If, as I believe, the sentence stands as the theme of the website you should use the infinitive ludere instead of the participle ludens. The latter means "who plays/is playing".
As for "with prime numbers", it is an adverb of means and in Latin (for inanimate objects) this is expressed by the simple ablative, which gives numeris primis.
All in all: ...
For basic mathematics, I’ve found some answers in the Institutiones Physicæ by Floriani Dalham, published in 1752:
1+2 = 3 would be read unus plus duo sunt tres
Additio est duorum, vel plurium Numerorum in unum collectio. Indicatur per signum + adjectum, id est : plus. (…)
Dicatur : 4+2+2+7 sunt 15
(Caput III, p. 26)
1-2 = -1 would be read unus ...
You're right to look at Vitruvius for this. The best expression in Latin for "perpendicular" is actually the Greek πρὸς ὀρθᾶς, as Vitruvius uses in 9.7.
Itaque in quibuscumque locis horologia erunt describenda, eo loci sumenda est aequinoctialis umbra, et si erunt quemadmodum Romae gnomonis partes novem, umbrae octo, linea describatur in planitia et e ...
There is one word that seems to fit the bill: quoad. Although this word has a temporal ("as long as") and spatial ("as far as") meaning, Lewis and Short also gives the following meaning:
B.3: With respect to, as to
It also suggests that it derives from quod attinet ad. An interesting note is that all three classical examples given are dubious readings, ...
The French national library has been scanning a lot of material throughout the years, available on their website Gallica. Using their advanced search tool we can narrow down to works in Latin about mathematics: here is a direct link to that query result.
Similarly on archive.org, by finding the collection on mathematics and narrowing down to those written ...
In linguistics there is a term horror aequi, referring to a tendency to word sentences so as to avoid repeating the same grammatical structure consecutively or nearly consecutively.
This term was coined fairly recently, in 1909, and the study usually cited to explain it is "Cognitive complexity and horror aequi as factors determining the use of ...
I guess it would be something like hypothesis continui. Alternatively, it could also be rendered as hypothesis de continuo.
Note that noun-noun compounds like "continuum hypothesis" or "string theory" are possible in some languages (e.g., English, Mandarin Chinese, A(merican) S(ign) L(anguage), Japanese, etc). In contrast, Latin is not to be classified into ...
Your translation horror aequalitatis is great!
When something is feared, the something is in genitive — an objective genitive.
Therefore aequalitatis is correctly declined.
The hardest question is choosing the best translation for "equality".
I support aequalitas, which also happens to be (rather obviously) etymologically connected to the English word....
The impersonal verb superest is regularly used for 'it remains (to)'/'all that remains is (to)': either superest ut + subjunctive, or quod superest.
superest ut ad extremas partes corporis ueniam, quae articulis inter se conseruntur (Celsus, De medicina 4.29.1)
superest ut promissis deus adnuat tandemque me hac sollicitudine exsoluat. (Pliny the ...
Option 1: sequitur, ut
Browsing L&S I came to the entry on the verb sequor, meaning II.B.4, that reads:
In logical conclusions, to follow, ensue; with subject-clause,
especially with ut. And it cites a pretty clean example from Cicero:
Si hoc enuntiatum: "Veniet in Tusculanum Hortensius" verum non est, sequitur, ut falsum sit.” (Cic. Fat. 28)
As far as I can tell, most mathematical discourse would be done in Greek. Latin was used for engineering purposes, but speaking unambiguously about mathematics became rather awkward.
For example, Vitruvius's description of the Pythagorean formula, from De Architectura IX.6:
namque si sumantur regulae tres e quibus una sit pedes III ...
I think the phrase neque aliter would fit. as in si, neque aliter fieri potest. . . .
Neque aliter has plenty of precedents, easily found by googling, including some classical (e.g. in Cic. pro Sest. 97), though not in the exact sense you are looking for. I'm fairly sure that I came across it some years ago while translating KF Gauss's disquisition on ...
As you say, the concept of digits is only meaningful if you are using Indian/Arabic numbers. These became known in Latin Europe by the 12th century, and with them the use of “digitus” for the numbers from 0 to 9. This usage is not classical, but it is of respectable antiquity.
There is a very common word in Latin that literally means "two and a half": sestertium, -i. This comes from semis + tertius, the idea being (I suppose) that it is "half-way to three [from two]."
This usage is antiquated and almost entirely replaced by the current meaning of a "serterce," which according to L&S is:
a small silver coin, originally ...
Judging by context, it must be an ordinal number in genitive.
It seems that Gauss would translate "nth" from English to Latin as "ntus".
