# The Vertical Heat Equation



## Nikephoros

Howdy y'all!

Could I have a little help translating a dissertation title from English to the Tongue of the Augustus?  In English, the title is, "The Vertical Heat Equation". It is about mathematics, and there is a well-known equation studied in that discipline called the, "Heat Equation". This is about a verticalized (whatever that would mean in math terms) version of the equation, something that is much less known even among mathematicians. The point of my last remark is that it is the equation that is "vertical", NOT the heat. My best guess on this was, per the title of post,

"Illud aequationem derectum caloris".

I'm not sure that's right as such, and in particular am doubtful of "grammatical agreement" of all words (nouns & adjectives) in my trial translation. KEY REMARK: because the verticalized version of the equation is NOT well known, would "Illud" be the right choice of pronoun? I need to get a CORRECT translation of this really soon, so any help would be hugely appreciated. Gracias!


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## Anne345

For a tittle : 
_de recta caloris aequatione_


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## Nikephoros

Hi Anne,

Thank you. Could you provide any explanation for the changes you made or alternatives to what you suggested? I would really like to understand. Thank you.


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## slado22

Hi,

usually titles in Latin are not expressed in the nominative case, but rather in a syntagm expressing the topic introduced by de + abl. It can be translated as "about" "about the vertical heat equation", because the title is but a partial clause that means in a supra-orational level "this book is "about the vertical heat equation". Think about "de bello gallico" (Caesar), "de rerum natura" (Lucretius), "de clementia" (Seneca) and so on.
Is it clearer?


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## Anne345

_de_ : preposition followzd by ablative, *concerning*
_aequatione_* :* ablative of aequatio
_(de/di)recta :_ feminine ablative of (de/di)rectus 
_caloris : _genitive,usually between noun and adjective.


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## Salegrosso

Anne345 said:


> _de recta caloris aequatione_


 
I don't know why, but to me *De recta aequatione caloris* sounds better.


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## brian

Hi Nikephoros,

How important is it that "vertical" be distinguished from, say, "horizontal"? The word "rectus" literally meanings "straight, in a (straight) line" and can refer to either the vertical _or_ horizontal positioning of something. Even the word "derigere" (past participle "derectus") means "to straighten out, align," and from that we get "to direct."

So could you maybe explain a little bit more what you mean by "vertical" here as it relates to the equation/concept? I'm familiar with the Heat Equation.


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## Salegrosso

I'm also curious about what the verticalised version of a differential equation is. 
Like Brian, I'm quite familiar with PDEs too.  

EDIT: searching on the MathSciNet 
(http://www.ams.org/mathscinet/ , but you need authorisation. It works when you are on a computer of the maths department of any university in the world), 
searching on the MathSciNet gives no article containing "vertical heat equation" in the title, nor anywhere. 
That's quite strange... are you sure about the name of that equation? 
As you probably know, MathSciNet contains little less than _all_ research papers in maths of the last fifty years (and probably more).

You said that this equation is much less known even by mathematicians. 
Well, of course I believe you, however, if _one_ mathematician in the world wrote a paper focused on an equation that he/she calls "vertical heat equation", with this expression appearing in the title or in the keywords or in the abstract, then the MathSciNet should give that item. 
This seems to suggest that that is not the common name of that equation.

EDIT 2. The same happens when searching for "verticalized heat equation".


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