Clay Mathematics Institute

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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

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

Folios 9-10: ADM to AAL

Sat, 2016-03-12 15:40 -- Nick Woodhouse

 [9r] My dear Lady Lovelac

I am in the middle 
of arranging my books and can
only just get room to write a
short note.

 I received yours relative to the
inquiry about the study of
Mathcs but did not answer as
you would have left town and
I did not know your country
address.

Folios 7-8: ADM to AAL

Sat, 2016-03-12 14:43 -- Nick Woodhouse

[7r] My dear Lady Lovelace

The Theorem in page 16 can be easily proved when
the following is proved

[\( \frac{a+b}{}\) crossed out] \(\frac{a+a'}{b+b'}\) lies between \(\frac{a}{b}\) and \(\frac{a'}{b'}\) 
\( \frac{a+a'}{b+b'}=\frac{a(1+\frac{a'}{a})}{b(1+\frac{b'}{b})}=\frac{a}{b}\times\frac{1+\frac{a'}{a}}{1+\frac{b'}{b}}\) 
Now if \(\frac{a}{b}\) be greater than \(\frac{a'}{b'}\) 

 \(ab'\) \(\cdots\cdots\cdots\cdots\cdot\cdot\) \(a'b\) 

Folios 5-6: ADM to AAL

Fri, 2016-03-11 16:21 -- Nick Woodhouse

[5r] My dear Lady Lovelace

I should be as able as willing to see 
you in town on Friday, but have first heard that
Mr Frend is not so well as he has been, and am
going to Highgate to day to see how he is.
In consequence, having various matters to complete
definitively by the 16th instant, I shall 
find it impossible to go to town again
this week.

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