Disputatio:Infinitas

Infinitas fuit pagina mensis Februarii 2007.

LATINITAS

• +1 (inspecta1) from the history 18:15, 2 Martii 2007 Ioshus Rocchio
• +2 (inspecta2) moved to here --Alex1011 18:39, 2 Martii 2007 (UTC)

Physica

ANyone have a copy of Physica in Latin?--Ioshus ^(disp) 20:27, 22 Decembris 2006 (UTC)

Anyone at all? I don't want to dare and translate parts of the Physica from greek or english into latin, I'm sure it's been done before...--Ioshus ^(disp) 02:07, 2 Ianuarii 2007 (UTC)

We almost certainly have a Latin translation at the U of C. But usually when I have quotes in Greek, I keep them in Greek, then write my own translation, as close to word-for-word as possible. BTW, I was just looking into John Wallis' Latin name. It does look like in his work Iohannes Wallis, th esurname being indeclinable, is indeed the prevelant form. He does also use Wallisii and Wallisi (in the genitive, natch). --Iustinus 05:25, 25 Ianuarii 2007 (UTC)

I'd planned to keep the greek, I just balk at translating it...--Ioshus ^(disp) 06:01, 25 Ianuarii 2007 (UTC)

OK, well tomorrow I can provide the Greek text, and either a published Latin translation, or my own. --Iustinus 06:06, 25 Ianuarii 2007 (UTC)

Wow, if you google the phrase "Aristoteles Latinus" you will find that there's actually an online database of Latin translations of Aristotle!! Unfortunately I don't have access to it. --Iustinus 23:43, 25 Ianuarii 2007 (UTC)

Wow...that's sweet. I probably have access on campus.--Ioshus ^(disp) 04:19, 27 Ianuarii 2007 (UTC)

That would be really cool, but I won't hold my breath: I didn't have it even on campus, and I'm at a fairly big university. --Iustinus 04:23, 27 Ianuarii 2007 (UTC)

Well we'll hold our breath. I've never been restricted to an online journal at UMD...--Ioshus ^(disp) 04:27, 27 Ianuarii 2007 (UTC)

Nu? Were you able to get it? Not that it's really that important at this point, but could be useful later. --Iustinus 19:38, 29 Ianuarii 2007 (UTC)

Aristotle at last?

The quote as given on en:

"... It is always possible to think of a larger number: for the number of times a magnitude can be bisected is infinite. Hence the infinite is potential, never actual; the number of parts that can be taken always surpasses any assigned number."

Here is the original Greek (207b 10-13):

ἐπὶ δὲ τὸ πλεῖον ἀεὶ ἔστι νοῆσαι· ἄπειροι γὰρ αἱ διχοτομίαι τοῦ μεγέθους. ὥστε δυνάμει μὲν ἔστιν, ἐνεργείᾳ δ’ οὔ· ἀλλ’ ἀεὶ ὑπερβάλλει τὸ λαμβανόμενον παντὸς ὡρισμένου πλήθους.

My literal Latin translation (probably requires some correction and polishing):

de maiore autem semper potest cogitari: infinitae enim [sunt] bipartitiones magnitudinis, ut potentia quidem sit, facto autem non: sed semper excedit subtractum omnem divisum multitudinem.

I still may pick up a published translation tomorrow. Goodnight. --Iustinus 08:27, 25 Ianuarii 2007 (UTC)

Published Latin translations

From the medieval Aristoteles Latinus, de Naturali Auditu:

... in plus autem semper est intelligere; infinite enim sunt decisiones magnitudinis. Quare potentia quidem est, actu autem non; sed semper excellit acceptum omnem determinatam multitudinem.

From the translation of Ioannes Argytopylus Byzantius, Physica Auscultatio:

versus plus autem fit ut semper intelligatur. divisiones enim magnitudinis duas in partes aequales sunt infinitae. quare potentia quidem est, actu non est: sed semper id quod accipitur, multitudinem omnem exsuperat definitam."

