Farthing / Riding [closed]

A 'farthing' is an an administrative quadrant (4 parts) Is a 'riding' an administrative triant (3 parts)? How do we call each of the parts of a circle divided in 3 parts? Not 'one third' but another other term(s)... Does the word 'triant' exist? Thanks in advance!

You're actually correct about the etymologies: they are cognate with four and three, respectively.

• Farthing is from Old English fēorthing, from fēortha "fourth" + -ing 1.
• Riding is from Middle English triding, Old English *thriding, which is from Old Norse thridjungr "third part"; the Middle English t- was a variant of Old English th-; this -t was later lost by assimilation to -t in east, west, which commonly preceded our word (e.g. east triding → east riding).

As to the third part of a circle, I don't think any word exists that is in common use. You could invent a new word, like *triant, if you like. Or you could use a semi-obsolete word and repurpose it:

Tierce

1. an old measure of capacity equivalent to one third of a pipe, or 42 wine gallons.
2. a cask or vessel holding this quantity.
3. Also terce. Ecclesiastical. the third of the seven canonical hours, or the service for it, originally fixed for the third hour of the day (or 9 a.m.).
4. Fencing. the third of eight defensive positions.
5. Piquet. a sequence of three cards of the same suit, as an ace, king, and queen (tierce major), or a king, queen, and jack (tierce minor).
6. Obsolete. a third or third part.

(Etymologies and quotation based on Dictionary.com, s.v.)

A farthing is an obsolete British coin, a quarter of an old (pre-decimal) penny. As far as I know it is only used for an administrative region in the works of Tolkien. A riding is one of the three former administrative regions of the county of Yorkshire. The word is not used in this sense in any other context.

I agree with Cerberus that there isn't a word for the third of a circle.

An the English word meaning "1/3 of a circle" is trine, but it is now only used in astrology.

It was also used in astronomy to describe the position of two objects when there was an angle of approximately 120 degrees between, until modern accurate measurements made such an imprecise term redundant.

How do we call each of the parts of a circle divided in 3 parts?

Like with alephzero's trine, this mostly just shows up in astrology, but another term that shows up is

trigon

2. Astrology (a) A set of three signs of the zodiac, distant 120° from each other, as if at the angles of an equilateral triangle... (Also figurative or allusively.) (b) The aspect of two planets distant 120° from each other...

It's usually just an archaic synonym for 'triangle', though. Its adjective 'trigonal' is more often used more generally for 120° angles in, e.g., geology, chemistry, & crystallography. Such angles are 'triequal'. 'Triradiate' and 'triradial' are used for things shooting out from a source in three sections/directions but not necessarily at equal angles from one another. Another synonym is

triplicity

3. a. spec. in Astrology. A combination of three of the twelve signs of the zodiac, each sign being distant 120° or the third part of a circle from the other two...

but its figurative and allusive uses are marked as completely obsolete right now.