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Folio 175: ADM to AAL

Sat, 2016-03-19 15:45 -- Nick Woodhouse

[175r] [in De Morgan's hand] This complete differential of \(\varphi\), as
it is called namely

 \(\frac{d\varphi}{dx}.dx+\frac{d\varphi}{dy}.dy+\frac{d\varphi}{dz}.dz\) 
is a perfectly distinct thing from

 \(\frac{d\varphi}{dx}+\frac{d\varphi}{dy}+\frac{d\varphi}{dz}\) 
and also from \(\frac{d^3\varphi}{dx\,dy\,dz}\) 

Read again page 86 when \(x\) is changed

 to of 87

 page 198--199 & the
 references

Folio 45: ADM to AAL

Sat, 2016-03-19 13:03 -- Nick Woodhouse

[45] [in ADM's hand] 

 \(\int_a^{a'}f\,ds\) 

 \(\int_a^{a'}\varphi s.ds\)  \(\varphi s\) meaning \(f\) 

 \(\int f\,ds\) 

 \(\int\frac{dv}{dt}.ds\) 

 \(\int\frac{dv.ds}{dt}\) 

 Negative & Impossible Qu. \(\int dv.frac{ds}{dt}\) 

  Operation  \(\int dv.v\) 

 Relation \(\int v\,dv\) [diagram in original]

\( v^2=2\int_a^{a'}f\,ds+C\)  \(dy/dx\) 

\( V^2=0+C\) 

\( v^2-V^2=2\int_a^{a'}f\,ds\) 

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