Tertiles suggest that Terti would be useful for this purpose, along with its’ friend tri.
Tertiannually: Every third of a year(four months).
Triannually: Every three years.
What the hell. I’m going to dredge this up from long ago!
Close. You can do this one-third, one-fourth, etc. kind of thing for certain time intervals in English. But first note that the prefix semi- is special. It’s useful for disambiguating with bi-, but this sort of thing doesn’t exist in English for any other divisor besides 2. Instead, there are two forms for the suffix part, according to whether it is multiplied or divided. So,
biannual (adj), biannually (adv) = twice a year
biennial (adj), biennially (adv) = every other year
triannual (adj), triannually (adv) = three times a year
triennial (adj), triennially (adv) = every third year
etc.
These forms also exist for the month, although rarely used in English. Nevertheless, I think they sound right, so to speak.
bimensual (adj), bimensually (adv) = twice a month
bimestral (adj), bimestrally (adv) = every other month
trimensual (adj), trimensually (adv) = three times a month
trimestral (adj), trimestrally (adv) = every third month
(Note the connection to the word trimester.) Latin had no week, and it seems especially silly to slice up a day in this way (as opposed to speaking of hours), so I guess that’s pretty much as far as it goes.
As long as this thread has been dredged up from the depths, I’ll comment on this.
It’s absurdly, ridiculously, totally trivial to divide a circle into thirds.
Without a protractor?
Straightedge and a marker will do it. https://www.youtube.com/watch?v=wFAAyqE7HT8
Isn’t a measuring device being used there to find centers of line segments? So that’d be a ruler not a straightedge, no? Still, no protractor.
ETA: Here’s a thread on Dr. Math discussing various solutions where a protractor and/or ruler are disallowed.
Too bad there wasn’t room in the margin for your proof.
You can find centres of line segments with compasses, the other traditional Euclidean tool.
Welcome to the SDMB, foobarbazqux! That you even noticed you were bumping an old thread, let alone acknowledged it, puts you in the 99th percentile of new members here. You’ll make a fine addition. 
If deci- is a tenth, i propose treci- or trici- as a third.
You can do it with compass and straightedge.
- Draw an arbitrary chord AB across the circle.
- Bisect this chord by drawing two intersecting arcs of equal radii centered at A and B.
- A line drawn through the intersection points CD will bisect the circle, intersecting the circle at points EF.
- Bisect line EF using the same technique. This gives you the center of the circle G.
- Place the compass at point E on the circle with its tip at the center G. Draw an arc that intersects the circle at two points H and I.
- Draw lines from the center G to points F, H and I on the circle. Trisected!
Not even a straightedge, just a compass.
Draw a circle. Keeping the same radius, stick the needle on the circle and draw another circle. Still keeping the same radius, stick the needle on the points where the new circle intersects the original one and draw two more circles. The two new circles intersect the original circle at the first “needle point” and at points distant 120º from it.
Yes, of course a compass would be a solution. I was just pointing out that a simple straightedge and marker alone won’t do it. As Nava states, though, a compass alone is enough.
True story:
During the summer vacation of 1963 (when I had just completed 6th grade), I got playing with a compass, and quickly discovered the seven-overlapping-circles construction (yes, with a compass alone, no straightedge required). (Diagram from this web page.)
Detailed step-by-step construction is shown on this page, along with various extended constructions based on that. (This page has a rather metaphysical slant to it.)
That construction, plus reading the first few chapters of One, Two, Three . . . Infinity by George Gamow, are what got me interested in math. Prior to that, math was nothing more than grade-school arithmetic, tedious and relatively dull.
I second your plug for One, Two, Three, Infinity …, by George Gamow. My favorite book of my childhood.
OK, we clearly have different definitions of “absurdly, ridiculously, totally trivial” - to me, that doesn’t involve at least 6 steps and two instruments.
I was the one who called the procedure (for trisecting a circle) “absurdly, ridiculously, totally trivial”, but it wasn’t The Hamster King’s absurdly, ridiculously, totally non-trivial procedure I had in mind.
Quad and Quart ?
I guess you are saying that there are numerous words that have quart at the start, but its not a prefix ?
But many prefixes and suffixes are only allowable on certain words…
You can’t ask someone for a semi-dollar, neither can I ask someone for a quad-dollar.
Trito means one third… however ALSO used to mean the third, as in number 3,
but not “times three” , three times larger…
Trient was the latin prefix,
but it only exists in the word triennally, which is no longer prefix-base, its lost syllables from “trientannually”, due to slurring , so its a word on its own. I see what he was saying about “not a prefix in english” now 
there may be some use of it in some medical name somewhere, but not in common use ( Not in a 120,000 word dictionary).