
Ph.D. A Doctor of Philosophy (PhD, DPhil; or ) is a terminal degree that usually denotes the highest level of academic achievement in a given discipline and is awarded following a course of graduate study and original research. The name of the deg ...
in technical sciences at the Lviv Polytechnic upon the dissertation ''On jets of liquid'', supervised by
Wojciech Rubinowicz Wojciech Sylwester Piotr Rubinowicz (February 22, 1889 – October 13, 1974) was a Polish theoretical physicist who made contributions in quantum mechanics, mathematical physics, and the theory of radiation. He is known for the Maggie-Rubinowicz ...
. As “Kazimierz etulaniwas eccentric and did not want to take the doctoral exam ''in front of people dumber than himself'', as the anecdote says, three professors took him for a walk in the park and the result of this conversation was considered to be a passed doctoral exam”. In Lviv, Kazimierz Vetulani lived by himself at the 31 Obertyńska Street (nowadays Zarytsky Street), on the second floor. In 1937 he received a scholarship from the National Culture Fund and took a scientific trip to Germany,
Belgium Belgium, officially the Kingdom of Belgium, is a country in Northwestern Europe. Situated in a coastal lowland region known as the Low Countries, it is bordered by the Netherlands to the north, Germany to the east, Luxembourg to the southeas ...
,
England England is a Countries of the United Kingdom, country that is part of the United Kingdom. It is located on the island of Great Britain, of which it covers about 62%, and List of islands of England, more than 100 smaller adjacent islands. It ...
and
France France, officially the French Republic, is a country located primarily in Western Europe. Overseas France, Its overseas regions and territories include French Guiana in South America, Saint Pierre and Miquelon in the Atlantic Ocean#North Atlan ...
, “where he became acquainted with the modern organization of mechanics teaching, with laboratories and with the use of mechanics in the field of railway construction, with the study of railway bridge vibrations and ground vibrations”. On 1 September 1938, he became deputy professor at the Department of General Mechanics at the Faculty of Civil and Water Engineering of the Lviv Polytechnic. He lectured in general mechanics,
strength of materials Strength may refer to: Personal trait *Physical strength, as in people or animals *Character strengths like those listed in the Values in Action Inventory *The exercise of willpower Physics * Mechanical strength, the ability to withstand ...
and
hydromechanics Fluid mechanics is the branch of physics concerned with the mechanics of fluids (liquids, gases, and plasmas) and the forces on them. Originally applied to water (hydromechanics), it found applications in a wide range of disciplines, including ...
. At the meeting of the Commission for the filling of the Department of General Mechanics on 18 March 1938, dean Adam Kuryłło stated that “the scientific activity of Dr. Vetulani is so serious that Dr. Vetulani deserves to be appointed a full professor, especially because of his age”. In the same year, the Lviv Polytechnic requested the Ministry of Religious Denominations and Public Enlightenment of Poland to present Vetulani for the nomination as full professor of general mechanics at the Faculty of Civil and Water Engineering. In June 1939, the Council of the Faculty of Civil Engineering of the Lviv Polytechnic unanimously accepted the postdoctoral dissertation of Kazimierz Vetulani, ''Considerations in Connection with Horizontal Buckling of the Railway Track on Flat, Rigid and Rough Ground'', which consisted of three papers published or written by Vetulani since 1937. His
habilitation Habilitation is the highest university degree, or the procedure by which it is achieved, in Germany, France, Italy, Poland and some other European and non-English-speaking countries. The candidate fulfills a university's set criteria of excelle ...
lecture ''General Mechanics Methods and Problems of Technical Mechanics'' took place on 17 June 1939. The Faculty Council applied to the Minister for approval of the application regarding the right for Kazimierz Vetulani to lecture in the field of general and technical mechanics. On 3 July 1939, Minister
Wojciech Świętosławski Wojciech Alojzy Świętosławski (Polish pronunciation: ; 1881–1968) was a Polish physical chemist, who is considered the "father of modern thermochemistry". He developed a static method of cryometric measurement and a new method of testing co ...
approved a resolution of the Council. In the academic year 1939/1940 Kazimierz Vetulani was nominated a full professor.


