Keywords

1 First Years

The needs of the growing industries and trades led to the founding of various special schools and proposals for new organizations (see, for example, Lechner 1940) until the Polytechnicum of Vienna was founded in Vienna in 1815 modeled on the École polytechnique in Paris. From the beginning, geometric drawing was an important topic since it was needed for most studies, including building, engineering, architecture, and so on. But contrary to the Paris École polytechnique, there was no chair devoted to it. The necessary courses—“machine drawing” and “preliminary technical drawing”—were held as part of the normal curricula. Soon this situation was considered as unsatisfactory, and in 1834 Johann Hönig ,Footnote 1 an assistant at the Faculty for Mechanical Engineering (Maschinenlehre), voluntarily offered to give courses on descriptive geometry and drawing. In 1839, he left Vienna to become a professor for Darstellende Geometrie und Zivilbaukunst at the Berg-und Forstakademie in SchemnitzFootnote 2 where he stayed until 1843. From 1843 to 1870, he was a professor for descriptive geometry at the Polytechnicum in Vienna and a rector from 1868 to 1869 (Ottowitz 1992, p. 499, Obenrauch 1897).

The situation in Vienna was considered to be very bad, and the board of professors repeatedly (1827, 1835, and 1839) demanded the installation of a chair for descriptive geometry, and—with Hönig away—the situation became even worse. In 1841, another application was made “auf das Dringlichste” (most urgent) with reference to Germany where similar chairs had already been installed and were very successful (see Benstein, Chap. 9, this volume).

In April 1842, a Konkurs was announced, and Hönig —having already successfully passed such an exam in Schemnitz—was declared to be the best candidate, and he became a professor of Descriptive Geometry in 1843.

In order to show the importance of this new chair, three assistants and nine rooms for drawing were assigned to it.

Hönig had to teach a course of 3 h (5 h from 1850) and 10 h of construction practice per week.

In addition, he gave a 2-h popular course on Sundays. For many years, his book Anleitung zum Studium der Darstellenden Geometrie (Hönig 1845) was also used at the other Polytechnica of the Austro-Hungarian Empire (Graz, Prague, Brno, and Budapest—all of them German-speaking Polytechnica, also in Lemberg (Lvuv) where also some courses were taught in German). Another influential book was written by a professor of the Military Academy (Stampfl 1845).

A big step forward happened in the middle of the nineteenth century caused by the growing importance of the Realschulen. In the middle of the nineteenth century, more than 60 such schools were founded and also many special schools for the military, mining, arts, and trade, which all needed descriptive geometry.

Their curricula contained a great deal of geometrical drawing and ornaments and descriptive geometry (much more than in the corresponding schools in the other German-speaking countries (see Benstein, Chap. 9, this volume)). The teachers needed for this were educated at the Polytechnicum (for more details about the teaching of descriptive geometry in Austria, see Stachel, Chap. 11, this volume).

2 Second Half of the Nineteenth Century

Hönig was a professor for 27 years until 1870. He was supported by Rudolf Niemtschik Footnote 3 as his assistant from 1857 to 1861 and then by Rudolf Staudigl as Privatdozent. Rudolf Niemtschik worked in the building industry and studied at the Polytechnicum Vienna from 1852 to 1856. He was also an assistant at the Polytechnicum Vienna from 1857 to 1861 and was a professor for descriptive geometry at the Joanneum in Graz from 1861 to 1870. He was a professor and chair of the First Institute for Descriptive Geometry at the TH (formerly Polytechnicum) Vienna until 1877. Rudolf Staudigl Footnote 4 studied in Vienna with Hönig and was his assistant from 1861 to 1867; in 1865, he obtained a teacher’s degree for descriptive geometry, mechanics, and theory of machines at the Oberrealschulen. In 1866, he received the Habilitation for technical and freehand drawing, and in 1868, he was promoted in absentia at the University of Rostock (the Vienna Polytechnicum had not yet the right to promote), and he obtained the Habilitation for ornamentics and newer geometry in Vienna in 1869. From 1870 to 1877, he was extraordinarius and a professor and chair at the Institute for Descriptive Geometry at the TH Vienna from 1877 to 1891 (Ottowitz 1992, pp. 499–500).

