JB/018/013/001

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18 Apr. 1815

Chrest Tab.II Particular Branches
2 Geometry
Purile Verbal

Enuntiation Designation of the proposition to be demonstrated or the operation to be performed
say naked proposition enuntiation.) demonstration - and preparatory additionsoperations made
to the figure for the purpose of the demonstration -
(say preparatory additions operations) the in every article to which
in a book of geometry the name of a proposition is given, these three distinguishable
parts are to be found: a very few instances excepted
in which for the purpose of the demonstration no such
additionspreparatory operations were found necessary

In Euclid's Elements without exception, and 12
In Euclid always, (in
higher branches commanding)
this purely
verbal mode of designation
is employed
in the enunciation
part.
to a considerable extent if not for the most part,
in other books, on the higher branches of geometry
in giving expression to the naked propositionsenuntiation, as above, explained, the mode
of purely verbal designation,here proposed for all the <add>abovementioned</add>parts, is actually so pursued. now But so As far as
this practice is pursued, employed. But, so far as the proposition (taking the word
proposition in the logical sense) are all general; the ideas 13
to this general mode
of designation, suppose
in the enuntiative part
of the proposition - substituted
the individual
mode employed in
the demonstration and
preparative parts, it
will be found not to
convey any instruction
untill the general
mode is restored
conveyed by them are all general ideas: and, in thistheir
original state it is, and without need of extension,that in so far
far as they are have place in the mind, are those
they lie there, readyin readiness to be applied, on occasion, to all such to all such
in the original state, and without need of extension, to be applied to all
individual figures, as are respectively comprehended
within their import.

But now, instead of their being this general,
suppose the mode of designating them such, as to confine
the application of them to the individual figure,
exhibited by the diagram that accompanies them. For
example instead of saying for example,-theA square, leaving for its side the longest ?  ?  ?
sideboundary of a right-angled triangle, as exactly equal to both the two
squarestaken together having for their sideswhich have respectively the two other sidesboundaries
of the same triangle, suppose the proposition worded thus —
In the triangle in question (describing it by letters) the square
described having for its side such boundary such side (describing it again by
letters) is exactly equal to the two both the squares taken together which squares having for their sides restructuring [+] boundary lines, (describing
them also
by letters)
the two other by ). By

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Identifier: | JB/018/013/001 "JB/" can not be assigned to a declared number type with value 18.
Date_1	1815-04-18	Marginal Summary Numbering	12-13
Box	018	Main Headings	chrestomathia
Folio number	013	Info in main headings field	chrest. tab. ii
Image	001	Titles
Category	text sheet	Number of Pages	1
Recto/Verso	recto	Page Numbering	c1 / e6
Penner	jeremy bentham	Watermarks
Marginals	jeremy bentham	Paper Producer
Corrections		Paper Produced in Year
Notes public		ID Number	6422
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