op.
10, you remember, when we bisected the stick of nougat. That's right.

Now from D draw DC at right angles to AB, and meeting the lawn at C.
You can do that with a hoe.

Produce CD to meet the lawn again at E.

Now we do some more of that bisecting; this time we bisect EC at F.

Then F shall be the middle of the bed; and that's where your rose-tree
is going.

PROOF???--Well, I mean, if F be _not_ the centre let some point
G, outside the line CE, be the centre and put the confounded tree
_there_. And, what's more, you can jolly well join GA, GD and GB, and
see what that looks like.

Just cast your eye over the two triangles GDA and GDB.

Don't you see that DA is equal to DB (unless, of course, you've
bisected that chord all wrong), and DG is common, and GA is equal to
GB--at least according to your absurd theory about G it is, since they
must be both _radii_. _Radii_ indeed! _Look_ at them. Ha, ha!

Therefore, you fool, the angle GDA is equal to the angle GDB.

Therefore they are both right angles.

Therefore the angle GDA is a right angle. (I know you think I'm
repeating myself, but you'll see what I'm getting at in a minute.)

_Therefore_--and this is the cream of the joke--therefore--really, I
can't help laughing--therefore _the angle CDA is equal to the angle
GDA!_ That is, the part is equal to the whole--which is ridiculous.

I mean, it's too _laughable_.

So, you see, your rose-tree is not in the middle at all.

In the same way you can go on planting the old tree all over the
bed--anywhere you like. In every case you'll get those right angles in
the same ridiculous position--why, it makes me laugh _now_ to think of
it--and you'll be brought back to dear old CE.

And, of course, any point in CE _except_ F would divide CE unequally,
which I notice now is just what you've done yourself; so F is wrong
too.

But you see the idea?

What a mess you've made of the bed!

BOOK I., PROPOSITION 20.

THEOREM.--_Any two sides of a triangle are together greater than the
third side_.

Let ABC be a triangle.

[Illustration]

CONSTRUCTION.--You know the eleventh hole? Well, let B be the tee,
and let C be the green, and let BC be my drive. Yes, _mine_. Is it
dead? Yes.

Now let BA be _your_ drive. I'm afraid you've pulled it a bit and gone
into the road by the farm.

You can't get on to the green by the direct route AC because you're
under the wall. You'll have to play further up the road till you