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Arithmetic Dec. 11 1794

length, your lines
must be each of
them an inch in
breadth: and universally,
make your
side as short as you
will, if the length
of it consists of any
number of equal
parts, your ra the
breadth of your radical
line must be
equal to the length
of one of those parts.

In geometry then, by
the square of a
line can not be
understood athe square
formedcapable by the repetition
of a line, as
in arithmetic by
the square of a
number is understood
byone number
formed by the repetition
of another

By the square of
a line must be
understood a square rectangular
figure leaving one of its
sides and being a
square every one
of its sides of a
length equal to that
of the line: a square
having that line
for one of its boundaries,
and three
lines equal to that line
for the three other boundaries.

---page break---

If the square figure so
formed is to represent,
to exhibit exemplify
the idea of a square
number it must
be divided into
lines not of the
geometrical and fictitious sort
having no breadth,
but of the material
and real sort
having a thickness breadth
equal to the
breadth of a unit
of that sort of which
the number is in
question of that
sort which is said
to exist in the
number in question
of which the number
in question
is said to be the number.
If the subject
in question is
a field, and the
number of in question
the number
of square feet in
that field, the
lines by the repetition
of which the
square figure in
question is composed
must be lines
of a foot broad.

---page break---

The idea presented
at first mentionglance
by the term square
root is that of
a root of a square
form: by that of
a cube root, a
root of a cubical
form. The image
presented being
in one case at
least susceptible
of realization,
the false meaning
is the more apt
to take place in
the mind conception of the
true. You may
conceive True it
is that you can not
figure to yourself
the root of a tree

Identifier: | JB/135/075/002
"JB/" can not be assigned to a declared number type with value 135.



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