I gather that some (but not all) of the translations in the Aristoteles Latinus were made by one Guillelmus ;)

Anyway, it's a good thing we didn't go with my translations, because it looks like I misunderstood that last bit. --Iustinus 00:39, 26 Ianuarii 2007 (UTC)

Oops, that's Ioannes Argyropylus Byzantius, with an r. I see that the OCR version of Lexicon Universale made the same mistake (but in my case it was just a dumb typo). Mr. Byzantius died in 1486, 1831 would be the date of the edition I used, nisi fallor. --Iustinus 22:53, 26 Ianuarii 2007 (UTC)

resuming

So I think Mr. Byzantius' translation is the best. What do you think? Also, since the English name of the symbol is "lemniscate", surely the Latin should not be lemniscus but lemniscata (for the gender, see es:Lemniscata). --Iustinus 18:13, 26 Ianuarii 2007 (UTC)

Yes, I liked Byzantii. And all three much bette rthan I could have done, thanks for the research. I'm trying to remember where I got lemniscus, let me see...--Ioshus ^(disp) 22:49, 26 Ianuarii 2007 (UTC)

It seems that the Galileo quote was originally written in Italian, but I just downloaded a Latin translation of the text, published in 1699 (well after Galileo's death). I'll try to find time to search it soon. --Iustinus 18:39, 26 Ianuarii 2007 (UTC)

Like Plato, we should probably include the original Italian, too. I'm sure that isn't hard to find. Let me see about this, too...--Ioshus ^(disp) 22:49, 26 Ianuarii 2007 (UTC)

OK, here it is:

"Non alio modo eum decidi posse video, quam dicendo infinitos esse omnes numeros, infinita quadrata, infinitas eorum radices; quadratorum multitudinem non esse minorem multitudine omnium mimerorum, [sic] nec istam hac majorem; & tandem concludendo, æqualitatis, majoritatis & minoritatis attributa in Infinitis nullum habere locum, utpote quæ in quantitates terminatas solummodo cadunt."

-Discursus et Demonstrationes Mathematicæ circa duas novas scientias, "Dialogus I", p. 30

If we ever write an article on en:Galileo's paradox, we will need to transcribe the rest of that conversation.

I don't know who wrote this Latin translation: if it's mentioned anywhere at all in the front matter, it is well buried and I can't find it at the moment.

Now, someone make me go do my "real work" before I start trying to track down the other quotes! --Iustinus 20:12, 26 Ianuarii 2007 (UTC)

Vide disputationem tuam =] --Ioshus ^(disp) 22:49, 26 Ianuarii 2007 (UTC)

Done. Thanks, again.--Ioshus ^(disp) 22:53, 26 Ianuarii 2007 (UTC)

Correcta

Comparativus magniorem==>maiorem et magnissimum==>maximum--Marc mage 22:46, 26 Ianuarii 2007 (UTC)

Factum. Gratias tibi.--Ioshus ^(disp) 22:53, 26 Ianuarii 2007 (UTC)

Pariter: parvus, minor, minimus. --Iustinus 23:55, 26 Ianuarii 2007 (UTC)

lemniscus/lemniscata

http://lysy2.archives.nd.edu/cgi-bin/words.exe?lemniscata

http://lysy2.archives.nd.edu/cgi-bin/words.exe?lemniscus

I can't find my original source for lemniscus, but Whitaker thinks lemniscata to be the adjective...--Ioshus ^(disp) 02:32, 27 Ianuarii 2007 (UTC)

I'm not sure what your point is here. Yes, it's an adjective, but so are conditum, nucatum, asteroides. As I just wrote this very day on the Grex Latine Loquentium: "Adiectivum substantivum factum haud res nova in Latinitate!" Futhermore, in English "lemniscate" and "lemniscus" refer to two separate symbols: ∞ and ÷ respectively. I haven't done any research into this, but you can bet the distinction is reflected in Mathematical Latin too. --Iustinus 03:21, 27 Ianuarii 2007 (UTC)

Actually now that I look at it, I think my source on this was (shame on me) english wp: the lemniscate, from the Latin lemniscus, meaning "ribbon." One can imagine walking forever along a simple loop formed from a ribbon, so I just assumed that lemniscus was the word...

Of course substantives reign freely, I wasn't suggesting they didn't.--Ioshus ^(disp) 03:57, 27 Ianuarii 2007 (UTC)

And now that I look at it, en:lemniscus does indicate that that name is an acceptable alternate to lemniscate. --Iustinus 04:03, 27 Ianuarii 2007 (UTC)

Other Comments

• Note that en:One-to-one correspondence is a redirect to en:Bijection, a term which is much easier to Latinize ;)

• Edited it in a preemptive strike. =] --Ioshus ^(disp) 04:22, 27 Ianuarii 2007 (UTC)

I know that Latin tendds to avoid combinations of /j/ and /i/, but I think here it's safe to spell the word biiectio. Honestly I don't think biectio can be correct. --Iustinus 21:37, 29 Ianuarii 2007 (UTC)

Typo, you're right.--Ioshus ^(disp) 21:48, 29 Ianuarii 2007 (UTC)

• Oy vey. Yajurvedae specimen cum commentario and Locke's De intellectu humano are not available online, but we DO have them at U of C.

