From d217cb6e3befd3c3f89128bf37703e43fd62317c Mon Sep 17 00:00:00 2001 From: Kenneth Odle Date: Fri, 23 Jun 2023 13:09:32 -0400 Subject: [PATCH] Added math formatting to chapter 15 to match original --- main.tex | 22 +++++++++++----------- 1 file changed, 11 insertions(+), 11 deletions(-) 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