JB/018/110/001

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6 May 1815

Fortunate on this occasion it is or may be for the learner in Algebra, if, being
an Englishman, he it is through the medium of the translations
that have been made into his own language, that
he betakes addresses himself for instruction to that celebrated work. At
the end of the first Volume are inserted a number of Notes
some by a former Translator of the work from German or Latin
into French – some by the Translator into English. In
the second of these Notes, should perseverance or fortune have
carried him thus far, or fortune set him down at the place, the learner will find what light
the subject admits of, thrown upon this the original darkness. Without
throwing employing the gloom of algebraic characters to
throw again their lig darkness upon this first light, a short passage
or two extracted from two pages may suffice serve to afford
to the intelligent though uninitiated unmathematical reader, a
hint clue which either if not immediately will, it is believed, with after
the help of a little reflection lead to a solution of the paradox to a station at which
the paradox will be seen through "The taking of a
"singularly negative quantity negatively destroys (says
"the intelligent annotator) “the very property of negation
"and is the conversion of negative into positive numbers.”
Of the non-conception or misconception so apt to have
place on in relation to this subject, he thus points had already pointed out the cause.
“Multiplication,” (says he) has been erroneously called a
compendious method of performing addition: (which by it
might have been acknowledged it really may without
impropriety be called when the quantities are both
positive,) “whereas,” (continues he,) it is the taking, or repeating
of one given number as many times, as the number by
which it is to be multiplied contains units. Thus ....
(any number multiplied by one half) for instance 9 multiplied by 1/2 means that it is to be taken half a time” (i. e. that
of that same number the half is to be taken instead of the whole.)
"Hence,” (continues he,
a little further on)
“it appears that numbers may
be diminished by
multiplication, as
well as increased, in
any given ratio,
which is wholly inconsistent
with
the nature of Addition.”

Identifier: | JB/018/110/001 "JB/" can not be assigned to a declared number type with value 18.
Date_1	1815-05-06	Marginal Summary Numbering
Box	018	Main Headings	chrestomathia
Folio number	110	Info in main headings field
Image	001	Titles
Category	text sheet	Number of Pages	1
Recto/Verso	recto	Page Numbering	c2 / e6
Penner	jeremy bentham	Watermarks
Marginals		Paper Producer
Corrections		Paper Produced in Year
Notes public		ID Number	6519
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