Im ersten Teil des Aufsatzes werden einige grundlegende Besonderheiten der projektiven Geometrie vorgestellt. Dieser liegt eine Denkweise zugrunde, die geeignet ist, das unendlich Ferne in die Betrachtung mit einzubeziehen. Die Grundelemente Punkt, Gerade und Ebene werden dadurch neu überschaubar. Ferner wird das Prinzip der Polarität erläutert und ein Blick auf den Raum geworfen. Rudolf Steiners Darstellung der Goetheschen Raumauffassung zeigt Spuren der Beschäftigung mit der projektiven Geometrie und arbeitet heraus, dass man die drei Dimensionen des Raumes als Erkenntnisstufen auffassen kann. Dies entspricht der organischen Raumauffassung Goethes. Die dreifache Ausdehnung und Zusammenziehung, die Goethe im Verlauf seiner Studien an der Pflanze als das Grundprinzip der pflanzlichen Entwicklung gefunden hat, zeigt die Pflanze als in den Raum eingebettetes und diesen auch zum Ausdruck bringendes Wesen. Die drei Dimensionen des Raumes (als Erkenntnisstufen aufgefasst) korrespondieren mit dieser dreifachen Ausdehnung und Zusammenziehung.
N1 -In the first part of this article some key elements of projective geometry are introduced. This geometry is based on a way of thinking that is able to take the infinitely distant into consideration. Through this, the fundamental elements of point, line and plane can be described in a new way. We will elucidate the principle of polarity and gain a new look at the concept of space. Rudolf Steiner's portrayal of Goethe's idea of space reveals that he had worked with projective geometry in his early years of study. Steiner points out that the three dimensions of space can be understood as three distinct levels of knowledge which correspond to Goethe's organic idea of space. Goethe studied the metamorphosis of plants and discovered three phases of expansion and contraction as constituting principles. They are expressed to different extents during the development of an individual plant. Thus, these three phases correspond to the three dimensions of space and therefore to the above mentioned levels of knowledge.
In the first part of this article some key elements of projective geometry are introduced. This geometry is based on a way of thinking that is able to take the infinitely distant into consideration. Through this, the fundamental elements of point, line and plane can be described in a new way. We will elucidate the principle of polarity and gain a new look at the concept of space. Rudolf Steiner's portrayal of Goethe's idea of space reveals that he had worked with projective geometry in his early years of study. Steiner points out that the three dimensions of space can be understood as three distinct levels of knowledge which correspond to Goethe's organic idea of space. Goethe studied the metamorphosis of plants and discovered three phases of expansion and contraction as constituting principles. They are expressed to different extents during the development of an individual plant. Thus, these three phases correspond to the three dimensions of space and therefore to the above mentioned levels of knowledge.