What the... apparently there IS an online edition of De Intellectu Humano afterall! --Iustinus 21:37, 29 Ianuarii 2007 (UTC)

Damn, I need to get to campus, and see about this. I meant to do this last night, but one of my friends brought over a bottle of Bushmills Black, and I've rarely been able to turn down fine Irish whiskey. I wouldn't want you to loan out your u of c password, but I can't read that. Actually...lemme see if I can access the research portal through our library's website...--Ioshus ^(disp) 22:57, 29 Ianuarii 2007 (UTC)

Yeah, sorry, I gave you the UC proxy version. Just take proxy.uchicago.edu out of the web address and it should be fine. HOWEVER, I cannot figure out how to access this site from off campus. Going through the proxy server does not in fact work. So you might be stuck. Fortunately I am on campus right now, so I'll just switch from my laptop to a public terminal and that should do the trick. --Iustinus 23:01, 29 Ianuarii 2007 (UTC)

Yeah, need access to Thomson Gale groupd. I'm not sure id UM subscribes, lemme call...--Ioshus ^(disp) 23:13, 29 Ianuarii 2007 (UTC)

Nevermind, I figuted out what the problem was, sort of. Basically that URL wouldn't work no matter what, if you started with it. YOu had to get there via the link in the library catalog. In any case, the point is moot because I have now emailed you the relevant pages. --Iustinus 23:23, 29 Ianuarii 2007 (UTC)

Yeah, I transcribed section 7, you mind taking a look? A few sit/fit discrepancies, and a few other things.--Ioshus ^(disp) 23:35, 29 Ianuarii 2007 (UTC)

As you presumably know by now, I have replaced this with the quote from section 8. Apparently either en: is wrong, or the English and Latin versions of Essay don't line up exactly. --Iustinus 17:15, 30 Ianuarii 2007 (UTC)

No I hadn't noticed that... :::yawns and rubs eyes::: Nice, was that you who added to the yajurveda section, too?--Ioshus ^(disp) 17:17, 30 Ianuarii 2007 (UTC)

The news for the Yajurveda is not quite as good. Mr. Albrechtus Webber Vratislaviensis only promissed us a specimen, and it's not the specimen we need, alas. --Iustinus 22:47, 29 Ianuarii 2007 (UTC)

Since I couldn't find a published translation, I had a friend who knows Sanskrit, user:RandomCritic, come do a good literal translation. I still have some questions about his version, but I've sent them by email, since I don't expect he'll be hanging around. --Iustinus 17:15, 30 Ianuarii 2007 (UTC)

Ahhhh, that's who it was!--Ioshus ^(disp) 17:18, 30 Ianuarii 2007 (UTC)

I asked RandomCritic what the force of the odd genitive in line three of his translation was. Here's his reply:

It is odd in Sanskrit as well. I would expect the ablative. As the sense may actually be something slightly different from "from", I simply rendered it literally rather than assume what it meant. It may simply be there to avoid redundantly using the ablative twice; in the Middle Indic languages the genitive tends to swallow up all the other oblique cases, and this might be a version of that phenomenon. But I don't know.

• Good man =]. --Ioshus ^(disp) 04:22, 27 Ianuarii 2007 (UTC)

• There are indeed Latin versions of Wittgenstein, but apparently not of Philosophical Remarks.

• Can't win em all... At least there's a cite of his name.--Ioshus ^(disp) 04:22, 27 Ianuarii 2007 (UTC)

--Iustinus 04:02, 27 Ianuarii 2007 (UTC)

Jaina

I believe that Hesychius γ364: "Γεννοί· οἱ Γυμνοσοφισταί" is supposed to refer to the Jains. --Iustinus 19:48, 30 Ianuarii 2007 (UTC)

I confess backward etymology on this one. I looked at all the romance languages. Sure we should latinize this?--Ioshus ^(disp) 23:11, 30 Ianuarii 2007 (UTC)

And of course I assume this is Hesychius Illustrius?--Ioshus ^(disp) 23:14, 30 Ianuarii 2007 (UTC)

Yes it is, Hesychius Alexandrinus, Hesychius Lexicographus, ille Hesychius. As for whether or not we shoudl call Jains genni, my vote would be yes definitely. If we have a classical name, why pass it up? As to how we shoudl translate the adjective Jain(a), or the abstract noun "Jainism", I am not entirely sure. --Iustinus 23:49, 30 Ianuarii 2007 (UTC)

I should probably mention that I already chainged religio Iainistica to religio Gennistica over at Crux gammata a couple days ago. --Iustinus 23:59, 30 Ianuarii 2007 (UTC)

