JB/135/076/003: Difference between revisions

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As the truth of the explanation of the meaning of the expression square root may be exemplified by a plan figure like that of a Draught board exhibiting sufficient containing a competent number of squares  so <gap/>may the truth of the explanation of the meaning of the expression cube root be exemplified by a sufficient number of dice. Upon a line of 3 dice considered taken as a base or 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 if 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
<p>As the truth of the <lb/>
explanation of the <lb/>
meaning of the expression <lb/>
<hi rend="underline">square</hi> <hi rend="underline">root</hi> may <lb/>
be exemplified by a <lb/>
plain figure like that <lb/>
of a Draught board <lb/>
<add>exhibiting sufficient</add> containing a competent <lb/>
number of squares  <lb/>
so <gap/>may the truth <lb/>
of the explanation of <lb/>
the meaning of the <lb/>
expression <hi rend="underline">cube</hi> <hi rend="underline">root</hi<lb/>
be exemplified by <lb/>
a sufficient number <lb/>
of <hi rend="underline">dice</hi>.</p>
 
<p>Upon a line of 3 <lb/>
dice considered <add>taken</add> as a <lb/>
base as root you <lb/>
may so heap up lines <lb/>
of dice (2 in number, <lb/>
making <del><gap/></del> 3 lines in <lb/>
the whole) that of the <lb/>
figure composed of <lb/>
them two of the surface <lb/>
shall exhibit <lb/>
each of them the <lb/>
appearance of a square <lb/>
<add>which done,</add> upon the square thus <lb/>
formed, taking it for <lb/>
a root or base, you <lb/>
heap up similar sets <lb/>
of dice, 2 in number, <lb/>
(making, <add>in the whole</add> 3 such sets <lb/>
of lines of dice, three <lb/>
dice in a line) in such <lb/>
manner that the figure <lb/>
composed of these <lb/>
<del>5</del><add>25</add> dice shall itself <lb/>
be of the form of a die. <add>In</add></p><pb/>
 
In the same manner you make a cube or die a compound cube or die by lines and sets of 2 dice of composed of a 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 mem intermediate number of dice between 8 27, and 64, and so on forth:
 
 
 





Revision as of 05:45, 27 December 2017

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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 make a cube or die a compound cube or die by lines and sets of 2 dice of composed of a 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 mem intermediate number of dice between 8 27, and 64, and so on forth:





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

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