Arrest and death

A few days after Germany invaded the USSR, Lviv was captured by the
Wehrmacht The ''Wehrmacht'' (, ) were the unified armed forces of Nazi Germany from 1935 to 1945. It consisted of the German Army (1935–1945), ''Heer'' (army), the ''Kriegsmarine'' (navy) and the ''Luftwaffe'' (air force). The designation "''Wehrmac ...
. German authorities planned to murder members of Polish intelligentsia in Lviv. In order to avoid the complications that had previously resulted in the mass arrest of professors in Kraków in 1939, the Germans decided to organize the immediate shooting of professors from Lviv universities, a large number of which were active during the
Soviet occupation During World War II, the Soviet Union occupied and annexed several countries effectively handed over by Nazi Germany in the secret Molotov–Ribbentrop Pact of 1939. These included the eastern regions of Poland (incorporated into three differe ...
of the city. The list of names of Polish professors was most likely made and delivered to Germans by Ukrainian students from Kraków, associated with the
Organization of Ukrainian Nationalists The Organisation of Ukrainian Nationalists (OUN; ) was a Ukrainian nationalist organization established on February 2, 1929 in Vienna, uniting the Ukrainian Military Organization with smaller, mainly youth, radical nationalist right-wing groups. ...
(OUN). Kazimierz Vetulani, according to his cousin Janusz Vetulani, was “respected and liked by students of three denominations and nationalities living in Lviv at the time,” and was “in time warned by Ukrainian students to avoid the area of his apartment for a few days and not stay in it”. However, he was to disregard this warning: “I was present when he visited us (as he did twice a week), mocked these warnings, bragging about his acquaintances among German scholars, and was convinced of his inviolability”. On the night of 3 July 1941, Kazimierz Vetulani was arrested by the
Gestapo The (, ), Syllabic abbreviation, abbreviated Gestapo (), was the official secret police of Nazi Germany and in German-occupied Europe. The force was created by Hermann Göring in 1933 by combining the various political police agencies of F ...
and shot along with a group of professors from Lviv universities at the Wuleckie Hills. The execution was carried out by the
Einsatzkommando During World War II, the Nazi German ' were a sub-group of the ' (mobile killing squads) – up to 3,000 men total – usually composed of 500–1,000 functionaries of the SS and Gestapo, whose mission was to exterminate Jews, Polish intellect ...
zur besonderen Verwendung (task force for special use) under the command of
Brigadeführer ''Brigadeführer'' (, ) was a paramilitary rank of the Nazi Party (NSDAP) that was used between 1932 and 1945. It was mainly known for its use as an SS rank. As an SA rank, it was used after briefly being known as '' Untergruppenführer'' in ...
Karl Eberhard Schöngarth Karl Eberhard Schöngarth (22 April 1903 – 16 May 1946) was a German lawyer and SS-''Brigadeführer'' in Nazi Germany. He was a war criminal who perpetrated mass murder and genocide in German-occupied Poland during the Holocaust. He participat ...
. Vetulani's neighbour, Lidia Szargułowa, witnessed his arrest by the Gestapo. Gestapo men showed great interest in the assets of those arrested. Most of the legacy and personal belongings of Kazimierz Vetulani found in his apartment, including some of his writings, were looted or destroyed during and following his arrest. The name of Kazimierz Vetulani (written as “Wetulani Franciszek or Kazimierz”) was mentioned twice in the testimony of
Stefan Banach Stefan Banach ( ; 30 March 1892 – 31 August 1945) was a Polish mathematician who is generally considered one of the 20th century's most important and influential mathematicians. He was the founder of modern functional analysis, and an original ...
, submitted in 1944 to the Soviet authorities, regarding the German murders of Polish scientists and intellectuals. Banach reported that to his knowledge Vetulani had been arrested on the wave of the first arrests in July 1941 and “all hearing of him was lost. They were certainly shot
long with other professors Long may refer to: Measurement * Long, characteristic of something of great duration * Long, characteristic of something of great length * Longitude (abbreviation: long.), a geographic coordinate * Longa (music), note value in early music mensu ...
. Banach added that he learned of Kazimierz Vetulani's arrest from Vetulani's cousin.


Scientific work

Kazimierz Vetulani was the author of several dozen scientific papers published, among others in the ''Czasopismo Techniczne'' (''Technical Journal'') and ''Przegląd Techniczny'' (''Technical Review''), including over fifteen technical papers, four mathematical papers, one original lecture script and several papers on the theory of musical scales. He published works in Italian, Spanish, German and English, and was fluent in Italian. He translated into Polish, among others one work and lecture by the Italian scholar
Tullio Levi-Civita Tullio Levi-Civita, (; ; 29 March 1873 – 29 December 1941) was an Italian mathematician, most famous for his work on absolute differential calculus ( tensor calculus) and its applications to the theory of relativity, but who also made signifi ...
. According to the authors of his biography in ''Wiadomości Matematyczne'', Vetulani “also showed great understanding of technical problems by writing papers on practical engineering issues. This is evidenced, for example, by his opinion on the cause of the cracks, the receding and tilting of the wing of the parallel bridgehead on the river Dłubnia of the Kraków-Miechów railway line, and a technical opinion issued in print on the utility of the stone from Mogielnica for communication and construction purposes (...), as well as a lecture on the foundation of the fourth bridge on the Vistula, delivered at the Technical Society in Kraków”.


