## Folios 5-6: ADM to AAL

[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.

With regard to the second chapter, pray

remember that you are not supposed to

know, or to want to know, what

differentiation is, but only that there

is a process of that name, which is

to be learnt by rule for the present,

[5v] as an exercise in algebraical work.

With regard to the logarithms, in the

first place, Bourdon is too long. If you

will look at the chapter in my algebra,

you will find it shorter.

In the equation

\(a^b=c\)

\(b\) __is called__ the logarithm of \(c\) to the

base \(a\) . This is the __meaning__ of the

term. But for convenience the

series \(1+1+\frac{1}{2}+\frac{1}{2\times 3}+\frac{1}{2\times 3\times 4}+\)\&c ad inf

or \(2.7182818\cdots\) (called \(\varepsilon\) ) is the base always

used __in theory__; while when assistance

in calculation is the object, 10 is

always the base; thus if

\(\varepsilon^x=y\) \(x\) is the logarithm of \(y\)

[6r] Thus \(a=\log b\)

is by definition

synonymous with \(b=\varepsilon^a\) \(\varepsilon\) being \(2.7182818\cdots\)

I remain

Yours very truly

__ ADeMorgan__

3 Grotes' Place, Blackheath

Wednesday M^{g}

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