## Folio 119: AAL to ADM

Ockham.

Monday Morning

16^{th} ['July' crossed out] Aug^{st}

['1841' added by later reader]

Dear M^{r} De Morgan. I send you today, 1^{stly}:

a paper in which I have proved the Theorem

\( \int fx\frac{dx}{dt}dt=\int fx.dx\) (of pages 102, 103), __backward{__s.

That is I have __assumed__ \(\int fx.dx\), & deduced

from it that when \(x=\psi t\), then \(\int fx.dx=\int fx\frac{dx}{dt}dt\);

whereas in the book \(\int fx\frac{dx}{dt}dt\) was __assumed__,

& the process was exactly reversed.

I do not send this as having __any advantage__

over the other proof. Merely because it happened

accidentally to strike me, & I wrote it down;

& I now ['may' crossed out] enclose it for inspection, to see that I

have correctly deduced each step.

2^{ndly} : I enclose you my S__econd__ Paper on ['the' inserted] Accelerating

Force subject. This one is the explanation of

\(S=\int v.dt\)

Tomorrow I hope to send you the one on \(t=\int\frac{ds}{v}\) .**[119v] ** I hope I am not plaguing you very much.

I am anxious to read up to a certain point

before moving to Devonshire.

Believe me

Yours most truly

A. A. Lovelace

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