# Tangent etymology



## ancalimon

Is the etymology of Tangent known in detail?

Tan-gent?  Tang-ent?


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## origumi

http://www.etymonline.com/index.php?term=tangent


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## berndf

It is very simple: _-ent-_ is a present participle suffix in Latin, akin to English -ing (originally _-end_) and German _-end_. The verb base in _tang-_ (_to touch_), hence _tangent_ means_ touching_ as an adjective and _the touching one_ as a noun.


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## Ben Jamin

berndf said:


> It is very simple: _-ent-_ is a present participle suffix in Latin, akin to English -ing (originally _-end_) and German _-end_. The verb base in _tang-_ (_to touch_), hence _tangent_ means_ touching_ as an adjective and _the touching one_ as a noun.


 Not '-ent' but '-ens'. The '-ent' form comes from the genitive: tangentis, the nominative being tangens.


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## berndf

Ben Jamin said:


> Not '-ent' but '-ens'. The '-ent' form comes from the genitive: tangentis, the nominative being tangens.


The suffix _-ens_ is only the nominative singular form. The morphological base is _-ment-_. The PIE nominative suffix is _-s_. The Latin nominative _-ens _is probably a contraction of _-ent-s_. Today, we often view the nominative singular as the basic, uninflected form. Historically, this is not correct.


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## Ben Jamin

berndf said:


> The suffix _-ens_ is only the nominative singular form. The morphological base is _-ment-_. The PIE nominative suffix is _-s_. The Latin nominative _-ens _is probably a contraction on _-ent-s_. Today, we often view the nominative singular as the basic, uninflected form. Historically, this is not correct.


 Well, if you put it this way ... I was thinking about the use of the term 'tangent' in English, while the Latin term is 'tangens'.


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## berndf

Ben Jamin said:


> Well, if you put it this way ... I was thinking about the use of the term 'tangent' in English, while the Latin term is 'tangens'.


When case distinctions were lost in Vulgar Latin, most (not all) words were retained in their accusative form. In the first declension, this was _-am_, in the second (masculine and neuter) _-um_ and in the third _-em_. The final _-m_ which was probably already mute in Classical Latin fell of producing the suffixes _-a_ (feminine), _-o_ (masculine) and _-e_ for all third declension nouns (masculine and feminine). This is best preserved in Italian where you find
_stella < stellam _(first declension feminine)_
muro < murum _(second declension masculine)
_fatto < factum _(second declension neuter)
_attore < actorem _(third declension masculine)
_attentione < attentionem_ (third declension feminine)

In French the final _-e_ of former third declension words was reinterpreted as a feminine suffix and was removed in the base/masculine version.

Neologisms like _tangent_ were created according to this paradigm. Consequently you find _tagent _in English and _Tangente_ (feminine) in German.


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## TitTornade

Ben Jamin said:


> Well, if you put it this way ... I was thinking about the use of the term 'tangent' in English, while the Latin term is 'tangens'.


 
Perhaps because latin "s" become a "t" through French language as in the following adjectives: "absent", "prudent", "violent", "ardent", "présent"...


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## berndf

TitTornade said:


> Perhaps because latin "s" become a "t" through French language as in the following adjectives: "absent", "prudent", "violent", "ardent", "présent"...


Yes, of course, they are all derived from the accusative forms of the respective Latin adjectives (_absentem > absent_, ...); as explained above.


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## ancalimon

thanks for your help.

Is there any information about some kind of Tangentis <> Tangentir transformation ?


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## berndf

ancalimon said:


> thanks for your help.
> 
> Is there any information about some kind of Tangentis <> *Tangentir* transformation ?


What is "Tangentir" supposed to mean? I don't think such a word exists.


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## bibax

The infinitive is *tangere* = to touch, as it is in the famous quote _"Noli tangere circulos meos" (Archimedes to a Roman soldier)_.

The present participle is tangens (*tang-ent-s, plur. tangentes), as a noun meaning 'a touching line' it is feminine: (linea) tangens (= tangent line).


