Only Connect: The Strange Triangle

The Latin adjective triquetrus ‘triangular’ (neuter -um, feminine -a) is baffling. It’s obviously a compound, and it obviously contains the compositional form of the numeral ‘three’, *tri-. What else it contains is anything but obvious. Unfortunately, it’s the only specimen of its kind. The mysterious element -quetrus does not occur in any other Latin compound. It looks as if it could have something to do with quattuor ‘four’. When ‘four’ occurs as the first part of a compound, it has the shape quadru/i-. This form must somehow go back to *kʷətwr̥-, its metathetic variant *kʷətru-, or a hybrid combination of both, but the voicing of the *t is odd, not to say perverse, because its exact opposite, *dr > tr, was a regular change in the prehistory of Latin. The word ‘four’ is evidently such a fickle fellow that it just can’t resist breaking some established rules. For greater inconsistency, the adverbial numeral quater ‘four times’, which in other IE languages (and presumably in Latin as well) derives from *kʷ(e)twr̥-s ~ *kʷ(e)tru-s, shows no voicing. We see a voiced stop again, though, in the denominal verb quadrō ‘to square; put in order, arrange’ and a few related words such as quadra ‘square piece or slice, plinth, dining table, etc.’ and quadrātus ‘square (n. and adj.)’.

Some connections are impossible.

[credit:  μο.]

The second part of triquetrus doesn’t simply reflect *kʷetru- (or *kʷatru- < *kʷətru-), because the word is a second-declension o-stem, which means that its pre-form ended in *-tro- rather than *-tru-. The form *kʷetro- (or possibly *kʷatro-, since pre-Latin *a would have merged with *e in this position) does not otherwise occur as a variant of ‘4’ in Latin, but since we are dealing with a capricious word-family, it’s hard to rule out a connection. If it does mean ‘four’, however, why’s that? A triangle has three sides, it has three angles, but has it got three “fours”? It would not be strange if a word for the right angle had something to do with squares or rectangles, and therefore indirectly with the numeral ‘4’, but a triangle can have at most one right angle, certainly not as many as three (the Penrose tribar, shown on the right, would be an exception if it could exist in ordinary Euclidean space).

Can external cognates help? It’s tempting to compare triquetrus with Old English þrifeoþor (sometimes glossed as ‘triangular’ in reference books such as Bosworth and Toller’s Anglo-Saxon Dictionary). It has been suggested earlier by one of the commenters on this blog [Douglas G. Kilday] that the Old English word is a loan from (unattested) Gaulish *petros ‘corner’ (< *kʷetros), which became Germanic *feþra- after the operation of Grimm’s Law. This tantalising suggestion, however, can’t be correct. The word þrifeoþor appears in Old English glossaries (Corpus, Erfurt, and Épinal) three times (spelt ðrifeoðor, trifoedur, ðrifedor), and is translated into Latin as triquadrum. One might think that triquadrum is a distortion of triquetrum caused by “folk etymology” (the mistaken identification of the second part as the compositional form of ‘4’), but in fact it’s no such thing. Old English authors took the adjective triquadrus from Orosius, a Christian priest and scholar from the Roman province of Gallaecia (today’s Galicia, Spain). Orosius, active in the first decades of the 5th century, was the author of several enormously influential works, including  Historiae Adversus Paganos, with a chapter on the geography of the world. Here is the relevant passage (Book 1, Chapter 2; emphasis added):

Maiores nostri orbem totius terrae, oceani limbo circumsaeptum, triquadrum statuere eiusque tres partes Asiam Europam et Africam uocauerunt, quamuis aliqui duas hoc est Asiam ac deinde Africam in Europam accipiendam putarint.

[Our elders made a threefold division of the world, which is surrounded on its periphery by the Ocean. Its three parts they named Asia, Europe, and Africa. Some authorities, however, have considered them to be two, that is, Asia, and Africa and Europe, grouping the last two as one continent.]

The epithet triquadrus refers to “the circle of all the earth” (orbis totius terrae = the world). Orosius certainly doesn’t mean that the Earth is a triangular circle, or that it has three corners. He means that the landmass of the world (as he knew it) is tripartite, divided by most ancient geographers into three continents (in this context, quadra means ‘part, division, area’, not literally a square). Anglo-Saxon translators coined a calque, mechanically replacing Latin quadr- with feoþor- < *kʷetwr̥-, the compositional form of Old English fēower ‘four’. Þrifeoþor was never intended to mean ‘triangular’. Its second member is the same feoþor- (= Late West Saxon fiþer-, fyþer-) that we find as the first element in numerous Old English compounds, e.g. fiþerfēte ‘four-footed’ (= Latin quadrupēs).

External support for *kʷetro- thus evaporates, but triquetrus still has to be explained somehow. I would suggest that its second element is a derivative of *kʷet- ‘join pairwise’ with the instrumental suffix *-tro-. When the suffix was added to a root ending in a dental stop, the last segment of the root was dropped already in Proto-Indo-European (this process is known as “the metron rule”). Thus we get *métrom (Greek métron ‘measure’) from *méd-trom (*med- ‘allot, mete out’), and *h₁étrom (Vedic átra- ‘nourishment’) from *h₁éd-trom (*h₁éd- ‘eat’). The noun *kʷétrom < *kʷet-trom would be ‘something that holds a pair of things together’, hence ‘joint, connection’ or the like. There were several Proto-Indo-European roots with similar meanings, and accordingly several nearly synonymous nouns for things like woodworking joints; joint itself comes (via French) from Latin iunctus ‘connected’ (the root here is *jeug-, as in yoke). Tri-quetrus (< *tri-kʷetro-) is built exactly like tri-angulus (a noun is used as the second member of a compound adjective without altering its stem class), and its etymological meaning is ‘having three connections (between pairs of sides)’.

The next post, in which I shall return to the numeral ‘four’ itself, will be the last in this series.

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