## Folios 38-39: ADM to AAL

**[38r] ** My dear Lady Lovelace

I have added a note or two

to your papers.

As to the subject of continuity, it

must be as much as possible your

object now to remember while proving

the things which are true of continuity

to remember that they are not __false__

of ['conti' crossed out?] dis continuous [*sic*] functions, be-

cause true of continuous ones. Thus,

you will afterwards see that

\(\varphi(a+h)=\varphi a+\varphi'(a+\theta h).h\)

is only an algebraical translation

of the following geometrical theorem

''Every continuous and ordinary arc

of a curve has somewhere a tangent

parallel to its chord''

**[38v]** [diagram in original]

But this is not always false

of discontinuous curves

[diagram in original]

Neither is the algebraical theorem

false of them.

The best way at present, is to

mark that discontinuous functions

are now excluded only because we

have no language to express them in.

This will come intime [*sic*] : you will

have enough of them when you

come to apply math^{cs} to the theory

of heat.

My wife has duly received**[39r] ** your letter & is much obliged to

you & Miss King.

Yours truly

__ADeMorgan__

69 G.S.

Feb^{y} 11/41 [?]

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