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## artion

The  "tangere" seems cognate to the Gr. angizo (αγγίζω), to touch. The initial a in Gr. has no aspiration to correspond to the initial T, though.


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## Flaminius

If you need further explanation on how the Latin _tango_ (inf. _tangere_) is from PIE *tag-, it is worth a while to mention that some Latin verbs have -n- inside the root in the imperfect forms.  Apparently _tango_ is one of them.  The infix is absent in the perfect forms.

"I touched" is _tetigisti_ with reduplication _te-_ and the regular first person perfect ending _-isti_.


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## ancalimon

Flaminius said:


> If you need further explanation on how the Latin _tango_ (inf. _tangere_) is from PIE *tag-, it is worth a while to mention that some Latin verbs have -n- inside the root in the imperfect forms.  Apparently _tango_ is one of them.  The infix is absent in the perfect forms.
> 
> "I touched" is _tetigisti_ with reduplication _te-_ and the regular first person perfect ending _-isti_.



So could the Turkic "Teg" (touch)  or Turkish Teğet (touch without crossing) be related with the this PIE "tag" as well? These PIE's are confusing for me.

Denge: balance  Tengri  :  " + "  isn't this related to balance and tangent at the same time?  or  O with a + in it which is the wheel (TEKER)  or DÖNGÜ (loop)

The thing about the symbolic shape of Tengri + in a circle is that the lines shouldn't cross. Otherwise the symbolic meaning is lost which I think is "balance".  In the shape X  the upper part is the feminine-female and the lower part is the masculine-male in Turkic culture.


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## Frank06

ancalimon said:


> So could the Turkic "Teg" (touch)  or Turkish Teğet (touch without crossing) be related with the this PIE "tag" as well? It's confusing.


Have you tried this website? I don't read Turkish, but this one seems to give some information on the word you're looking for.


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## ancalimon

Frank06 said:


> Have you tried this website? I don't read Turkish, but this one seems to give some information on the word you're looking for.



Thanks.  I also suspected that the geometrical meaning of tangent is inspired from French word. But what about this PIE "teg" ?

I reached the word Tangent while trying to solve the etymology of Tengri. (and I needed all the geometry   I can get to solve this equation)


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## Ben Jamin

Flaminius said:


> If you need further explanation on how the Latin _tango_ (inf. _tangere_) is from PIE *tag-, it is worth a while to mention that some Latin verbs have -n- inside the root in the imperfect forms. Apparently _tango_ is one of them. The infix is absent in the perfect forms.
> 
> "I touched" is _tetigisti_ with reduplication _te-_ and the regular first person perfect ending _-isti_.


 Tetigisti is "you touched". I touched i "tetigi".


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## Ben Jamin

ancalimon said:


> Thanks. I also suspected that the geometrical meaning of tangent is inspired from French word. But what about this PIE "teg" ?
> 
> I reached the word Tangent while trying to solve the etymology of Tengri. (and I needed all the geometry  I can get to solve this equation)


 You use *algebra* to solve equations, not *geometry*. Tangens/tangent is a term from *trigonometry*. All these are separate branches of mathematics.


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## Outsider

Trigonometry can be considered a subset of geometry. The concept of tangent is definitely a geometric one. Furthermore, geometry and algebra often intersect.


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## berndf

ancalimon said:


> Thanks.  I also suspected that the geometrical meaning of tangent is inspired from French word. But what about this PIE "teg" ?


If I understand the it correctly _*teg-_ is a Proto-Turkic root which happens to be similar to the Proto-Indo-European root _*tag-_.  I don't think there is enough evidence out there to determine whether  this is a chance coincidence or derived from a common ancestor. There is  a highly controversial theory proposing a superclass called "Altaic"  which Turkic is supposed to belong and an even more controversial theory where Indo-European and Altaic languages are grouped together call the "Eurasiatic" family, a sub-group of what is called the "Nostratic" super-family. Proponents of this theory would see a connection (cf here). But these theories are not linguistic main stream and this is not the appropriate forum to discuss such highly speculative theories.


