How to Learn Neo-Latin (New Latin) For Scientific and Math Papers
How should one go about learning New Latin with no background in classical Latin, or any Latin for that matter? What is New Latin, and how is it different from classical Latin? What resources are available for a student of New Latin? These are the questions I wish to answer, as I have had to discover these things for myself, and it wasn't always easy. This post will cover the fascinating world of scholarly Latin.
Latin: How it Changed, How it Stayed the Same
When Latin is taught in schools today, it is taught by focusing on classical (1st century BC to 1st century AD) authors, with the most common by far being Caesar, Cicero, and Virgil. Learning the grammar and basic vocabulary, and reading these three authors, typically covers about 4 years of Latin education; year 1 is grammar, year 2 is mostly Caesar, year 3 is Cicero, year 4 is Virgil. This system of education, we can imagine, has been popular for a long, long time. Thus the Latin which most people learned in the Medieval period, up through the 17th, 18th, and 19th centuries, was based around classical authors.
In the middle ages, Latin was used as a lingua franca to facilitate communication between Europeans. At the same time, it was the standard language of the church, a form of Latin called ecclesiastical. Because of the various languages in use during this time, more 'exotic' language features and vocabulary (e.g. from Greek, or Hebrew) were sometimes added in. Other times, especially in formal documents, the author might be trying to show off his command of the language by using anachronisms, classical and early Latin phrasing, and so on.
For natural philosophers, beginning (we will say) around 1550 AD, the classical Latin teaching program remains popular. These early scientists would, of necessity, coin new terms, with Greek roots being particularly popular. Leading into the 1700s and 1800s, the 'golden age' of scientific and mathematical Latin, schooling may have been slightly more uniform, and so classical Latin still remains the base for Euler, Gauss, Newton, etc. However, the newly coined Greek terms gain in popularity, though they are often combined seamlessly into suitable Latin forms that any classical author would be comfortable with.
Beyond classical Latin, the vocabulary and style of scientific and mathematical authors had to be determined by personal taste, exposure to different authors, and external social or political pressures. It is often cited that Gauss's Latin is very Ciceronian, and in fact Gauss took some pride in the quality of his Latin. Euler, on the other hand, seems to have been more expository, with writing that is short and to the point, rather than flowery or poetic.
So, should one like to learn Latin in order to read Newton, or Euler, or Gauss, it stands to reason that classical Latin is essential, and highly relevant. A standard course of study, using a grammar textbook such as Wheelock's Latin, or the Henle series, is appropriate. This will expose you quickly to the Latin language, and you will be able to understand the language as a whole within just a few weeks of good study. For really learning to read the language, Lingua Latina per se Illustrata is a favorite, as are real Latin texts, at least up to Cicero.
That all being said, the aforementioned books are weak in one area: vocabulary. To read Caesar, you must know words like servus (servant) and dominus (master), agricola (farmer), rex (king), and so on. These words build a base for understanding, but it is most helpful to have a large mathematical and scientific Latin vocabulary to practice with. The problem is, finding New Latin vocabulary is somewhat difficult. Fortunately, there are online resources.
Resources for New Latin
For all Latin, the standard references are Lewis and Short, and the Oxford Latin Dictionary.
There are a number of online dictionaries which will have entries for New Latin words. My go-to resource is Wiktionary.
Less user friendly but still powerful dictionaries and lexicons are listed below:
An issue you'll find with New Latin dictionaries, is they tend to have entries relating to everything from biology and mathematics to architecture to modern consumer electronics. Thus the number of mathematical and scientific entries can be slightly weak, as the coverage must be so broad.
There are also print books which, though very hard to find, serve as common references for New Latin. Some are listed conveniently on Wikipedia in Latin,
Pleased but not satisfied with the above, I began collecting as many words as possible from random writing from Euler and Lambert, because I was going through their math anyway. But the process was slow, requiring a lot of 'reverse engineering' to determine what is a stem and what is an ending, whether the word is a noun or an adjective or a verb, what declension, whether it's a gerund or an adverb or a past participle, etc. It can be a big challenge. So I sought out an automated way to process arbitrary amounts of Latin text, and to produce vocabulary lists.
