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<head> | <head>-rch 9.<lb/> | ||
-diments</head> | |||
<p><add>Methods or</add> Orders | <p><add>Methods or</add> Orders in which mathematical<lb/> | ||
proportions may<lb/> | proportions may<lb/> | ||
be delivered.</p> | be delivered.</p> | ||
| Line 21: | Line 21: | ||
of course be principally <hi rend="underline">conjectural</hi>.</p> | of course be principally <hi rend="underline">conjectural</hi>.</p> | ||
<p>Concomitant or | <p>Concomitant or distinct <add>separate</add><lb/> | ||
with relation to the<lb/> | with relation to the<lb/> | ||
historical order will<lb/> | historical order will<lb/> | ||
| Line 33: | Line 33: | ||
of the problem, or the<lb/> | of the problem, or the<lb/> | ||
demonstration of the<lb/> | demonstration of the<lb/> | ||
theorem, | theorem, i.e. the putting<lb/> | ||
the truth of the proposition<lb/> | the truth of the proposition<lb/> | ||
out of doubt.</p> | out of doubt.</p> | ||
| Line 56: | Line 56: | ||
<p>To this sort of quantity<lb/> | <p>To this sort of quantity<lb/> | ||
belong <hi rend="underline" | belong <hi rend="underline">events.</hi></p> | ||
<p>Events <gap/> | <p>Events <gap/> as a<lb/> | ||
<del><gap/></del> <add> | <del><gap/></del> <add>subject of posology</add> here not properly<lb/> | ||
expressible by<lb/> | expressible by<lb/> | ||
any thing but numbers</p> | any thing but numbers</p> | ||
<p>Figures are expressible<lb/> | <p>Figures are expressible<lb/> | ||
to senses without<lb/> | |||
numbers, viz. by<lb/> | numbers, viz. by<lb/> | ||
graphical or substantial<lb/> | graphical or substantial<lb/> | ||
| Line 84: | Line 84: | ||
viz. a <sic>plain</sic> figure<lb/> | viz. a <sic>plain</sic> figure<lb/> | ||
any one of the forms<lb/> | any one of the forms<lb/> | ||
of a solid <gap/> | of a solid <gap/> itself<lb/> | ||
ought to be taken in<lb/> | |||
any of its parts for the<lb/> | any of its parts for the<lb/> | ||
subject of mathematical<lb/> | subject of mathematical<lb/> | ||
| Line 102: | Line 102: | ||
<gap/>stusion, Euclids Elements<lb/> | <gap/>stusion, Euclids Elements<lb/> | ||
<unclear>the</unclear> first and 11th or 12th books</p> | <unclear>the</unclear> first and 11th or 12th books</p> | ||
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{{Metadata:{{PAGENAME}}}} | {{Metadata:{{PAGENAME}}}}{{Completed}} | ||
-rch 9.
-diments
Methods or Orders in which mathematical
proportions may
be delivered.
1. Logical Tactical viz. in
classes, Instance Euclids
data is something in this way
2. Probative or demonstrative.
3. Historical — that in
which they were brought
to light. The history will
of course be principally conjectural.
Concomitant or distinct separate
with relation to the
historical order will
be the hermeneutics:
in the part thus designated
will be given indications of the several
contrivances employed
by inquirers for the accomplishment
of the
object: viz. the shape
of the problem, or the
demonstration of the
theorem, i.e. the putting
the truth of the proposition
out of doubt.
Euclids data or something
in this way.
For an exemplification
of the Tactical method
see in Montesclu's history
of the Mathematics
the comparative view
of the properties of the
several Conic Sections
---page break---
Quantity is
1. that which has relation
to figure
2. that which has no
relation to figure.
To this sort of quantity
belong events.
Events as a
subject of posology here not properly
expressible by
any thing but numbers
Figures are expressible
to senses without
numbers, viz. by
graphical or substantial
tations.
They are not so by
numbers except in
so far as their boundaries
are considered as
divisible into
parts, and numbers
are employed in
giving expression to the
ratio as between part
and part.
Modes of giving existence
to a figure
viz. a plain figure
any one of the forms
of a solid itself
ought to be taken in
any of its parts for the
subject of mathematical
demonstration. .
1. Analytical working
by the imaginary decomposition
of a solid
into its component surfaces.
Instance Conic
Sections
2 Synthetical: working
by the delineation exhibition of
lines and surfaces.
stusion, Euclids Elements
the first and 11th or 12th books
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Identifier: | JB/135/363/002"JB/" can not be assigned to a declared number type with value 135. |
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1831-03-09 |
7-11 |
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135 |
posology |
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363 |
posology |
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002 |
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text sheet |
1 |
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recto |
e2 |
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jeremy bentham |
street & co 1830 |
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antonio alcala galiano |
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1830 |
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46481 |
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