Clay Mathematics Institute

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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.

Folios 1-2: ADM to AAL

Thu, 2016-03-10 15:50 -- Nick Woodhouse

[1r] My dear Lady Lovelace

I have of course but little to say
on your report of progress up to the 21st.

With regard to your music, if you have any
wish to begin the study of acoustics, you may find
an elementary compendium of the most material
points directly connected with music, in the following
articles of the Penny Cyclopaedia

  AcousticsCordHarmonicsPipe

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