**August Adler** was born and brought up in Opava. Opava was the capital of Austrian Silesia for almost all of Adler's life, only becoming part of Czechoslovakia after the defeat of Germany and Austria-Hungary in World War I. All Adler's publications were in German but he did publish a few in Czech journals.

In 1879 Adler graduated from the secondary school in Opava and entered the university in Vienna. After taking undergraduate courses at the University of Vienna, Adler undertook research in descriptive geometry graduating in 1884. He began publishing during these years with papers on ruled surfaces and space curves such as: *Striktionslinien der Regelflächen 2. und 3. Grades* Ⓣ (1882); *Raumkurven vierter Ordnung 2. Art* Ⓣ (1883); *Weitere Bemerkungen über Raumkurven vierter Ordnung 2. Art* Ⓣ (1883); and *Spezielle Raumkurven vierter Ordnung 2. Art* Ⓣ (1883).

Adler was appointed as an assistant in astronomy and geodesy in Vienna in 1885 holding this position for two years. He made visits to the University of Berlin and to the University of Göttingen to further his studies. In 1901 he submitted his habilitation thesis on descriptive geometry to the University of Vienna. He became a professor at Vienna in 1909.

In 1797 Mascheroni had shown that all plane construction problems which could be made with ruler and compass could in fact be made with compasses alone. His theoretical solution involved giving specific constructions, such as bisecting a circular arc, using only a compass.

In 1906 Adler applied the theory of inversion to solve Mascheroni construction problems in his book *Theorie der geometrischen Konstruktionen* Ⓣ published in Leipzig. Since he was using inversion Adler now had a symmetry between lines and circles which in some sense showed why the constructions needed only compasses. However Adler did not simplify Mascheroni proof. On the contrary, his new methods were not as elegant, either in simplicity or length, as the original proof by Mascheroni.

This 1906 publication was not the first by Adler studying this problem. He had published a paper on the theory of Mascheroni's constructions in 1890, another on the theory of geometrical constructions in 1895, and one on the theory of drawing instruments in 1902.

As well as his interest in descriptive geometry, Adler was also interested in mathematical education, particularly in teaching mathematics in secondary schools. His publications on this topic began around 1901 and by the end of his career he was publishing more on mathematical education than on geometry. Most of his papers on mathematical education were directed towards teaching geometry in schools, but in 1907 he wrote on modern methods in mathematical instruction in Austrian middle schools. He produced various teaching materials for teaching geometry in the sixth-form in Austrian schools such as an exercise book which he published in 1908.

One final work by Adler should be mentioned, namely the five figure logarithm tables which he published in 1909.

**Article by:** *J J O'Connor* and *E F Robertson*

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