## Folios 18-19: ADM to AAL

**[18r] ** My dear Lady Lovelace

**[18r] ** My dear Lady Lovelace

**[16r] ** My dear Lady Lovelace

**[14r] ** My dear Lady Lovelace

Your inquiries were received just after I

had dispatched the receipt for Lord L's subscription to the Hist.Soc.

**[12r] **My dear Lady Lovelace

You have got through the

matter about which you write

better than I should have expected.

I have finished what you sent

as you will see

**[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

Math^{cs} but did not answer as

you would have left town and

I did not know your country

address.

**[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 \(\frac{a'}{b'}\)

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

[5r] My dear Lady Lovelace

I should be as able as willing to see

you in town on Friday, but have first heard that

M^{r} 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.

** [3r]** My dear Lady Lovelace

[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

__Acoustics__, __Cord__, __Harmonics__, __Pipe__