JB/135/076/002

Click Here To Edit Arithmetic 11. Dec 1794

Square root means
the root of the
square: not a figure root
of a square form,
but the root of a
figure of a square
form.

The ambiguity arises
from the double
signification of
the word square,
having either a substantive
or an adjective,
Then In
the above expression
square root it appears
to be used
shews at first sight
as if used adjectively
(that being its
original signification)
whereas it
is intended to be
taken substantively
The square root,
just as
meaning the root
of the square, just
as we say the Parish
Priest, meaning
the Priest of
the Parish.

By means of this
ambiguity the
same sort of perplexity
is produced
as would be produced
if meaning to the stile
a particular man
the Man of the Green,
we were to speak of
him by the name of
the green man.

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So the Cube Root ,
means the root of
the Cube.

A Square number
is so called from
this circumstance,
from this property
belonging to it, that
supposing the units
denoted by it to
be squares, they
would, taken together,
be capable
of being arranged
in the form of a
square: which is
not the case of with
any number that
is not a square.
Thus 4 is a square
number: for 4 equal
squares are capable
of being arranged in
the form of a square.
For the same reason
so is 9: so isare 16,
25 &c. Whereas
at the same time
that no numberthat property
between is not found
in any of the intermediate
numbers.
You can not make
a square out of two
squares: nor out of
3 squares: nor out
of 5 squares; nor
out of 6,7, 8, 10,
11,12,13,14,15, or
17 squares, and so
on.

Four being a square
number, 2 is the
square root of that
number: that is
4 being such a
number that a
set of squares
composed of such
a number of squares are
capable of being
placed in form
of a square, when
that form is produced
[+], two of those
component squares
will form the seat
bottom, base, or
root as it may
be called of such
square.

A square number
may accordingly therefore
be defined, any
number of which
the component units
if squares, are capable
of being arranged
in form of
a square without
any interstices, in
the form of a square.

In like manner a cube number may be defined any number which the component units, if cubes, are capable of being arranged without any interstices in the figure of a cube.

Identifier: | JB/135/076/002"JB/" can not be assigned to a declared number type with value 135.
Date_1	1794-12-11	Marginal Summary Numbering
Box	135	Main Headings
Folio number	076	Info in main headings field	arithmetic
Image	002	Titles
Category	rudiments sheet (brouillon)	Number of Pages	2
Recto/Verso	recto	Page Numbering
Penner	jeremy bentham	Watermarks
Marginals		Paper Producer
Corrections		Paper Produced in Year
Notes public		ID Number	46194
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