Clay Mathematics Institute

Dedicated to increasing and disseminating mathematical knowledge

Folios 38-39: ADM to AAL

Sat, 2016-03-12 17:22 -- Nick Woodhouse

[38r] My dear Lady Lovelace

I have added a note or two
to your papers.

As to the subject of continuity, it
must be as much as possible your
object now to remember while proving
the things which are true of continuity
to remember that they are not false
of ['conti' crossed out?] dis continuous [sic] functions, be-
cause true of continuous ones.  Thus,
you will afterwards see that

Folios 35-36: ADM to AAL

Sat, 2016-03-12 17:17 -- Nick Woodhouse

[35r] My dear Lady Lovelace

We shall be happy to 
see you on Monday Evening, and
Lord Lovelace too if he be not
afraid of the algebra

 Your points in your letter are
are [should be 'I'] think, clear enough in
your own head.  A little addition
however may be made as follows.

Folios 31-32: ADM to AAL

Sat, 2016-03-12 17:09 -- Nick Woodhouse

[31r] My dear Lady Lovelace

You are right about
the writing down of the
terms:

 \(\frac{z}{(2n-2)(2n-3)}\) 

 is the \(n\) th term divided
by the \((n-1)\) th and the
\( \overline{n+1}\) th divided by the 
\( n\) th is \(\frac{z}{2n(2n-1)}\) as you
make it.

Folios 29-30: ADM to AAL

Sat, 2016-03-12 17:08 -- Nick Woodhouse

[29r] My dear Lady Lovelace

I have made some additional
notes on your papers.

[diagram in original] The meaning of \(\frac{\theta}{\sin\theta}\) is as follows

 \(\theta:1\) and \(1:\sin\theta\) compounded
give it in arithmetic

In fact \(\frac{a}{b}\) in arithmetic is another way of writing
\( a:b\) .

In geometry \(AB:AO\) is \(\theta[:]1\) 

 and \(AO\) or \(OB:BM\) is \(\sin\theta\) 

Folios 20-22: ADM to AAL

Sat, 2016-03-12 16:53 -- Nick Woodhouse

[20r] My dear Lady Lovelace

With regard to the error in Peacock you will see
that you have omitted a sign.  It is very common to suppose that
if \(\varphi x\) differentiated gives \(\psi x\), then \(\varphi(-x)\) gives \(\psi(-x)\), but
this should be \(\psi(-x)\times\text{diff.co.}(-x)\) or \(\psi(-x)\times-1\) .  Thus

 \(y=\varepsilon^x\)  \(\frac{dy}{dx}=\varepsilon^x\) 

Pages

Subscribe to Clay Mathematics Institute RSS