JB/135/030/002

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You complain to me of the difficulty
you find in retaining what you learn of Euclid.
Ideas rise all along in your mind in correspondence
to the termsexpressions, & the nor one you insensibleconvinced
to the necessity wherewith each inclusion follows
from it's premises.

founded on
vanishes with it

But that conviction

terms presented under no
other than a particular
aspect

It is demanded to make a Parallelogram equal to any
right line figure Euclid has drawn one of
By this Prop one learns how to make 4 sides only. it is necessary to divide that
a parallelogram the figure should be divided into triangles.
of Triangles if therefore you meet Euclid has told you only to draw B.D. which
with a figure is divided into triangles does individe that individual right lines figure into
you can make a parallelogram equal triangles. now was the assumed figure
to all these divisions [party] taken a Triangle it would not be necessary to Inacuracy
of B.D.
Prop XLV

1. 1. 
      

together and if any draw any lines for it could be as well of
figure can be divided into triangles made to this triangle as to
this may equal any take sum of the two divisions of it.
Again if the learner should make any general
Idea from the ing had to draw B.D. which
are situated at two angles of the figure and
on that account imagine that in all cases he was
—
to draw a line from one angle to another
he in the case of this triangle could
not divide by so doing for that
line drawn would coincide with one
of the boundaries.

NB. The consequenceconclusion A Youngman
much cononant in lines and figures
being decidand who had thought he understood
the 3 first books of Euclid at
least being desired to make
a parallelogram equal to a
given right lined figure which
had more than 4 sides
could no confessed he could not
do it for the he could tell where
to draw B.D. adding at the same
time that if he knewthe in figure
had but four sides he could do
it and Rome concluded that
the expression of any right lined figure
must be faintly it being only demonstrated with respect to four sided figures. Simpsons Euclid he had before him all the time.

At your age or thereabouts I too was read reading the
6 first books of Euclid, & understandstood no
better. At this somewhat maturer stage of my
faculties, I will attack him once more, of if
conquer it will be your's to pursue the victory.
My pursuit you,
into my affection, lead me into other very distant regions.
If I understand him his motives, it must be by superadding
a few others of my own+. OfAs those
I will communicate them to you, & then you too
will understand them in the same manner.

+ for his alone I see
more and more are
not sufficient to explain
the case

Identifier: | JB/135/030/002"JB/" can not be assigned to a declared number type with value 135.
Date_1		Marginal Summary Numbering
Box	135	Main Headings
Folio number	030	Info in main headings field	euclid prefat:
Image	002	Titles	classificat. prefat
Category	text sheet	Number of Pages	2
Recto/Verso	recto	Page Numbering
Penner	jeremy bentham; samuel bentham	Watermarks	[[watermarks::gr [with crown] [britannia motif]]]
Marginals	jeremy bentham	Paper Producer
Corrections	jeremy bentham	Paper Produced in Year
Notes public		ID Number	46148
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