## Folios 29-30: ADM to AAL

**[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 \(\sin\theta\)

The compounded ratio is that of \(AB:BM\)

which approaches without limit to the

ratio of \(1\) to \(1\) as \(AB\) is diminished

Your notion of the ratio approximating to

unity is correct. The term 'ratio approximating

to \(a\) ' is a mixture of the geometrical and**[29v] ** arithmetical mode of speaking, it

should be 'ratio approximating to

\(a:1\) .

I think you have got over the diffi-

culty of that part of the subject

I was sorry to have been out

when Lord Lovelace called, and

could not get down to S\) ^\textup{t}\) James' Square

till you had gone. With best

remembrances I am

Yours very truly

__ADeMorgan__

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