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<head>1821 Dec<hi rend="superscript">r</hi>. 22 M 2<lb/> | |||
Posology Arithmetic</head> | |||
<note>135<lb/> | |||
Course of Instruction<lb/> | |||
Order for teaching</note> | |||
<p>3 3</p> | |||
<note>14<lb/> | |||
Thence shew — only<lb/> | |||
by arithmetic can<lb/> | |||
geometrical ideas be<lb/> | |||
clarified.</note> | |||
<p>11. When the relation between arithmetic and geometry is <sic>shewn</sic><lb/> | |||
then may be the time for <sic>shewing</sic> that it is only by means of<lb/> | |||
arithmetic that any clear ideas can be obtained in the<lb/> | |||
subject of geometry.</p> | |||
<note>15<lb/> | |||
Analogous to arithmetical<lb/> | |||
repetends and<lb/> | |||
circulates are geometrical<lb/> | |||
<del>rep</del> incommensurables</note> | |||
<p>12. <sic>Shew</sic>, on this occasion, the relation of incommensurable<lb/> | |||
quantities in <hi rend="underline">geo</hi>metrical language to <hi rend="underline">repetends</hi> and<lb/> | |||
<hi rend="underline">circulates</hi> in <hi rend="underline">arith</hi>metical</p> | |||
<note>16<lb/> | |||
A circulate is a<lb/> | |||
compound repetend</note> | |||
<p>13 A <hi rend="underline">circulate</hi> is a compound repetend: a<lb/> | |||
continually repeated quantity, designated by a multitude<lb/> | |||
of figures instead of a single one.</p> | |||
<note>17<lb/> | |||
Source of repetends<lb/> | |||
the <hi rend="underline">decimal</hi> system<lb/> | |||
Would they be extirpated<lb/> | |||
by the <hi rend="underline">duo</hi>decimal?</note> | |||
<p>14 Repetends and circulates seem to have <add>it is believed</add> their origin<lb/> | |||
in the decimal form <add>system</add> of arithmetic. It would be curious<lb/> | |||
to see what would become of them in the <hi rend="underline">duodecimal</hi><lb/> | |||
system.</p> | |||
<note>18<lb/> | |||
Fraction supposes<lb/> | |||
division: <sic>shew</sic><lb/> | |||
relation <del>of</del> <add>between</add> <hi rend="underline">vulgar</hi><lb/> | |||
and <hi rend="underline">decimal</hi>.</note> | |||
<p>15 <hi rend="underline">Fraction</hi> supposes <hi rend="underline">division</hi>. <foreign>Quere</foreign> where would be the place<lb/> | |||
<add>in which</add> to <unclear>insert</unclear> the language of fractions — vulgar and decimal?</p> | |||
<p>16 Would not the operation <del>of <gap/></del> called <hi rend="underline">squaring<lb/> | |||
the circle</hi> be effected by the substitution of <add>the</add> <hi rend="underline">duodecimal</hi> system<lb/> | |||
to the <hi rend="underline">decimal</hi>?</p> | |||
<p>17 By the duodecimal system might not the mode of<lb/> | |||
designation by cleared by the obscurity involved in the idea<lb/> | |||
of mutually <hi rend="underline">incommensurable</hi> quantities?</p> | |||
<note>19<lb/> | |||
Arithmetic explains<lb/> | |||
geometry: <add><gap/> of</add> <hi rend="underline">atoms</hi><lb/> | |||
constitute <hi rend="underline">figures</hi>,<lb/> | |||
<hi rend="underline">atom</hi> means <hi rend="underline"><sic>indivible</sic></hi></note> | |||
<p>18 Essential to clearness of conception is geometry is clearness<lb/> | |||
of conception in arithmetic. Essential to clearness of conception<lb/> | |||
in arithmetic is the idea of <hi rend="underline">atoms</hi> or portions of matter<lb/> | |||
regarded as not susceptible of ulterior division. See <hi rend="underline">Arnot</hi>.</p> | |||
<note>20<lb/> | |||
In actual division<lb/> | |||
chemistry goes further<lb/> | |||
than mechanics; <hi rend="underline">colour</hi><lb/> | |||
than <hi rend="underline">lines</hi></note> | |||
<p>19 In the case of <hi rend="underline">actual</hi> division, <hi rend="underline">chemistry</hi> goes much<lb/> | |||
further <del>than</del> — much lower down than <hi rend="underline">mechanics</hi>. The<lb/> | |||
<del><gap/>,</del> <add>divisions,</add> the marks of which are <sic>shewn</sic> by <hi rend="underline">coloured</hi> solutions<lb/> | |||
in vastly more minute, than any division which can be made<lb/> | |||
on the surface of a large body by <del><gap/></del> the tracing of <del><gap/>.</del> lines.</p> | |||
1821 Decr. 22 M 2
Posology Arithmetic
135
Course of Instruction
Order for teaching
3 3
14
Thence shew — only
by arithmetic can
geometrical ideas be
clarified.
11. When the relation between arithmetic and geometry is shewn
then may be the time for shewing that it is only by means of
arithmetic that any clear ideas can be obtained in the
subject of geometry.
15
Analogous to arithmetical
repetends and
circulates are geometrical
rep incommensurables
12. Shew, on this occasion, the relation of incommensurable
quantities in geometrical language to repetends and
circulates in arithmetical
16
A circulate is a
compound repetend
13 A circulate is a compound repetend: a
continually repeated quantity, designated by a multitude
of figures instead of a single one.
17
Source of repetends
the decimal system
Would they be extirpated
by the duodecimal?
14 Repetends and circulates seem to have it is believed their origin
in the decimal form system of arithmetic. It would be curious
to see what would become of them in the duodecimal
system.
18
Fraction supposes
division: shew
relation of between vulgar
and decimal.
15 Fraction supposes division. Quere where would be the place
in which to insert the language of fractions — vulgar and decimal?
16 Would not the operation of called squaring
the circle be effected by the substitution of the duodecimal system
to the decimal?
17 By the duodecimal system might not the mode of
designation by cleared by the obscurity involved in the idea
of mutually incommensurable quantities?
19
Arithmetic explains
geometry: of atoms
constitute figures,
atom means indivible
18 Essential to clearness of conception is geometry is clearness
of conception in arithmetic. Essential to clearness of conception
in arithmetic is the idea of atoms or portions of matter
regarded as not susceptible of ulterior division. See Arnot.
20
In actual division
chemistry goes further
than mechanics; colour
than lines
19 In the case of actual division, chemistry goes much
further than — much lower down than mechanics. The
, divisions, the marks of which are shewn by coloured solutions
in vastly more minute, than any division which can be made
on the surface of a large body by the tracing of . lines.
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Identifier: | JB/135/296/001"JB/" can not be assigned to a declared number type with value 135. |
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1821-12-22 |
14-20 |
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135 |
posology |
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296 |
posology - arithmetic |
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001 |
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text sheet |
1 |
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recto |
c3 / d2 / e3 / g135 |
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jeremy bentham |
c wilmott 1819 |
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andreas louriottis |
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1819 |
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46414 |
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