In 1870, the chair in Vienna was divided into two, and Niemtschik followed Hönig as chair of the institute until his early death in 1877. He became a professor, and Staudigl was extraordinarius ad personam.

Niemtschik took over the courses for mechanical engineering students and Staudigl for the various building students, and both taught courses for future teachers of descriptive geometry. Both were also very much engaged in scientific publishing, often in competition as they considered the same kind of problems. While Staudigl used projective geometry for his solutions, Niemtschik used more original methods in the field of elementary descriptive geometry (Niemtschik 1866a,b).

Teachers for descriptive geometry spread all over the Austro-Hungarian Empire and most were also very interested in the field of research. They could publish their results in various journals, for example, in the so-called Schulprogramme, which were edited yearly by the schools. The Austrian Academy of Sciences (founded in 1848) also provided the possibility to publish and promote the field of descriptive geometry—each mentioned professor was a member of the academy.

After Niemtschik’s death, Staudigl took over all his courses and became chair of the institute.

In 1872, the Polytechnicum became the Technical High School of Vienna (Technische Hochschule, abbreviated as TH), and it was granted the right to promote students in 1903 (Neurath 1915).

The Staudigl’s courses had a very tight structure and combined various methods, and he always had practical applications as his goal. It was Staudigl , for sure, who laid the foundation for what later became the famous Vienna School of Descriptive Geometry. For his students, he distributed the first collections of reproduced examples. From 1884 on, the training of teachers took 6 years (instead of 4 years as before), and Staudigl taught courses on modern geometry and selected fields of modern geometry (Staudigl 1868, 1870, 1875).

Staudigl was responsible for both parts of the chair and the following list of his courses in 1890/1891 is a good example of the extent and the contents:

Descriptive geometry: orthogonal, axonometric, skew and perspective projection of points, lines and planes; exercises on the relations between these elementary fundamental elements, first by orthogonal projection and then by all other methods of projection; drawings of simple technical objects, bounded by planes including shadows; pyramids and prisms, curves and curved surfaces, mainly cones and cylinders; rotational surfaces, regulated, skew and envelopes surfaces. 4 hours per week, 4 hours for a seminar, and 10 hours for construction drawings (Vorlesungsverzeichnis der TH Wien, translated by the author).

Newer Geometry: basic figures (Grundgebilde) of the first degree (Stufe), their projective relationship, confocal and involutory basic figures of the first degree, products (Erzeugnisse) of these figures, curves of the second degree, collinear and reciprocal figures of the second degree, their relationship and products, surfaces of the second degree, and space curves of the third degree, collinear and reciprocal systems in space. For engineers, mechanical engineers and building engineers: 2 semesters, 4 hours per week, and 10 hours for construction drawings (Vorlesungsverzeichnis der TH Wien, translated by the author).

After the death of Staudigl in 1891 a second chair was installed and Gustav Peschka became his successor. Peschka studied at the Polytechnicum and the University of Prague, and worked as a constructor in a factory for machines. Then, he had positions at the Polytechnicum in Prague (from 1852 to 1857, he was “Adjunct” for mechanics, drawings of machines, and physics), at the TH Lemberg (from 1857 to 1863, he was a professor for mechanics, mechanical engineering and drawings of machines, and descriptive geometry), and at the German TH Brno (from 1863 to 1891, he was a professor for mechanics, mechanical engineering, and constructive drawing), Peschka (1877, 1882) he was dean from 1880 to 1882. From 1891 to 1901, he was chair for descriptive geometry at the TH in Vienna. Gustav Peschka Footnote 5 was the successor of Staudigl though he was only ranked second place by the committee. He is said to have been a “favorite of the court” (and the ministry). He was, in fact, not a good choice since Peschka had no interest in the practical applications, and he gave no courses for the teacher students. His main scientific contributions were in steam machines and their construction and safety (Einhorn 1985, pp. 565–571) (Lechner 1940, pp. 154–155).

In Vienna, Peschka taught courses for mechanical engineers, and it was said that he—contrary to his colleagues before and after—graded the student’s works only by their size and number, and not by their content. It was also said that he was a master in drawing on the blackboard. He did most of his scientific work during his stay in Brno, including the four volumes of Darstellende und projektive Geometrie (Peschka 1883–1885, 1899). This book had an important influence, and his book (Peschka 1868, 1882) was famous for the excellent typography and its 336 wood carvings.

