unless you do the same, you cannot expect to be like them. Also, clever
untrained people often feel very much hampered by their want of training;
you see the cleverness, but they feel how much more they could have done
if they had been trained. Therefore, do not allow yourselves to think
"Euclid is no good, because 'Aunt So-and-so' is quite clever enough, and
she never did it;" depend upon it, that is not going the right road to be
like her. I feel quite sure that if this "not impossible aunt" had had
opportunities of learning Euclid when she was young, she would have done
it, and very well too! Of course, if you mean to read Mathematics from
choice by-and-by, you will work hard at the subject now, but I can quite
understand that those who are not going to do this, perhaps sometimes
feel, "What is the good? I shall never look at a Euclid again after I
leave school--I want to learn how to hold my own in after-life,--I want to
be able to talk when I come out,--I want to be a sensible woman, whose
opinion will be asked by other people,--I want to be clever at house-work
or cooking, or to be able to manage a shop,--I want to be strong enough
and wise enough to be a support and comfort to others,--I want to be a
useful woman and not a mathematician!" Well! that is just what I want you
to be, but I am quite sure that Mathematics will help you to this, by
making you accurate and reasonable and attentive, without which qualities
you will be no use and very little comfort. If you work hard at
Mathematics while you are here, and gain these qualities, you have my free
leave to shut your Euclid for good on the day you leave school,--you will
have learnt his best lessons.

Is there any great mental good which you can gain by the study of
Languages, quite apart from the advantage of being able to read and speak
when you go abroad? Yes; it enlarges your mind to know the various ways in
which things are expressed by different nations. A person who knows no
language but his own is like a man who can only see with one eye. It opens