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 om 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 6,7,,,10,11,12,13,14,15, or 17 squares, and so on.

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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