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## berndf

Ben Jamin said:


> You use *algebra* to solve equations, not *geometry*. Tangens/tangent is a term from *trigonometry*. All these are separate branches of mathematics.


Trigonometry is one of the fundamental tools of analytic geometry linking algebra and geometry.

We have to be aware that there are two completely things in mathematics which are designated by the term _tangent _in English:
1. The trigonometric function tan()
2. A straight line which touches a curve in exactly one point.
In some languages (among them German, Czech, Hungarian and Polish), the two meanings are differentiated and the trigonometric function is called "tangens" with and "s".

If I understand it correctly (I don't speak Turkish), Turkish also distinguishes these two meaning:
1. _tanjant_
2. _teğet_


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## ancalimon

berndf said:


> If I understand the it correctly _*teg-_ is a Proto-Turkic root which happens to be similar to the Proto-Indo-European root _*tag-_.  I don't think there is enough evidence out there to determine whether  this is a chance coincidence or derived from a common ancestor. There is  a highly controversial theory proposing a superclass called "Altaic"  which Turkic is supposed to belong and an even more controversial theory where Indo-European and Altaic languages are grouped together call the "Eurasiatic" family, a sub-group of what is called the "Nostratic" super-family. Proponents of this theory would see a connection (cf here). But these theories are not linguistic main stream and this is not the appropriate forum to discuss such highly speculative theories.



TEG is the Turkic root for many words. It's still widely used as roots of many words old and new. Mostly for 
TEK: single, peerless, unique, wondrous, odd, identical ... (not to be confused with BİR:ONE) 
DEĞ: touch
DOKU: outer part of something, ~texture
DOKUN: touch&feel
DAĞ: mountain (touching Tengri)
DENK: equal, reflection, coherent, someone worthy of being loved by another. (I think the Hungarian word for mirror is related to this: tükör.  In Turkish mirror: ayna  from aynı, aynısı: the same, unique (see TEK))
DENGE: balance

The evocation sign of Tengri is + in a circle.  I think it represents the most important aspect of Tengri (God) and it's balance because Tengri does not intervene in the business of humans. Things happen because of Tengri's will but not as a punishment or a reward. It's just the way it is. Another aspect is Tengri is the force that takes you higher, further.  I connect this with the momentum of the wheel and maybe even the word "Turk" (if we accept Turk as not being an ethnic identity but a unity of people)

I'm trying to find the connection between TENGri  and TEG

There are two shapes we know as Greek Gamma letters inside the Tengri circle. They are "DENK" They connect at a point but never cross; meaning they are not two lines crossing each other but rather two Gammas touching each other at a single point.

The same sign can be seen on top of Yurts (Turkic tent). In the Yurt the sign represents balance: DENGE.  The balancing point is the center point where all lines touch.

The edges of the lines are always tangent to the ground when the wheel (TEKER) is turning.  (Proto-Turkic *deg- is also supposed to mean "circle" and we find a similar word in Sanskrit. _cakraṃ_ चक्रं [ˈtʃəkrə̃] from my other thread: http://forum.wordreference.com/showthread.php?t=2119131 )

Also daire (circle, inside the circle, and also home)  seems to be related to English "tyre" as well.


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## DenisBiH

How does PIE *tag- fit into the vowel system of PIE? Does anyone reconstruct an h2 there?


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## Frank06

*<Moderator deleted text>*


DenisBiH said:


> How does PIE *tag- fit into the vowel system of PIE? Does anyone reconstruct an h2 there?


Watkins' _Dictionary of Indo-European roots_, which normally also gives "Old PIE forms", with laryngeals, only mentions *tag- 
"tag- To touch, to handle. 1. Nasalized form *ta-n-g- [...]"


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## L'irlandais

ancalimon said:


> ...Also daire (circle, inside the circle, and also home)  seems to be related to English "tyre" as well.


In what way?  Refer to this etymology of tyre, nothing to do with circles what-so-ever etymologically speaking :


> Comes appearantly from attire :  .1300, from O.Fr. atirier "to equip, ready, prepare," from a- "to" + tire "order, row, dress" (see tier). The noun is attested from c.1300.  Source.


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