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Added math formatting to chapter 15 to match original

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Kenneth John Odle 2023-06-23 13:09:32 -04:00
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1 changed files with 11 additions and 11 deletions
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@ -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