The second chair was first held by Franz Ruth (1850–1905) from 1891 until 1895 and then from 1897 until 1899 by Jan Sobotka (1862–1931)—both as extraordinarius, and both later went to the Czech countries: Ruth to Prague and Sobotka to Brno.

3 The Era Emil Müller–Theodor Schmid

At the turn of the century, both chairs were vacant, and excellent mathematicians were found for both: Emil Müller Footnote 6 and Theodor Schmid . Both were students of Staudigl and followed his tradition, thereby making Vienna the center of descriptive geometry in the German-speaking countries. Both were interested in various fields of mathematics, in applications for all engineering studies, and in the education of student teachers. They were dominating the field for many years and solidified the reputations of the Wiener Schule der Darstellenden Geometrie (Vienna School of Descriptive Geometry). Müllers interests were widespread. He made many contributions to Grassmannian methods—he was considered to be one of the main experts in this field (Grassmannsche Ausdehnungslehre)—and he applied these methods to different aspects of geometry. He also developed the theory itself, and introduced the calculation of “Faltprodukte” (inner products), stressing the advantage of his methods for the theory of invariants.

During his long career at the TH in Vienna, he continued to work in different fields, but, of course, his main interest became descriptive geometry. He taught the introductory courses for building engineers and architects and enlarged the curriculum for the student teachers. Up till then the student teachers had to take the general introductory courses for the engineers and some specialized courses. Müller changed this situation and introduced a special seminar and a four semester cycle of courses: methods of projections in descriptive geometry, cyclographic and stereographic projection, constructive treatment of regulated surfaces, and constructive treatment of Schraub- und Schiebflächen (helicoidal and translation surfaces) Müller 1908, 1918, 1920 and Müller 1916, 1919, 1923.

His goal was not only to produce good teachers—with great success because teachers of descriptive geometry from the TH Vienna spread all over the whole Austro-Hungarian Empire—but also to further the scientific treatment of the field. His goal was to establish descriptive geometry as a part of geometry, in combination with projective geometry, non-Euclidean geometry, group theory, and so on. Müller was a very inspiring teacher with many students and followers. He also expressed his ideas in lectures given at the Versammlung der Naturforscher (the predecessor of the German Mathematical Society) in Germany (Müller 1910), where he also organized an exposition of his students’ drawings. These construction exercises were always very important and much time was devoted to them. In order to provide examples from which the students could choose, he edited collections of sample drawings (Müller 1910, 1911, 1920, 1926).

Figures 12.1 and 12.2 show the level of complexity. The first one uses trimetric projection, a parallel projection with three different scale factors on the three orthogonal axes. The second one uses perspective drawing. You also should keep in mind that they had to be done with Indian ink; thus, one wrong line or a single splash would ruin it, and you would have to do it all over again.

Fig. 12.1
figure 1

Bridge, by H. Sequenz, student of architecture in his first year under Peschka, in 1899/19007

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Fig. 12.2
figure 2

House, by J. Jenikowski, student of architecture 1900/1901

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Footnote 7

Theodor Schmid Footnote 8 held the Second Chair for Descriptive Geometry for 29 years. He regularly delivered the introductory courses in descriptive geometry for future mechanical engineers and on projective geometry for the student teachers. His examples of machine drawings (Schmid 1911, 1925) were very highly regarded in many places. Figures 12.3 and 12.4 show drawings by his students.

Fig. 12.3
figure 3

Surfaces of revolution: the hyperboloid in axonometric projection. The drawing is from 1902 and by Richard von Mises (1883–1953), who was studying mechanical engineering in his first year

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Fig. 12.4
figure 4

Reproduction of a screw by R. Höhlmüller, a student of Schmid

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Schmid worked on transmission devices (Getriebe)—very important for machines—on the construction of various curves and on the building of geometrical models. He was also interested in the shape of the earth and in photogrammetry. His goal was to combine descriptive geometry with projective geometry (Schmid 1912, 1919, 1922 and 1921, 1923).