Well, are the religion and the doctrines mutually inclusive? I balk at calling the pilosophy religio. I have, temporarily changed it to Gennismus from Iainismus in the text.--Ioshus ^(disp) 02:27, 31 Ianuarii 2007 (UTC)

I'm not sure what you mean. It is true that Jainism is essentially non-theistic, but it does overall seem to fit in the category of "religion." The article on en: repeatedly uses that word to refer to it. I suppose what you're asking is if the philosophy is separate from the religion... well, this is India we're talking about, and for a religion to be philosophical is hardly surprising. I know it's hard for you to believe that something called a religion can come up with something so deep :P But if it's an issue for you, I don't see why we can't call it Gennismus. The disadvantage to taht is that it lacks parallelism with the other religion articles. The advantage to that we don't have to figure out what the adjective is: for some reason, Gennismus seems much less of a leap than Gennisticus does. So it's OK with me either way. --Iustinus 03:26, 31 Ianuarii 2007 (UTC)

Actually, come to think of it, would it make more sense to cover the topic under Genni? That is, afterall, the attested word (I typically count proper nouns taht show up in Greek as close enough to attested in Latin). Article titles are supposed to be in the plural, but I figure that the same words that are typically listed in the plural in Latin dictionaries (notably, the names of tribes) should probably be listed that way here too. --Iustinus 18:09, 1 Februarii 2007 (UTC)

Yajurveda

The news for the Yajurveda is not quite as good. Mr. Albrechtus Webber Vratislaviensis only promissed us a specimen, and it's not the specimen we need, alas. --Iustinus 22:47, 29 Ianuarii 2007 (UTC)

Since I couldn't find a published translation, I had a friend who knows Sanskrit, user:RandomCritic, come do a good literal translation. I still have some questions about his version, but I've sent them by email, since I don't expect he'll be hanging around. --Iustinus 17:15, 30 Ianuarii 2007 (UTC)

Ahhhh, that's who it was!--Ioshus ^(disp) 17:18, 30 Ianuarii 2007 (UTC)

I asked RandomCritic what the force of the odd genitive in line three of his translation was. Here's his reply:

It is odd in Sanskrit as well. I would expect the ablative. As the sense may actually be something slightly different from "from", I simply rendered it literally rather than assume what it meant. It may simply be there to avoid redundantly using the ablative twice; in the Middle Indic languages the genitive tends to swallow up all the other oblique cases, and this might be a version of that phenomenon. But I don't know.

Other names that show up in the English version

Some more "official" Latin names that will be needed:

• Leopold Kronecker: Leopoldus Kronecker [1]
• Thomas Hobbes: at least three Latinizations attested in his works, I don't ahve time to figure out which is most frequent: Thomas Hobbes, Thomas Hobbius, Thomas Hobbesius
• Evangelista Torricelli: Evangelista Torricellius
• Guillaume de l'Hôpital: Marchio Hospitalius (as mentioned previously)
• David Hume: David Humius (gen. Davidis)

--Iustinus 00:52, 31 Ianuarii 2007 (UTC)

We may want to change all the Möbii to Moebii: it looks like Möbius himself spelled his name both ways in Latin, but used Moebius more than Möbius. --Iustinus 02:40, 1 Februarii 2007 (UTC)

(oops, didn't mean to say that twice) --Iustinus 02:58, 1 Februarii 2007 (UTC)

• J. B. Listing: dammit, the usual thing. He wrote his dissertation in Latin only, and of course his Latin name isn't given in the library listing. --Iustinus 02:58, 1 Februarii 2007 (UTC)

Empirices

Surely it's empirice -es? Cf. L&S --Iustinus 03:38, 31 Ianuarii 2007 (UTC)

Yah, f.--Ioshus ^(disp) 06:21, 31 Ianuarii 2007 (UTC)

intro

Usurpatur doesn't bother me at all, and I love excogitari. Talibus is much better than his. And fit, of course, we aren't wishing infinity to become god optitavely now are we? While I'm on god though, I had god uncapitalized on purpose the first time, and only capitalized in the Judea Christian part (the separation of which doesn't bother me too much, but maybe we can alter it to be a tad more inclusive: for my part Judeo-Christian tells me about Judeo-Christian, but Judaism and Christianity say to me "Judaism and Christianity and nothing else"). But regarding this, you'd know better the habits of authors writing about god, so if it deus is orthographically unsound let's keep the edit, if not I'd prefer the first way. Antimonia just embarasses me =]. Also, the per vim bit 'was' a little clunky...--Ioshus ^(disp) 21:33, 31 Ianuarii 2007 (UTC)

