In observing the growth of the plant, Goethe had perceived that this proceeds simultaneously according to two different principles. On the one hand the plant grows in an axial direction and thereby produces its main and side stems. To this growth principle Goethe gave the name ‘vertical tendency’. Were the plant to follow this principle only, its lateral shoots would all stand vertically one above the other. But observation shows that the different plant species obey very different laws in this respect, as may be seen if one links up all the leaf buds along any plant stem; they form a line which winds spiral fashion around it. Each plant family is distinguishable by its own characteristic spiral, which can be represented either geometrically by a diagram, or arithmetically by a fraction. If, for example, the leaves are so arranged in a plant that every fifth leaf recurs on the same side of the stem, while the spiral connecting the five successive leaf-buds winds twice round the stem, this is expressed in botany by the fraction 2 / 5. To distinguish this principle of plant growth from the vertical tendency, Goethe used the term ‘spiral tendency’.