Works

*
Wyznaczanie natężeń normalnych w łukach płaskich
' (1911) *
Mechanika ogólna i techniczna według wykładów w Akademii Górniczej w Krakowie w roku 1921–22
' (1922) * ''Obliczanie naprężeń normalnych w przekrojach żelbetowych, pod wpływem kurczenia się betonu'' (1923) * ''Obliczanie pracy istot żywych'' (1925) * ''Konstrukcja wykreślna największego momentu zginającego w zagadnieniu wytrzymałościowem podłużnic skrzydeł samolotu. Przyczynki do artykułu Prof. M. T. Hubera'' (1930) * ''Tłumaczenie z włoskiego na polski odczytu T. Levi-Civity ''O wysiłku dynamicznym ustrojów sprężystych'', wygłoszonego 24 IV 1928 w Wiedniu'' (1930) *
W sprawie wyboczenia
' (1930) * ''Wartość siły podłużnej podczas powstawania wyboczenia'' (1931) *
Orzeczenie techniczne o użyteczności kamienia z Mogielnicy dla celów komunikacyjno-budowlanych
' (1931) * ''Sistema dellescale a 7-tte toni'' (1931) * ''Circular models of music scales'' (1932) * ''Una contribución ́a la cuestión del esfuerzo el ́astico de dos cuerpos'' (1932) *
O zastosowaniu pewnego przedstawienia geometrycznego do biometrii i statystyki
' (1932) * ''Wzór przybliżony dla projektowania nakładek belki blaszanej'' (1932) * ''Przykład ustroju kratowego dopuszczającego układ nieokreślonych sił wewnętrznych'' (1932) * ''Przedstawienie zmiany naprężeń skrajnych podczas powstawania wyboczenia'' (1932) * ''The values of archyp found erroneous in Keiichi Hayashi tables'' (1932) *
O strugach cieczy
' (1933); published in Italian as: ''Suf getti liquidi'' (1933) * ''Uber Anwendung einer geometrischen Darstellung auf Biometrie uns Statistik'' (1935) *
Rozważania w związku z wyboczeniem poziomym toru kolejowego na podłożu płaskim, sztywnym i szorstkim
' (1937) * ''O pewnym przedstawieniu parametrycznym związanym z ogólnym równaniem 4-go stopnia'' (1937) *
Wybrzuszenie nieprzerwanego toru kolejowego traktowane zgrubsza jako zjawisko quasi-statyczne (Hypoteza „B”)
' (1938) *
Przyczynek do Coulomb’owskiej teorii naporu ziemi
' (1938) * ''Wybrzuszenie pionowe toru kolejowego ściskanego podłużnie traktowane elementarnie z grubsza (hipoteza „A”)'' (1950, pośmiertnie) * ''On problems of music scales'' (manuscript at the Bibliothèque nationale de France) * ''Wstęp do rozprawy o problemie skal'' (manuscript) * ''O kompozycji w muzyce''


Distinctions

Austro-Hungary * Golden Civil Merit Cross on the ribbon of Medal for Bravery (before 1916); * Brown Military Merit Medal on the ribbon of Military Merit Cross (before 1917). Poland * “Orlęta” Distinction for fights in defense of Lviv during the Polish-Ukrainian war.


Commemoration

Kazimierz Vetulani's name was on memorial plaques and other objects commemorating the murders of professors from Lviv universities. During the Jubilee Congress of the Friends of the High School in Sanok on the 70th anniversary of the first Matura on June 21, 1958, the name of Kazimierz Vetulani was mentioned in an appeal to those killed in defense of the homeland in 1939–1945 and on a memorial plaque in the high school devoted to the fallen and murdered high school graduates. In 1962, Kazimierz Vetulani was commemorated among other people mentioned on the plaque of the Mausoleum of Victims of World War II at the Central Cemetery in Sanok.


Family


Notes


References


Bibliography

* * * * * {{DEFAULTSORT:Vetulani, Kazimierz 20th-century Polish engineers 20th-century Polish mathematicians Lviv Polytechnic alumni Academic staff of Lviv Polytechnic Academic staff of AGH University of Science and Technology 1889 births People from Sanok Austro-Hungarian Army officers Austro-Hungarian military personnel of World War I Polish Army officers Polish people of the Polish–Ukrainian War Victims of the Massacre of Lwów professors Executed people from Subcarpathian Voivodeship Polish people of Italian descent Recipients of the commemorative badge Orlęta 1941 deaths