&c. The theorem of Pascal remains
still the theorem of Pascal, and will always remain so.--

Sec. 105. (2) But the subject must be adapted to the consciousness of the
pupil, and here the order of procedure and the exposition depend upon
the stage which he has reached intellectually, for the special manner of
the instruction must be conditioned by this. If he is in the stage of
perception, we must use the illustrative method; if in the stage of
conception, that of combination; and if in the stage of reflection that
of demonstration. The first exhibits the object directly, or some
representation of it; the second considers it according to the different
possibilities which exist in it, and turns it around on all sides; the
third questions the necessity of the connection in which it stands
either with itself or with others. This is the natural order from the
stand-point of the scientific intelligence: first, the object is
presented to the perception; then combination presents its different
phases; and, finally, the thinking activity circumscribes the restlessly
moving reflection by the idea of necessity. Experiment in the method of
combination is an excellent means for a discovery of relations, for a
sharpening of the attention, for the arousing of a many-sided interest;
but it is no true dialectic, though it be often denoted by that name.

--Illustration is especially necessary in the natural sciences and also
in aesthetics, because in both of these departments the sensuous is an
essential element of the matter dealt with. In this respect we have made
great progress in charts and maps. Sydow's hand and wall maps and
Berghaus's physical atlas are most excellent means of illustrative
instruction; also Burmeister's zooelogical atlas.--

Sec. 106. The demonstrative method, in order to bring about its proof of
necessity, has a choice of many different ways. But we must not imagine,
either that there are an unlimited number, and that it is only a chance
which one we shall take; or that they have no connection among
themselves, and run, as it were, side by side. It is not, however, the
business of Pedagogics to develop different methods of proof; this
belongs to Logic. We have only to remember that, logically taken, proof
must be analytic, synthetic, or dialectic. Analysis begins with the
single one, and leads out of it by induction to the general principle
from which its existence results. Synthesis, on the contrary, begins
w