In order, however, that this demand be accommodated to the time at disposal and the capabilities of the students, the following rules are to be observed:—
1. The students of the first cœtus having already passed their examination for Portépée ensign, and the Predicate ziemlich gut, in their mathematical examination, being requisite for entry into the School, it is to be presumed that they enter with a good or at least sufficient preparatory knowledge. Still, as it is not to be expected that the necessary requirement in arithmetic and algebra will be possessed throughout, the first part of the instruction must be considered as the most important, and be given thoroughly and fundamentally.
2. Such portions of mathematics as are less necessary for Artillerists and Engineers (for instance, astronomy and the higher geodesy,) are to be entirely omitted from the lectures.
3. As even in such portions as fall within the scope of the lectures, there is much that can not be exhausted, therefore all that belongs solely to speculative views, or possibly only serves to the rounding or perfecting a system, must be passed over. The instruction in mathematics stands in near and frequent connection with the lectures on artillery, architecture, mechanics, physics, theory of surveying, and with drawing lessons, as well as with practical mensuration.
These belong specially—
a. To Artillery: architecture, mechanics; the application of all those formulas which the mathematical lectures have to deduce and to prove.
b. To Physics: the theories of dioptrics, and catoptrics, which the students require to a perfect understanding of the construction of telescopes and reflecting instruments; what is necessary from aerometry and aerostatics.
c. To Drawing lessons: practical working out of the theory of perspection, and the construction of shadows.
d. To the theory of Surveying: a knowledge of all the instruments requisite for mensuration and leveling, and the principal theorems, with their application to cases occurring in mensuration.