I stumbled across the late William Whitaker's WORDS program, originally written in Ada and released for Windows. There were some attempts at porting this program over into Python, and I experimented a lot with them, but was not satisfied because they seemed pretty bare bones. The dictionary data files are filled with information about relative frequency of words, subject areas, time periods, even geographies.
Well, it took a solid week of working full days but I did it, I wrote the program PyWORDS. It's available on Github now. It's able to interpret any amount of text, optionally filtered by whatever parameters you want, and it can generate vocabulary lists including complete entries for each word, optionally including the relative frequency, subject area, etc, in addition to the main forms and senses of the words. There's more functionality, and it has a very strong infrastructure that allows you to freely explore the dictionary, to e.g. build declension or conjugation tables (but you'll have to do that yourself), to search for words, to interpret words based on the given stem and ending, etc. And it works! I tried it out on Euler's
Institutionum Calculi Integralis Vol. 1 (text obtained from Ian Bruce's amazing website) and it produced a vocab list in 31 seconds. The program is not without its limitations, and it typically errs on the side of including extra vocab rather than excluding words. But it is quite good at processing words quickly and conveniently, so I recommend it. I know I'm getting good use out of it already.
Speaking of Ian Bruce, his work translating works of Euler (among many others) is truly amazing, and it is certainly an inspiration. I consider it a learning resource as well, as English and Latin versions can be compared side-by-side to clear up confusion or difficult syntax.
Going Forwards
I have been learning Latin for about a month, and in that time I have learned many of the rules of grammar (but not all, by any means!) and have learned a reasonable amount of vocabulary, at least considering the timeline. I have to put in 1-1.5 hours each day, and sometimes I read Lingua Latina before bed; I do all the exercises in Wheelock's and Lingua Latina, and practice declensions and conjugations with the mathematical words I learn. I would say it's a successful system, and I would recommend anyone interested in learning enough Latin to read old math and science papers to do the same. It should take me another 5-6 months to get through the grammar in Wheelock's and Lingua Latina, if I keep up this pace, though that may be optimistic. Once I'm employed again (thanks quarantine) I'm sure the pace will slow down or stop, but for now I'm rolling fast and learning plenty.
Mathematical Vocabulary and Practice Sentences for Latin
I'd like to provide here a few educational 'units' which will be useful to the student of mathematical Latin. I'm learning myself, so this is very much a work in progress. The units are rated by Wheelock's, but there may also be vocabulary etc assumed known from e.g. the first few chapters of LLpsI.
Unit 1 (>Wheelock's Ch. 13)
Vocabulary
calculus -i m calculation; calculus integralis integral calculus
functio, functionis f (math) function
methodus, methodi f method; mode of proceeding
ordo, ordinis m order/rank; row; succession, series; class
progressio, progressionis f progress/development; advance/forward movement; rising figure of speech; climax;
quadratura -ae f quadrature
series, seriei f row, series, secession, chain, train, sequence, order (gen lacking, no pl.);
summa, summae f summary; chief point, essence, principal matter, substance; total; (math) sum;
summandum -i n summing (gerund)
primus -a -um adj first; foremost; best; nearest, next;
algebraicus -a -um adj (math) algebraic
curvus -a -um adj curved, bent, crooked (also seemingly used as a noun, curve)
differentialis adj differential (3rd decl adj., won't be declined)
datus -a -um part. given; offered; yielded
innumerus -a -um adj innumerable, countless, numberless; without number; immense;
praeteritus -a -um adj past; annus praeteritus the last year (the year having just passed; the last 12 months)
variabilbis -e adj variable, changeable (another 3rd decl)
divido, dividere, divisi, divisum vt divide
exhibeo, exhibere, exhibui, exhibitum vt present; furnish; exhibit; produce;
