often overwhelmed with
quantity and variety of material that makes formation
impossible to them."

"The demand of the new gift, therefore, is that the oblique
line, hitherto only transiently indicated, shall become an
abiding feature of its material."

"In the forms made with the fifth gift there rules a living
spirit of unity. Even members and directions which are
apparently isolated are discovered to be related by
significant connecting members and links, and the whole shows
itself in all its parts as one and living,--therefore, also,
as a life-rousing, life-nurturing, and life-developing
totality." FR. FROEBEL.

1. The fifth gift is a three-inch cube, which, being divided equally
twice in each dimension, produces twenty-seven one-inch cubes. Three
of these are divided into halves by one diagonal cut, and three others
into quarters by two diagonal cuts crossing each other, making in all
thirty-nine pieces, twenty-one of which are whole cubes, the same size
as those of the third gift.

2. The fifth gift seems to be an extension of the third, from which it
differs in the following points:--

The third gift is a two-inch cube, the fifth a three-inch cube; the
third is divided once in each dimension, the fifth twice. In the third
all the parts are like each other and like the whole; in the fourth,
they are like each other but unlike the whole; and in the fifth they
are not only for the most part unlike each other, but eighteen of them
are unlike the whole.

The third gift emphasized vertical and horizontal divisions producing
entirely rectangular solids; the fifth, by introduction of the
slanting line and triangular prism, extends the element of form. In
the third gift, the slanting direction was merely implied in a
transitory way by the position of the blocks; in the fifth it is
definitely realized by their diagonal division.

In number, the third gift emphasized two and multiples of two; the
fifth is related to the fourth in its advance in complexity of form
and mathematical relations.

3. The most important characteristics of the gift are: introduction of
diagonal line and triangular form; division into thirds, ninths, and
twenty-sevenths; illustration of the inclined plane and cube-root. As
a result of these combined characteristics, it is specially adapted to
the production of symmetrical forms.

It includes not only mult