Capitolo 60
answers had been so satisfactory that I had been incited for compensating him/it
giving him some suggestions on Arithmetic, as applied to the Geometry.
Nine Plazas that you/they take, every one thumb every way, I had put together them
then as to make a great Plaza with a side of three thumbs,,
and I had it tried to mine small Nephew from now that--although it
it was impossible for us to See the inside of the Plaza--
we would still verify the number of square thumbs in a Plaza
simply squaring the number of thumbs in the side: "and this way,"
says me, "we know that three-to-the-second or nine, represent the
number of square thumbs in a Plaza whose side is three thumbs along."
The small Hexagon meditated on this once and then it told me;
"But you are teaching to raise me numbers to the third power:
I suppose that three-to-the-third has to intend anything in Geometry; that that ago
does he/she want to say?" "Nothing to all", he/she answered me, "not at least in Geometry;
for the Geometry it only has Two Dimensions." And then I started to shew the boy
as a Point moving ago himself/herself/itself through a length of three thumbs a Line of
three thumbs that can be represented within three; and as a Line of three
thumbs, parallel touching to him through a length of three thumbs,
ago of a Plaza of three thumbs every way that can be represented
within three-to-the-second.
xxx
On this, my Nephew, returning again to his/her first suggestion,
rather suddenly takes me on and it exclaimed, "Well, then, if a Point from
three touching thumbs, ago a Line of three thumbs represented within three;
and if a right Line of three thumbs, parallel touching to him,
ago of a Plaza of three thumbs every way, represented within three-to-the-second;
it has to be that a Plaza of three thumbs every way, transporting somehow parallel
to him (but I don't see how) it has to do anything other (but I don't see that that)
of three thumbs every way--and this must be represents within three-to-the-third."
"Goes in bed", it said me, an a little ruffled by this interruption: