The paper will be dedicated to the analysis of geometric constructions discussed in secondary schools operating in Polish lands under the Prussian Partition in the 19th century. The analysis will cover schools preparing for the secondary school leaving examinations (Matura examinations), primarily gymnasia and selected types of real schools. An attempt will be made to discuss the intended, implemented and attained curricula in the field of geometric constructions. Intended curricula will be characterized based on the material placed in the textbooks, the content of ministerial orders and analysis of certain reformation attempts made by selected teachers and described in their publications. The basic sources that allow us to discuss the implemented and attained curricula will be teachers’ publications containing a description of the material they taught in schools, Matura tasks, e.g. from the gymnasium in Kwidzyn, or preserved geometry notebooks of students.


In gymnasia, geometric constructions were discussed during mathematics lessons. In real-type schools, they were also explored in “line drawing” (descriptive geometry) lessons, and were covered in preparation for more difficult topics. For example, F. Kronke, a teacher of the real school in Grudziądz, in 1901 published an article in which he presented the geometric constructions he discussed during linear drawing lessons in the Upper Tertia class [1].


The most popular textbooks in the Prussian Poland were [2], [3], [4], less popular ones include: [5], [6]. On the one hand, “the quality of the most widely used books allows conclusions to be drawn about the level of teaching generally achieved on this topic” ([7], p. 21). On the other hand, the most popular textbooks were often “non-scientific, e.g. Kambly’s and Mehler’s”, which means that they allowed, and perhaps sometimes even forced, a broader contribution of individual teachers to the material they taught ([8], p. 25).


In the paper, the expansion of teaching programs, which was done by Prussian Poland teachers to better prepare young people for Matura exams and university studies, will be analyzed. The fact that young people in schools are insufficiently prepared for studies in the field of geometric constructions were raised by, among others, graduates of the Gymnasium in Toruń. Therefore, the local teacher, O. Reichel, decided to expand the material regarding geometric constructions in a way discussed in [9]. Other teachers also prepared publications supplementing the curricula in this field, including: K. Güßlaff from the Gymnasium in Kwidzyn, who in [10] discussed about 20 construction tasks (along with methodological notes) recommended for discussion in schools, the teacher of Gymnasium in Chojna, F. v. Lühmann, who in [11] presented various ways to solve the problems of Appolonius, and the teacher of the Gymnasium in Gdańsk, W.A. Förstemann, author of the textbook “Lehrbuch der Geometry” (Danzig, 1827). There were also publications in which teachers corrected certain information contained in the most popular and most valued school textbooks. For example, F. Funck, a teacher at the Gymnasium in Chełmno, in [12] improved selected geometric constructions from [3]. The paper will discuss the material contained in these publications along with the authors’ original contributions. The way in which publications selected from the ones mentioned above were assessed by the mathematical world at that time will also be analyzed. An important part of the paper will be the solution of selected construction problems from the 19th century.



[1] Kronke, F. (1901). Das Linearzeichnen in der Realschule. Ein Beitrag zur Frage über die Gestaltung des geometrischen Zeichenunterrichts an den höheren Lehranstalten. Städtische Oberrealschule zu Graudenz, XIII. Jahresbericht über das Schuljahr Ostern 1900/1901. Graudenz.

[2] Kambly, L. (1877). Die Elementar Mathematik, vol. 2: Planimetrie (ed. 44). Breslau.

[3] Koppe, K. (1852). Anfangsgründe der reinen Mathematik für der Schul- und Selbst-Unterricht, vol. 2: Planimetrie (ed. 4). Essen.

[4] Mehler, F.G. (1869). Hauptsätze der Elementar-Mathematik zum Gebrauche an Gymnasien und Realschulen (ed. 4). Berlin.

[5] Brettner, H. (1847). Lehrbuch der Geometrie für Gymnasien, Realschulen und höhere Bürgerschulen. Breslau.

[6] Lieber, H. & Lühmann, F. (1887). Geometrische Konstructionaufgaben. Berlin.

[7] Schotten, H. (1890). Inhalt und Methode des Planimetrischen Unterrichts. Leipzig.

[8] Simon, M. (1906). Ueber die Entwicklung der Elementar-Geometrie im XIX Jahrhundert. Leipzig.

[9] Reichel, O. (1866). Beiträge für den Unterricht in der Geometrie. Thorn.

[10] Güßlaff, K. (1852). Ueber das Auflösen planometrischer Aufgaben. Jahresbericht über das königliche Gymnasium zu Marienwerder 1852. Marienwerder.

[11] Lühmann, Friedrich (1882). De sectio rationis, sectio spatii und sectio determinata des Apollonius nebst einigen verwandten geometrischen Aufgaben. Programm des Friedrich-Wilhelms-Gymnasium zu Königsberg in der Neumark, mit welchem zu der öffentlichen Prüfung der Schüler am 30. und 31 März. Königsberg i. d. N.

[12] Funck, F. (1855). Beiträge zu einer genauem Würdigung des Wesens der Anwendung der Algebra auf die Geometrie, Culm.