JB/135/030/002

Click Here To Edit Prefat:

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

---page break---

EXPRESSION
Area confounded
with Boundaries Take care you do not confound the notion of the whole contents of a figure, with that of the mere boundaries
because one triangle is equal to another, it does not follow that every or that any of the sides or of the angles of the 1st
is equal to any of the sides or angles of the 2nd. I used to be every now & then thinking that the square of a line was always
four times that line, because four such lines are put for the more broad sides.

A striking example that Euclid confounded the figure with
its boundaries is, in the 34" Prog Book 1 Parallelogramorum
Spatiorum. Example.

Show us Euclid's the
inclinations be
are than are more generally
read throughout
the world in general than
those of Payne &
Cowley & probably
ever will be, how
so ever may
be the method of those
authors, hence we see the reason why it is Euclid that must be always always to be
quoted

If a man has converted himself of the truth
of the proportion referred to, & by the demonstration +
given by the author referred to, the reference
will ?????tion in him the memory of his having done
---page break---
so: & perhaps in virtue of the ????ate done that
—
of the method which he took to do so,

—

for if it there would be no use in these
references, nor would they be ever made.

[+] 2ly that Euclid's
demonstration is
a true one. For so long therefore
his conviction of the
truth of the
proposition rests upon
the authorities of 2
persons, & Euclid's.
It may be said, that
his persuasion is fored
on this reference,
particular
but upon his own internal
persuasion of
truth of the prior
proportion: & this
may often be the case:
it is not always

Mathematical demonstrations must in the nature of
things rest in some measure upon authority, &
be received upon trust. When if posterior imposition
I build the demonstration upon a prior
what do I do.2 I refer for the time to part of somesome book
where that prior has been proved. I refer for example
to the 5th props of the 1st book
of Euclid. He therefore who is satisfied for the moment
or the truth of the prior by this reference, is
for so long satisfied of two things. 1st that I have
mentioned a proposition as demonstrated by
Euclid, that really is demonstrated by Euclid [+]

CLASSIFICAT
prefat Euclid having been master of our masters indecessors & our,
will be the master of our Scholars necessary & our I succeed
in the world's eye It is now too late to think of establishing any
other Elements. Authority the mistressempress too often
vindicate [claim] her
influence
+
continue to sway the tyrant of mankind will + still here influence govern
over [a people]that every class of men that piques itself most that pique themselves in being independent
of her power. In vain would
others seek to substitute any<add>their mistakes to his by any superiority</add> improve upon Euclid of perpicacity, in
degree of superiority exemplified in any under
p or if d any , whither of perspicacity of pr
or of method.

Nothing that any one
can do for the clearing
of these paths of this
which heEuclid has
trodden will bear
any proportion to what
he has done
— The reason is, whatever is said in Geomtery
must be spoken to all nations. [+]

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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