https://www.loc.gov/resource/gdcwdl.wdl_18198/?sp=7
The most excellent labor of The Elements by Euclid of Megara arranged together with the most sharp-sighted Campanus on the art of geometry happily begins:
A point is that of which nothing is a part.
But the most fantastic thing on the entire first page is the abbreviated form of ūnīuscuiusque; the genitive masculine/feminine/neuter singular form of ūnusquisque.
https://en.wiktionary.org/wiki/unusquisque#Latin
It should be noted that the genitive masculine/feminine/neuter plural forms are, apparently, ūnōrumquōrumque, ūnārumquārumque, and ūnōrumquōrumque, respectively.
It is, perhaps, this transition from the Greek into the Arabic and then again from the Arabic into the Latin, which causes a relatively literal translation from the Latin into the English to feel relatively belabored. Or charming.
Anyway, the most sharp-sighted Campanus begins his rather-lengthy interjections and elucidations on the source material starting on page two of the 1482 print-edition in a voice that is relatively less belabored than the relatively more charming source material.
Besides the switch in vocabularial proclivities, the voice of Campanus is denoted with a visibly smaller font size (printed books using #blackletter along with other vestiges from the hand-written era make for some incredibly labor-intensive #skeuomorphs.)
Blackletter as a script works so beautifully with written Latin because blackletter was made for--or at the very least primarily evolved to primarily support--writing in Latin, with its emphasis on speed and its de-emphasis on difficulty.
Which is a pretty conventional quirk given the importance of #kerning. A more unconventional grammatical proclivity would be, as another example, combining sibi & invicem into one word to create a fever-dream monstrosity.
But it’s all a matter of taste—which is to say that quirks and fever-dream monstrosities aside, blackletter is a fantastic means by which the written #Latin language may be expressed. What blackletter is less fantastic for, however, is expressing math. Like Euclidean geometry.
Overspecialized utilitarian glyphs aside, Latin supports The Elements of geometry rather well. The language’s built-in frameworks for spacial relationships and movement as directed through its procedural declension tables lend themselves nicely to the actual diagramming-out of Euclid's propositions.
Also, the adjectival form of the f-word may oftentimes be used interchangeably with "procedural" in regards to #Latin #DeclensionTables, if it so pleases.
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.
ivlia sē animadvertit