This makes sense, given how many ordinals look: quartus, quintus, sextus, septimus.
The genitive of -tus is -ti.
(Alternatively, it could be -tius and -ti as a short form of -tii. But this is ruled out by the other two ...
If I get you right, the part you have trouble with is the one starting with unde, right?
The translation seems clumsy to me. Euler is explaining the notation he will use for functions.
unde: hence/from where
cauendum erit: it is to be taken care of
ne: that not/so that not/not to
littera f pro quantitate habitur: letter f be taken as a quantity (i.e., ...
videtur usually means "it seems," but it can also mean "it seems good," which appears to be the case here. senatui videtur means "the Senate decides" (literally, "it seems good to the Senate"). The translation should be as follows:
..., for which reason it has seemed good (to me) to append a colon to it (i.e., to the letter f).
..., for which ...
To complement Rafael's excellent answer, here's my own translation.
The original, as copied from above:
Huiusmodi functiones arbitrarias, prouti hic feci, eiusmodi signandi modo f:y indicabo, unde cauendum erit ne littera f pro quantitate habitur, quocirca ipsi colon suffigere visum est.
Arbitrary functions of this sort, just as I ...
Why not simply say restat demonstrare, or restat ut demonstremus? It was good enough for Cicero, e.g. restat ut summa negligentia tibi obstiterit. (Quint. XII, end).
In more recent Latin, you might be further reassured by finding yourself in the company of Newton, (e.g. in Princ. Prop. III): Restat igitur ut vis illa, quæ ad Terram spectat, sit reciprocè ut ...
Draconis and sumelic have done most of the work, but there are some new relations.
Let me analyze the structure of the group itself and collect all the simplifying relations.
It is worth noting that the relations are based solely on spelling variants, not homophones.
Unfortunately the resulting group has no relations — it is free.
This is because all ...
While Etymonline isn't particularly reliable (and has a strong aversion to citing any sources), this line almost has it right:
The Latin word translates Greek apolambanomene.
It's a calqued Greek word, though not the one Etymonline claims.
As far as I can determine, Apollonius of Perga is the one who first introduced the term, in his enormous treatise ...
The following extract from the Oxford English Dictionary, art. "plus", is perhaps of interest:
The prepositional use (sense A. 1), from which all the other English
uses developed, did not exist in Latin of any period. It probably
originated in the commercial language of the Middle Ages (see
discussion at minus prep., n., adv., and adj.). The signs + ...
If I understand correctly, "order" in this context is conventional or idiomatic: it's used at this point because it's always been used that way.
In this case, I'd suggest ōrdō. Not only is it a decent translation of the English (in the sense of "methodical arrangement, ordering"), but it'll be immediately clear to mathematicians that the "order" is meant.
Maybe an alternative is "si et modo si". I constructed it like a literal translation of "if and only if", so not sure if it makes much sense. Yet, I found two sources using it:
A mathematical page:
Nota 3. Duo essentiae quaecumque elementi x necessarie aequivalentes sunt.
"φ essentia elementi x (φ Ess.x) est si et modo si omni proprietati ψ elementi x, ...
I think it is worth mentioning in this context that a modern notation like
p ⇒ q
which we read in English either as p implies q or if p then q, can be read in Latin as ex p, (sequitur) q with an optional sequitur, along the lines of ex falso, (sequitur) quodlibet. In most examples of si p sequitur q, p is a proposition; when it is not, ex + Abl. can be ...
First, valor seems to be indeed a good word for "value" in the sense of mathematics and computer science.
It appears in Newton's Philosophiae naturalis principia mathematica and is also used by Gauss.
However, I found no hits for a verb containing -valor-.
We may need to coin a new verb; I will discuss the reasons for this at the end.
Here are my suggested translations:
You ask further, esteemed colleague, if imaginary quantities are neither nothing nor bigger or smaller than zero, what can they be? I reply that they are imaginary for just that reason; for if they were zero, or bigger or smaller than zero, they would be real and therefore not imaginary.
I translated the salutation vir ...
Fractions were written, as you might expect, using Roman numerals. This wasn't particularly elegant for anything more complex than adding and subtracting, but it worked great for commerce, and that was where it was most often used.
The units worked sort of like this:
I = 1 (as) [vertical line]
S = 1/2 (semis) [letter S]
𐆑 (or •) = 1/12 (uncia = ounce) [...
(Partial answer, pending a better/more complete one)
Not a native English speaker, so you may want to correct my English:
You further ask, great man, if imaginary numbers are neither zero, nor greater nor less than zero, what are they then? I respond that this is why they are imaginary. Were they either zero or greater than or less than zero, [then] ...