1. Introduction. The following remarks concern two different parts of the theory of extreme quadratic forms. In §2, I shall give a new proof for the theorem of Voronoï (4), which asserts that a form is extreme if and only if it is both perfect and eutactic. (For the definitions see, e.g., Coxeter (2) or the text below.) There is indeed a comparatively simple proof in Bachmann's Zahlentheorie, IV, 2. For two reasons, however, it may not be useless to communicate another proof here.