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Folio 175: ADM to AAL

[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

\( \left.\begin{array}{rrr} \frac{d\varphi}{dx}dx& \text{is}& d\varphi\\ \frac{d\varphi}{dy}dy& \text{is}& d\varphi \end{array}\right\}\) \(\begin{array}{l} \text{But the first means the} ~d\varphi ~\text{which}\\ \text{is caused by variation of}~x,~\text{and the}\\ \text{second has the same reference to}~ y.\end{array}\) 

About this document

Date of authorship: 

18

Holding institution: 

Bodleian Library, Oxford, UK

Collection: 

Dep. Lovelace Byron

Shelfmark: 
Box 170