JB/135/076/003

Click Here To Edit

As the truth of the
explanation of the
meaning of the expression
square root may
be exemplified by a
plain figure like that
of a Draught board
exhibiting sufficient containing a competent
number of squares
so may the truth
of the explanation of
the meaning of the
expression cube root</hi
be exemplified by
a sufficient number
of <hi rend="underline">dice.

Upon a line of 3
dice considered taken as a
base as root you
may so heap up lines
of dice (2 in number,
making 3 lines in
the whole) that of the
figure composed of
them two of the surface
shall exhibit
each of them the
appearance of a square
which done, upon the square thus
formed, taking it for
a root or base, you
heap up similar sets
of dice, 2 in number,
(making, in the whole 3 such sets
of lines of dice, three
dice in a line) in such
manner that the figure
composed of these
525 dice shall itself
be of the form of a die. In

---page break---

In the same manner
you may make
a cube or die
a compound cube
or die by lines
and sets of 2 dice
of composed of 4
dice, or the square
of the square of 2
dice, of 64 dice,
or the square of the
square of 4 dice,
and so on: but
not of any of num
intermediate number
of dice between 8
27, and 64, and
so on forth:

---page break---

Surd in its archetypal
meaning is
deaf: analogically, & therefore better ashizous,
rootless.

Second, 3d, 4th power
of a number: the
expression elliptical: -
at length it means
the 2d, 3d, 4th product of the self-
multiplicative power
of the number. The
tir power, thus
accompanied is
proper and significative:
since no
other power number
in question is
capable of producing
the product in
question, at least without
the help of some
other number.

Biquadrate used
improperly for the
4th power of a number:
it should rather
be applied to
the 3d power, to the
cube: the cube being
the square of the
square: being to the
square what the
square is to the
line

A circulate is a
compound repetend:
i:e: a repetend
composed of
several figures instead
of one.

---page break---

At the 3d power or cube the analogy between the figure and number ceases. By raising the number of elementary units to the 4th power, you do not get a figure an object which is to 4th cube what the cube is to its component square It cannot be called a double cube: for though were the elementary line is composed of two units two component cubes, by involving raising the number of those units to the 4th power you get enough to make 2 cubes, yet this is not the case with the cube of any other number: by raising 3 to the 4th power you get units enough not merely to make 2 cubes each leaving for its cube root a line of 3, but 4,3 such cubes: so by raising 4 to the 4th power 4 such cubes, by raising 5, 5 cubes and so on.

Identifier: | JB/135/076/003"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	003	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
Box Contents