In this paper the theory of the striction lines on a ruled surface of the second degree is studied in a purely geometrical way and the characters of the striction lines on a ruled surface of the third degree are determined. The simplest possible construction methods are sought for the striction lines on a second degree surface. In addition, there are also theorems about general rational space curves.

When you look at the absolute numbers, the year 1880/81 and the following year catches your eye, because initially the number of native Czech speakers at German secondary schools rises by more than 200, but drops almost a year later to their old level back. During the increase primarily with the foundation of the German high school in Smichov and especially the German Oberrealschule in Karolinental, which 122 native speakers still choose in spite of the opening of the Municipal Czech Upper Real School in Karolinental in the same year, the following decline is spread across all institutions with the German language of instruction. The division of the university at this time appears to be the obvious reason for this development, because it makes secondary schools teaching in the Czech language more attractive to the developing Czech circles of the education-oriented middle class, which has so far preferred German secondary education.

The book gives a coherent presentation of the methods and theories for solving geometric construction tasks, the development of which the author himself is known to have played a significant part. After a description of the construction methods found by Petersen, the Steiner and the Mascheroni constructions are explored, as well as those with the help of a parallel ruler, one or more movable right angles, a gauge or a bisector. This is followed by theoretical considerations about the classification of the geometrical construction tasks and the proof of the possibility and impossibility of solving a specific geometric task with a compass and ruler. After a section on circle division, in which seventeen different divisions are described, there follow solutions of the Delian problem, angle trisection and, in general, third and fourth degree equations by means of various construction methods, as well as historical remarks on the rectification of the circle. A final section is devoted to Lemoinian geometrography.

In the direction of the investigation initiated by Mascheroni (Pavia 1797) and von Steiner (Berlin 1833) about the aids or tools that are unnecessary or necessary to solve geometric construction tasks, a noteworthy work is written here, which shows that any problem that can be solved with a compass and ruler can also be solved, if further aids are not allowed other than either only the ruler (two parallel lines at a constant distance) or only the right angle (for example made of wood) or only a certain acute angle (for example made of wood). Since we know from Steiner's work that using the ruler alone can only solve any second degree problem if a fixed circle can be used in the plane, the use of the ruler in the sense of Mr Adler is of course different understand as with Steiner, namely in such a way that it also allows a parallel to a straight line to be drawn at a fixed distance (width of the ruler). Likewise, the application of the wood angle should also allow, for example, the search in a straight line for the point from which a fixed distance appears at the angle of the wood angle. So it is shown that in "practice" each of the four most important drawing tools (compass, ruler, right angle, acute angle) alone is sufficient to solve all tasks of the second degree. At the end it is proven that by using several right angles, tasks of the third and fourth degree can also be solved. Such tasks were once shown by Kortum that they can only be solved with a ruler if a fixed cone can be used.

Hilbert [refers to Adler's 1890 paper], which deals with constructions executable by a draughtsman whose only means of construction is a wooden right-angle. He shows that, assuming one has several right-angled triangles at one's disposal, one can solve in principle any cubic equation, and with perfect accuracy, assuming the means used to draw the right-angles are perfect. Hilbert's remark implicitly suggests replacing the use of the draughtsman's right-angle tool with the 'movement' of an angle, that is, with a congruence assumption which allows one to construct right-angles at any point and on any line.

... he showed that both a ruler to be used in a certain manner with two parallel edges and a set square, the edges of which meet in the arbitrarily fixed angle, have the same level of performance as circles and straight edge.

A subject like descriptive geometry, for example, can hardly be said to occupy any definite position, so rapidly changing are the views concerning its importance, its significance, and the schools in which it should be taught. Austria makes much of it in the Realschule, less of it in the Realgymnasium, and almost nothing of it in the Gymnasium.... In Austria, in the Realschulen, the subject [of geometric drawing and graphic representation] is nominally in the hands of a special teacher examined and appointed for the purpose. ... At present, in about a third of the schools, the teacher of mathematics is also the teacher of descriptive geometry in the three upper classes (V-VII). There is a well-defined line of demarcation between stereometry and descriptive geometry as the work is carried on, although the latter is employed in representing the solids met in the former. It appears, therefore, that certain definite work in descriptive geometry is done in the upper classes of the Realschulen. In the Gymnasien descriptive geometry is not a separate object of study. In the work in stereometry, however, plans and elevations are drawn, and orthogonal projections of parallelepipeds, octahedrons, pyramids, and the like are prepared.