ng cannot be
acquired late in life without _unusual_ labour, and uncommon
fortitude.

FOOTNOTES:

[15] V. A strange instance quoted by Mr. Stewart, "On the Human Mind,"
page 152.

[16]

NOTE.

1 Two is 1 the - name for 2 =

1 1 1 1 2 - - 3 3 = =

1 1 1 1 1 1 2 1 2 3 2 - - - - 4 4 4 4 = = = =

1 1 1 1 1 1 1 1 1 1 1 2 3 1 2 3 4 2 2 - - - - - - 5 5 5 5 5 5 = = = =
= =

1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 2 2 3 4 2 3 1 2 3 4 5 2 2 2 2
3 3 - - - - - - - - - - - 6 6 6 6 6 6 6 6 6 6 6 = = = = = = = = = = =

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 2 1 1 1 1 1 1 1 2 2 3 4
5 2 3 4 1 2 3 4 5 6 2 2 2 2 2 3 3 3 - - - - - - - - - - - - - - 7 7 7
7 7 7 7 7 7 7 7 7 7 7 = = = = = = = = = = = = = =

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 1 1 1 1 2 2 1
2 1 2 1 1 1 1 1 1 1 1 2 2 2 2 2 3 3 4 1 2 3 4 5 6 7 2 2 2 3 3 3 3 3 -
- - - - - - - - - - - - - - 8 8 8 8 8 8 8 8 8 8 8 8 8 8 8 = = = = = =
= = = = = = = = =

1 1 2 1 1 5 2 2 3 4 2 2 3 4 4 4 4 5 6 - - - - - - - 8 8 8 8 8 8 8 = =
= = = = =

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 1
1 2 1 1 1 1 1 1 1 1 1 2 2 1 2 2 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 3 1 2 3
4 5 6 7 8 2 2 2 3 3 3 3 - - - - - - - - - - - - - - - 9 9 9 9 9 9 9 9
9 9 9 9 9 9 9 = = = = = = = = = = = = = = =

1 1 1 1 1 1 2 3 1 2 1 1 2 1 1 2 1 3 3 4 4 5 6 2 2 4 5 2 2 2 2 3 3 3 3
3 3 4 4 4 4 5 5 6 7 - - - - - - - - - - - - - - 9 9 9 9 9 9 9 9 9 9 9
9 9 9 = = = = = = = = = = = = = =

[17] The word calculate is derived from the Latin calculus, a pebble.

[18] This method is recommended in the Cours de Math, par Camus, p.
38.

CHAPTER XVI.

GEOMETRY.

There is certainly no royal road to geometry, but the way may be
rendered easy and pleasant by timely preparations for the journey.

Without any previous knowledge of the country, or of its peculiar
language, how can we expect that our young traveller should advance
with facility or pleasure? We are anxious that our pupil should
acquire a taste for accurate reasoning, and we resort to Geometry, as
the most perfect, and the purest series of ratiocination which has
been invented. Let us, then, sedulously avoid whatever may disgust
him; let his first steps be easy, and successful; let them be
frequently repeated until he can trace them without a guide.

We have recommended in the chapter upon Toys, that children should,
from their earliest years, be accustomed to the shape of what are
commonly called