JB/135/291/001

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1824 Apr 23 M
Posology

Alegomorphic
125

2

4
Geometricians have
thought they had
found a proportion
inexpressible in
numbers.

Using the geometrical form of designation, geometricians
have thought they had found a proportion not expressible
in numbers. The proportion borne by the diagonal of a
square to one of the sides — is not that an example?
whether it be or no, sure it is such examples there are.
True it may be that in that case the proportion may
not be in our decimal arithmetic expressible otherwise
than by a repitend or what comes to the same thing a
circulate which is no more than a compound repitend.
Still it is not the less true, that of this proportion, a
clear idea may be obtained by the help of numbers, &
that it may not be obtained by any other means.
What we see in this case is, that we cannot obtain a
perfectly correct idea of the proportion by this means
but baiting this incorrectness the idea we obtain is a perfectly
correct one, and at the same time, the satisfaction
of knowing that by adding numbers to numbers, we may
reduce the incorrectness to as small an amount as we
please.

5.
Numbers aside,
the idea of proportion
is, that of two lines
one is
greater than the other —
by how much we
cannot tell.

Now then lay aside the use of numbers, see what sort
of idea, the idea of proportion we have is in this case. It
amounts to no more than this viz that of the two lines
one is greater than the other, but how much we
cannot tell.

Identifier: | JB/135/291/001 "JB/" can not be assigned to a declared number type with value 135.
Date_1	1824-04-23	Marginal Summary Numbering	4-5
Box	135	Main Headings	posology
Folio number	291	Info in main headings field	posology
Image	001	Titles
Category	copy/fair copy sheet	Number of Pages	1
Recto/Verso	recto	Page Numbering	e2 / g125
Penner	richard doane	Watermarks	j whatman turkey mill 1824
Marginals	richard doane	Paper Producer	admiral pavel chichagov
Corrections		Paper Produced in Year	1824
Notes public		ID Number	46409
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