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As the truth of the explanation of the meaning of the expression square root may be exemplified by a | <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: | |||
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
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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. |
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1794-12-11 |
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135 |
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076 |
arithmetic |
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003 |
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rudiments sheet (brouillon) |
2 |
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recto |
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jeremy bentham |
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46194 |
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