★ Keep up to date with the latest news  subscribe to the Transcribe Bentham newsletter; Find a new page to transcribe in our list of Untranscribed Manuscripts
1820 June 26
Posology Alegomorphics
Alegomorphics
56
Question. or 1 In what do the operations performed
upon fractions, vulgar and decimal, agree with
and in what do they differ from, the two radical operations,
namely addition and substraction, and those others
abovementioned? and first as to vulgar fractions?
Answer. In so far as the subject of the
alteration is the sort of fraction called a vulgar fraction,
antecedently to any further operation the operations of
multiplication and division are considered as performed:
in the first place multiplication, in the second place division.
Question. or 2 What is the subject of the multiplication
considered as performed?
Answer. It is any quantity whatsoever
of which it being considered a whole, not the whole
but only a certain number of its parts are, for the purpose
in question, to be taken. This whole being a unit
is, in the first place, with a view to its being divided, multiplied
by the number expressive of the parts of which
a certain number may without further division, be,
it is supposed, sufficient for the purpose.
Question. or 3 Give an example.
Answer, Suppose that to guide my pen,
in the describing of a circle, having a stick, which I
am told is a foot in length, it appears to me that a
portion of it, if exactly marked out, would be more
convenient than the whole: a portion somewhat less
than half the length of it. Dividing it as nearly
as I can into twelve equal parts, I mark them upon
the stick in the first place. Here then to obtain the
twelve, being the number of which I want no more
than a part, I multiply number one which is the number belonging to the whole by the number twelve. When
these twelve parts thus marked out lie before me,
it seems to me that few of them will be sufficient
for my purpose. I then say that not the whole of the
stick but five twelfths of it will be the quantity best
adapted to my purpose. In this way I obtain the sort
of number called a fractional number.
☞ Quere whether a fraction with a smaller denomination
might not be employed as an example, to more advantage?
Identifier:  JB/135/251/001 "JB/" can not be assigned to a declared number type with value 135.



18200626 
or 1  or 7 

135 
posology 

251 
posology alegomorphic 

001 

copy/fair copy sheet 
2 

recto 
g56 / / g59 / 

john flowerdew colls 
c wilmott 1819 

andreas louriottis 

1819 

46369 