ordino, ordinere, ordinavi, ordinatum vt order, arrange; adjust, regulate
pendeo, pendere, pependi vt to depend on (used with ab, ex, in, or plain ablative); to hang, hand down
propono, proponere, proposui, propositum vt display; propose; relate; put or place forward;
summo, summare, summavi, summatum vt to sum
Sentences
1. Proposui anno praeterito methodum innumeras progressiones summandi, quae non solum se ad series algebraicam summam habentes extendit sed earum etiam, quae algebraice summari nequeunt, summas a quadraturis curvarum pendentes exhibet. (Euler; habens, habentis n having; extendo, extendere, extendi, extensum vt stretch/thrust out; make taut; extend/prolong/continue; enlarge/increase; make even/straight/smooth; stretch out in death; summari = passive infinitive of summare)
2. Calculus integralis dividitur in duas partes, quarum prior tradit methodum functionem unius variabilis inveniendi ex data quadam relatione inter eius differentialia tam primi quam altiorum ordinum. (Euler; trado, tradere, tradidi, traditum vt hand over, surrender; deliver; bequeath; relate; altior, altius adj 3rd decl. higher)
Appendix: Useful and Important Verbs for Euler (and in General)
Here is a base list of important verbs that e.g. Euler uses often, along with example sentences. The example sentences mostly come from my own translations, which should not be assumed completely accurate, because I'm still learning Latin.
pendeo, pendere, pependi [2] v intr. (w/ abl) to depend on, depend upon; spes pendet ex fortuna (Cic.), hope depends on fortune; cuius seriei summa S ita pendet a resolutione huius aequationis (Eul.), of which the series the sum S thus depends on the resolution of these equations
accipio, accipere, accepi, acceptus [3] to take, receive, accept; pro x earum maximam vel minimam accipi oportet (Eul.), for x the maximum or minimum of them should be taken
oportet, oportere, oportuit [2] v. impers. it is proper, it is right; one should; pro x earum maximam vel minimum accipi oportet (Eul.) for x the maximum or minimum of them should be taken; simili modo operationem institui oportet (Eul.), the method of operation should be set in a similar way
licet, licere, licuit/licitum est [2]v. impers. it is allowed, one may, one can, it is allowable (w/ dat.; w/ infin. as subject; w/ subjunc.; w/ acc. + infin., etc); hoc cognomine appelare liceat (Eul.) with this name one may call; ex quo igitur aliam seriem exhibere licet (Eul.), from which, therefore, another series may be produced
exhibero, exhibere, exhibui, exhibitum [2] vt. show, present, exhibit; produce; ex quo igitur aliam seriem exhibere licet (Eul.)
consisto, consistere, constiti, constitum [3] (w/ abl. + 'in') depend on; praecipua guius series proprietas in hoc consistit (Eul.), the special properties of this series depend on this
noto, notare, notavi, notatum [1] observe, note; write, record;
pono, ponere, posui, positum [3] set, put; place; pro valore ipsuis n quocunque n=p summa seriei ponatur =P (Eul.), for the value of n for some n=p the series sum is set =P; posito autem B=A (Eul.) however by setting B=A
occurro, occurrere, occurri, occursum [2] to fall upon, attack; to be present at, engage in; (fig.) to occur to any one, present itself, come into the thoughts; hic igitur ante omnia casus notatu dignus occurrit (Eul.), thus here, before all else, a case worthy of note presents itself
cognosco, cognoscere, cognovi, cognitum [3] to become acquantied with, aware of; recognize; learn, find to be; (in the perfect) know, understand;
Common Mathematical Idioms and Fillers
The following are some idioms (mostly subjunctive) and filler words that appear often in mathematical writing. These are similar to e.g. the French subjunctive used in mathematical writing. E.g. "soit x=1" might translate to "x=1 be", but it is more idiomatically translated let x=1. The future tense is also often used to show a result, e.g. it will be might be better translated we then have, and so, etc. The translations below are not universal, and the correct translation depends mostly on the context.
si fuerit... if ... should be
sit x=... let x=...
fiat: ... erit let: ... then
erit x=... then x is ...; x becomes; we [then] have;
habebitur: ... there is obtained: ...
Then I'm going to learn Latin next...
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