# Latin for: hypotenuse, catheti [in a right triangle]



## linguos

I'm looking for mathematical terms in Latin, especially regarding trigonometry. I tried to look it up in several online dictionaries, but couldn't find what I wanted. 

In the right triangle we've got a hypotenuse and two catheti - the adjacent one and the opposite one. How should I call them in Latin? Would _cathetus_ _adiacens_ and _cathetus oppositus_ do it? 

I'm completely new to Latin (I've just started learning it on my own two days ago), so I'm not familiar with the declension forms yet, nor do I know whether the adjective should be in congruence with the noun (I hope you know what I mean).


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## linguos

I believe you do not need to know the precise mathematical terms here. I would appreciate if somebody could just tell me whether "cathetus adiacens" is a proper phrase?


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## Spharadi

*From Wikipedia 

Triangulum rectum* seu *triangulum anguli recti* est triangulum cui est unus angulus rectus (i.e., 90° magnus). Latus angulo recto contrarius dicitur _hypothenusa_, et alia duae latera dicuntur _catheta._ 

Hypothenusa *2 = catheta prima *2 + catheta secunada *2

Maybe it helps

Regards
Spharadi


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## Cagey

Thank you for the helpful suggestion.  However, I cannot explain why Wiki has '_catheta_'.  Lewis & Short's dictionary of classical Latin has _cathetus_: "a perpendicular line." _Catheti _would be the plural.  There is no entry for _catheta_. 

The mathematical text from the Internet Archive that I linked to below uses _cathetus_ as well.  It also uses _cathetus adiacens_, as linguos proposes.  It refers to the second _cathetus_ as _alter cathetus_, that is, as the 'other' _cathetus_.  (_Alter_ means "the other of two", as you may already know.) 

_Alter_ seems to me a better description.  This is not my field, but I am not certain what the opposite [_oppositus_] cathetus in a triangle would be. 


Wolfgangi Bolyai de Bolya Tentamen  iuventutem studiosam in elementa matheseos puræ elementaris ac  sublimioris methodo intuitiva evidentiaque huic propria introducendi,  cum appendice triplici (1897)
_
Note:_ If you search the above text for 'Trigonometriae' you will find the section devoted to this topic.  It may interest you.  Just be aware that it is a scanned book, so contains odd errors in reproduction.  If something puzzles you, it may be a typo rather than a failure in your understanding.  Of course, you are welcome to start a thread to discuss any question you have about that text.


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## linguos

Thank you very much for your helpful suggestions, *Spharadi* and *Cagey*. 

@*Cagey: *The opposite cathetus in the right triangle is a relative term. Apart from the right angle, we've got two acute angles, let us call them "α" and "β", as we have it in this picture: 
	

	
	
		
		

		
			





. Thus each angle has its own adjacent side and the opposite one. In the picture from the link we've got side a being the adjacent cathetus for the angle β and side b being the opposite cathetus for this angle.

The specific names for the catheti are very important, because they make it much easier for students to memorise the trigonometric formulae. For instance, the formula for sine function in the right triangle is _sin β = the length of the opposite (to the angle ß) cathetus divided by the length of the hypotenuse_, which we can abbreviate to: _sin β = o/h_.

What I'm looking for is the Latin translation of "the opposite cathetus", something like the German "_Gegenkathete"._ We have already established that by all probality the Latin term for the adjacent side is "cathetus adiacens". The second cathetus is in some sources referred to as "alter cathetus", however according to Vicipaedia it should be "catheta contraria", which I find to be very interesting. Why is there "cathet*a*", not "cathetus", as you have already noticed, and why "contraria" instead of "opposita"? It puzzles me. Perhaps, there were no definite terms for this, although I find it hard to believe, as both Mathematics and Latin are said to be very strict and organised structures.


I would, of course, appreciate any addition to this discussion from any user of this forum.


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## Cagey

Right. I was stuck on thinking of this as describing the relationship of the sides to one another.  I hadn't thought of the relationship of the sides to an angle.


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