By Schlepkin A.K.

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37), a Discomedusa of octagonal symmetry. For the coelentera occupy a place in the phylogenetic evolution where cyclic has not yet given way to bilateral symmetry. Haeckel's extraordinary work, in which his interest in the concrete forms of organisms finds expression in countless drawings executed in minutest detail, is a true nature's codex of symmetry. Equally revealing for Haeckel, the biologist, are the thousands and thousands of figures in his Challenger Monograph, in which he describes for the first time 3,508 new species of radiolarians discovered by him on the Challenger Expedition, 1887.

There exist special coordinate systems, the Cartesian ones, in which this form assumes the simple x:; they consist of two muexpression x; tually perpendicular vectors el, es of equal length 1. I n metric geometry all Cartesian coordinate systems are equally admissible. e. by a homogeneous linear transformation ( 2 ) , (2') which leaves the form x: xi unaltered, x: x; = x:" xy. But with a slight modification such a transformation may also be interpreted as the algebraic expression of a rotation.

As long as we use no other concepts than those introduced so far, namely (1) addition b, (2) multiplication of a vecof vectors a tor a by a number A, (3) the operation by which two points A,B determine the vector + variables xl, x2 except forxl = x2 = 0 . There exist special coordinate systems, the Cartesian ones, in which this form assumes the simple x:; they consist of two muexpression x; tually perpendicular vectors el, es of equal length 1. I n metric geometry all Cartesian coordinate systems are equally admissible.

### 2-complete subgroups of a conjugately biprimitively finite group with the primary minimal condition by Schlepkin A.K.

by Paul

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