He often complained about having too many students, so he was not able to write down his ideas on projective geometry. He was a very inspiring teacher, but he always remained a bit in the shadow of his charismatic colleague Emil Müller. Nevertheless, he received many honors, including that of dean. He was also elected to be a rector of the TH but could not accept this honor because of health problems.

4 The Era Erwin Kruppa–Ludwig Eckhart–Josef Krames

After Müller’s death in 1927 and Schmid’s retirement in 1929, both chairs were vacant. Müller’s assistant Josef Krames substituted the chair of the First Institute for 2 years until Erwin Kruppa Footnote 9 became successor of Müller. Kruppa succeeded in maintaining the international reputation of the Vienna School of Descriptive Geometry.

His education and former occupation as a professor of mathematics and his knowledge of modern analysis influenced his treatment of descriptive geometry (Kruppa 1932, 1933, 1936). He introduced exact limits instead of an intuitive treatment of neighboring elements, he also treated non-Euclidean geometry and geometry in higher dimensions. He edited and enlarged Müller’s book (Müller 1923), which consisted of three volumes, had at least four editions, and was very popular (Kruppa 1936, 1948, 1961).

In his later years, he also worked on differential geometry (Kruppa 1957).

Ludwig Eckhart Footnote 10 became chair of the Second Institute of Descriptive Geometry in 1929. He had already found a new Schrägrissverfahren (a particular form of axonometry), which soon found its way into many text books. He introduced cinematics as a basis for Getriebelehre into the courses for mechanical engineers and Ausdehnung des Einschneideprinzips in die schiefe Axonometrie (extension of the method of sections in skew axonometry). He was dismissed from office in 1937, a decision he could not understand and that hit him very hard. It seems that the reasons for this dismissal were political since he was active in the Vaterländische Front (Fatherland Front),Footnote 11 and one of his assistants was Jewish. He committed suicide in 1938.

Krames Footnote 12 was always very much engaged in teaching student teachers and he played a major role in introducing courses on selected topics in descriptive and projective geometry in Brno. In Graz, he was also responsible for the final examinations of teachers in descriptive geometry. But, in spite of his many duties, he continued to work scientifically. He published a series of articles on symmetrische Schrotungen (a type of symmetric motions in space), which were much valued by his French colleagues. From 1937 on, he studied the so-called gefährliche Flächen (dangerous surfaces), a problem in photogrammetry, and solved it using purely geometrical methods.

Descriptive geometry lost its importance after 1938: The hours required in engineering studies were reduced, and descriptive geometry was dropped in schools. Krames protested against this. In 1939, after the death of Eckhart , he became chair of the Second Institute of Descriptive Geometry at the TH Vienna. His main duties were the courses for machine engineering (Krames 1947, 1952). After the war in 1945, he was dismissed for political reasons and for the next years he worked at the Bundesamt für Eich-und Vermessungswesen (Federal Office of Metrology and Surveying), mostly in photogrammetry and improving instruments.

In 1946, the chair of the second institute was given to Walter Wunderlich Footnote 13 as extraordinarius. He was a pupil of Kruppa and had been working as an assistant and a Privatdozent during the war. In 1955, he became a professor.

He had many interests in all areas of geometry, especially in kinematics, höhere Radlinien (higher cycloidal curves), wobbly structures, and much more generally solving them in a very original way using intuitive geometric arguments.

In 1957, Krames was back at the TH Vienna succeeding Kruppa as chair in the First Institute of Descriptive Geometry. In the same year, both institutes changed their names to the First and the Second Institute of Geometry and became open to other fields of geometry such as differential geometry and computer aided design.

Together with his colleague Wunderlich , Krames reorganized the studies for teachers. Alternatingly they gave courses on projective geometry I and II. They also introduced two new seminars; Krames gave a 2-year course on Konstruktive Abbildungsmethoden (constructive methods of representation) and Konstruktive Strahlgeometrie (constructive line geometry), whereas Wunderlich taught Konstruktive Differentialgeometrie (constructive differential geometry) and Nichteuklidische und mehrdimensionale Geometrie (non-Euclidean and higher dimensional geometry) (Wunderlich 1966, 1967).

With Krames’ retirement in 1969 and Wunderlich’s in 1980, we come to the end of the classical period of descriptive geometry in Vienna. In 1975, the TH became the University of Technology of Vienna (Technische Universität Wien, TU).