diff --git a/main.tex b/main.tex
index f9d82f7..5aa6c03 100755
--- a/main.tex
+++ b/main.tex
@@ -2147,27 +2147,27 @@ make one large Square, with a side of three inches, and I had hence proved to
my little Grandson that --- though it was impossible for us to see the inside of
the Square --- yet we might ascertain the number of square inches in a Square by
simply squaring the number of inches in the side: ``and thus,'' said I, ``we know
-that three-to-the-second, or nine, represents the number of square inches in a
-Square whose side is three inches long.''
+that $ 3^2 $, or 9, represents the number of square inches in a
+Square whose side is 3 inches long.''
The little Hexagon meditated on this a while and then said to me; ``But you
have been teaching me to raise numbers to the third power: I suppose
-three-to-the-third must mean something in Geometry; what does it mean?''
+$ 3^3 $ must mean something in Geometry; what does it mean?''
``Nothing at all,'' replied I, ``not at least in Geometry; for Geometry has only
Two Dimensions.'' And then I began to shew the boy how a Point by moving
through a length of three inches makes a Line of three inches, which may be
-represented by three; and how a Line of three inches, moving parallel to
+represented by 3; and how a Line of three inches, moving parallel to
itself through a length of three inches, makes a Square of three inches every
-way, which may be represented by three-to-the-second.
+way, which may be represented by $ 3^2 $.
Upon this, my Grandson, again returning to his former suggestion, took me up
rather suddenly and exclaimed, ``Well, then, if a Point by moving three inches,
-makes a Line of three inches represented by three; and if a straight Line of
+makes a Line of three inches represented by 3; and if a straight Line of
three inches, moving parallel to itself, makes a Square of three inches every
-way, represented by three-to-the-second; it must be that a Square of three
+way, represented by $ 3^2 $; it must be that a Square of three
inches every way, moving somehow parallel to itself (but I don't see how) must
make Something else (but I don't see what) of three inches every way --- and
-this must be represented by three-to-the-third.''
+this must be represented by $ 3^3 $.''
``Go to bed,'' said I, a little ruffled by this interruption: ``if you would talk
less nonsense, you would remember more sense.''
@@ -2184,12 +2184,12 @@ Straightway I became conscious of a Presence in the room, and a chilling
breath thrilled through my very being. ``He is no such thing,'' cried my Wife,
``and you are breaking the Commandments in thus dishonouring your own
Grandson.'' But I took no notice of her. Looking around in every direction I
-could see nothing; yet still I felt a Presence, and shivered as the cold
+could see nothing; yet still I \textit{felt} a Presence, and shivered as the cold
whisper came again. I started up. ``What is the matter?'' said my Wife, ``there
is no draught; what are you looking for? There is nothing.'' There was nothing;
and I resumed my seat, again exclaiming, ``The boy is a fool, I say;
-three-to-the-third can have no meaning in Geometry.'' At once there came a
-distinctly audible reply, ``The boy is not a fool; and three-to-the-third has
+$ 3^3 $ can have no meaning in Geometry.'' At once there came a
+distinctly audible reply, ``The boy is not a fool; and $ 3^3 $ has
an obvious Geometrical meaning.''
My Wife as well as myself heard the words, although she did not understand