To excerpt very briefly from Proposition 1:
and because these (nominative plural [lines]) a.b and a.f (exit [using a verb implying motion, as opposed to placement]) from the (ablative singular [center]) of the (genitive singular [circle]) c.d.f to of its own (accusative singular [circumference]), they will be equal.
Having spacial relationships and movement as an integral part of a word's grammatical function adds a stylish, eurhythmic element to geometric diagrams.
Declension tables be damned.
The difficulty with reading medieval Latin is actually reading it; punctuation, capitalization & spelling can be pretty variable and nothing written in #blackletter naturally stresses legibility.
Though blackletter itself is relatively fast and mechanical for the scribe, it is still extraordinarily labor-intensive given the scope at the time (all the books).
The letter m takes 9 separate strokes to make in blackletter; its abbreviated form is a single line over the preceding vowel. So, yeah.
Proposition 5: The angles above the base of all triangles that are of two equal sides must be equal: that if its two equal sides are drawn out straight, the two angles beneath the base will likewise be mutually equal.
This paper is not playing nice with my dip pens & after much failure I decided to maybe not be so sentimental about proposition 5 and move on; so three cheers for Wilson Jones transfer letters. 🎉🎉🎉
The failure is just part of the art now.
#EuclideanGeometry #triangleThursdayLol
Proposition 7: If from two points which are terminating any line, two lines are to concurrently exit to one point, it is impossible to draw out from the same points other single lines that are equal to the other, which run concurrently to the same part.
Deciphering the Latin for proposition 7 was like trying to decipher dream-logic; honestly the entire thing felt a little belabored.
& this is partially because of the subject matter, & partially because of the style (at the time), & partially because of how medieval Latin flows (or doesn’t flow) literally into English.
Describing Euclidean geometry from first principles is going to be knotty in any language, more so when that explanation has been subjected to a second-hand translation into c. 12th century Latin; & so is thereby awash with demonstrative, intensive, & reflexive pronouns and, as well, a vacillating verb tense.
But the problem here (if it is indeed a problem and not, say, a feature) is really how the subjunctive mood comes into English when doing a fairly literal third-hand translation.
That, along with an unusual favoritism towards passive voice verb tenses and, again, the aforementioned pronoun abuse, all naturally guide one who is doing a fairly literal English translation from circa 12th century Latin, into using (what I refer to as) The Biblical Voice. & that certainly reads a certain way.
The accompanying diagram for proposition 12 is more or less the same as the one I made but for a vertical line alongside the far-right edge of the circle that includes point (e), thereby creating the line (ec). This point and that line are not actually mentioned in the corresponding text; maybe I’m missing something fundamental here but it could also just be a printing error. I did not include either point (e) or line (ec) in my diagram.
Prop 14 is the second time that “the adversary” (or “an adversary” if you prefer—though I do not) is mentioned (the first time being prop 7) and is (I guess?) a hypothetical entity who wishes to confound your ability to do Euclidean geometry through the deployment of logical fallacies…?
Anyway, neat character.
My #fanCasting for the adversary in the inevitable movie-version of the 1482 print-edition of Euclid’s Elements is currently tied between Prince Demande from Sailor Moon R and Le génie du mal.
Proposition 16: If any such number of sides of a triangle are protracted, the angle from without will be larger than either the angle from within the triangle itself or the angle opposite.
#EuclideanGeometry
Edit: This honestly doesn't read correctly; I'm going to instead go with:
Proposition 16: If any number of the straight sides of a triangle will be made protracted, the angle from without will be larger than both the angle from within the triangle as well as either of those which are opposite to that.
& "that" in this case means "the angle from within"...so yeah lol much clearer
While verbs in the subjunctive mood could ideally lend assistance as to which of the two spheres (hypothetical shadow realm vs demonstrable abject reality) the proposition commentary is currently operating in, the text does just generally have a tendency to sort of waffle in and out of the subjunctive on its own & as it pleases.
It’s really. Not. That. Big. Of a. Deal.
But yeah, making out whether Campanus is referring to point (a) in the hypothetical shadow realm or just, like, point (a), can take some work.
and then he’s just like “lol draw a triangle" (but in Latin)
Proposition 19: Of every triangle, the greatest angle is opposite to the longest side.
#EuclideanGeometry #omnisTrianguli
Prop 24 puts me about halfway through the first book of Elements, which is honestly much longer than what I would have originally assumed; I could have checked but I did not.
The translation so far is uneven but within the bounds of being “fine” and the corresponding illustrations have finally fallen into a somewhat-retraceable methodology (regarding the construction thereof) that still allows for enough variation to fend off boredom (mine).
I’ll continue, then, at least until the end of the first book before I reevaluate the scope.
Though #blessed is the time sink that can elicit from me absolutely nothing; I didn't expect to enjoy this quite so much. And yet.
Also:
It looks as though I have mostly settled on Zerkall’s Frankfurt White, which is good because I have an entire shelf full of it from an abandoned project circa three years ago—which is in itself, it so turns out, doubly-good because apparently their mill was fucking destroyed by a flood in fucking 2021. So that's it. Which sucks.
But!
It takes additive & reductive techniques equally well, works beautifully with a dip pen, and—and!—can be ran through a typewriter without suffering injury; it’s very resilient!
Really sucks about the flood, though. 😞
The word “equidistant” will be taken here & elsewhere as essentially meaning “parallel.”
"Aequidistantes lineae,” back on page 2, were defined as "those which likewise occur side by side on a surface and yet protracted in either direction do not convene, even if they are protracted neverendingly,” and so two lines that would normally be referred to as being “parallel” will hereby be referred to as being “equidistant” because, per the definition provided in context: they are equidistant.
ivlia sē animadvertit