★ Find a new page on our Untranscribed Manuscripts list.
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
—
a place away
the great benefactor
of human kind
—
The aity of the Author's
character, will
to the eye of him that takes the
pains to look for them
make penetrate their appearance
through a composition
even on this subject
ently so un-
{TEXT HIDDEN BY FOLD IN PAGE}
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 equal to any 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 [parts] taken
a Triangle it would not be necessary to Inacuracy
of B.D.
Prop XLV
[++]
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 being 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 consonant 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 that 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 thence 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, & understandstooding him 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 pursuits you,
into my affection, lead me into other very distant regions.
If I understand him his notions, it must be by superadding
a few others of my own+. IfAs those notions arise,
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 convinced himself of the truth
of the proposition referred to, & by the demonstration +
given by the author referred to, the reference
will in him the memory of his having done
---page break---
so: & perhaps in virtue of the ation if done, that
—
of the method which he took to do so,
—
for if it came 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 posterior
proposition rests upon
the authorities of 2
persons, mine & Euclid's.
It may be said, that
his persuasion is formed
on this reference,
particular
but upon his own internal
persuasion of
truth of the prior
proportion: & this
may often be the case:
if it is not always
Mathematical demonstrations must in the nature of
things rest in some measure upon authority, &
be received upon trust. When if a posterior proposition
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 incessors & 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
science 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. [+]
[++] This Prop: might be a corollary
to the preceding in which it is shewn how
to make a parallelogram of a given line
and angle equal to any triangle and this
is only making a such joined together
as a right lined Figure is divided into.
vouch
[+]
what Frenchman or what
German will abandon
into authority Euclid for that of Payne
or Cowley?
— Qu: is it necessary first to shew that
any rightlined figure may be divided into triangles
at least the one Euclid &or his adorer
No other elements that
can be written will superceed
the necessity of learning these. Simpson should have done it.
---page break---
|
Identifier: | JB/135/030/002"JB/" can not be assigned to a declared number type with value 135. |
|||
|---|---|---|---|
|
135 |
|||
|
030 |
euclid prefat: |
||
|
002 |
classificat. prefat |
||
|
text sheet |
2 |
||
|
recto |
|||
|
jeremy bentham; samuel bentham |
[[watermarks::gr [with crown] [britannia motif]]] |
||
|
46148 |
|||