The other thing I might suggest now after quarum omnes=>quibus omnibus, we might displace modis variis a little bit, just to avoid four ablatives in a row which might confuse a tiro...--Ioshus ^(disp) 21:44, 31 Ianuarii 2007 (UTC)

Another tiny nagging wonder: should aeternitas be capitalized?--Ioshus ^(disp) 22:13, 31 Ianuarii 2007 (UTC)

• Deus vs. deus: I would say that it depends on exactly what you mean. If it is "...becomes a god" then go with lower case. If you mean "...becomes God" (whether or not you mean the God of the Bible) then it should be capitalized.
• Judeo-Christian: Latin often uses hendiadystic (I made up that adjective) adjectives where English would use a compound one. BUt your argument is not without merit. But if you want to change it, it should be Iudaeochristiana or Iudaeo-Christiana, i.e. the first part shouldn't be declined.
• Per vim: not only is it clunky, but it implies a different kind of force than I think you meant ;)
• modis variis: that's a good idea.
• aeternitas: I have no idea.

--Iustinus 01:26, 1 Februarii 2007 (UTC)

it:Infinito...

...for the record has some excellent info on infinity's philosophical history in western culture.--Ioshus ^(disp) 22:21, 31 Ianuarii 2007 (UTC)

And while you're at the link, what do you think of the quote banner at the top? Definitely one of the most well known quotes on infinity from one of the history's most revered scientists. But then again, maybe it's a little tacke on an FA page. I don't know, could be cool =]--Ioshus ^(disp) 22:24, 31 Ianuarii 2007 (UTC)

Haven't checked out the history yet, but the epigram is good quote. I'm not sure I'd put it up at the top though: there's probably a good place for it in the body. --Iustinus 01:26, 1 Februarii 2007 (UTC)

BTW, that history section looks pretty damn good. Maybe you want to adapt it after I'm done with this editing pass? --Iustinus 18:33, 1 Februarii 2007 (UTC)

Three doubts

Is it only a perception of mine or "sunt gnotae" et "popularitim" remind me of the XII tables and of the Cista Ficoroni? I understand that cognitae sunt is a perfect tense, therefore misleading, but is cognoscuntur so trivial? Third point: Why "ab renascente ad hodie" when we have a more regular Renascentia (follow wikilink: the title reads Aevum antiquitatis renascentis, but in its text tthe word Rinascimento is translated Renascentia... I'd better write a Renascentia usque ad hodierum diem. - 87.9.248.125 23:22, 31 Ianuarii 2007 (UTC) (i.e. Usor:OrbiliusMagister

XII tables ey? =] Correct on all three counts, Edoardo, thanks!--Ioshus ^(disp) 23:36, 31 Ianuarii 2007 (UTC)

Orbilius, I am currently doing a sweep through the article, proofreading, but have only gotten through the intro so far. Some of those errors will be fixed when I get to them (renaissance is one thing I was going to fix. Latinists get kind of picky about how to say that, but more on that later). --Iustinus 01:14, 1 Februarii 2007 (UTC)

History section

Hey, Josh, what does this mean: "Cum intellectionibus antiquis infiniti spatii a philosophis Taoistis in Sina, ex primis sapientiis infinitatis gnotis inventa est de Indica Yajurveda"? I can't figure it out. --Iustinus 18:12, 1 Februarii 2007 (UTC)

Good lord I'm not sure even I can figure out what the heck I meant there... Lemme take a look...--Ioshus ^(disp) 18:15, 1 Februarii 2007 (UTC)

Ok, now it says "Cum textibus antiquissimis infiniti spatii philosophorum Taoistorum in Sina, ex primis sententiis infinitatis notis est de Indica Yajurveda " in which I take myself to have meant "With the ancient texts on infinite space of the Taoist philosophers in China, among the first ideas of infinity known is from the Yajurveda"... Probably ought to change the genitive on spatii infinit.--Ioshus ^(disp) 18:23, 1 Februarii 2007 (UTC)

It still sounds confusing to me. I guess cum here really means "in addition to." But if we're goign to mention the Taoists at all, why do it in a way that so begs a question (in the colloqual sense)? Honestly I dont' knwo what we should say, because neither en: nor it: mentions the Taoists, and I don't really want to go tracking them down. But presumably it woudl be better not to burry the mention of them at the beginning of a paragraph about the Yajurveda, but rather give them their own little one-sentence paragraph, such as "The Taoists had some early discussions of infinity, but we arent' going to deal with it because of such-and-such a reason. Let's move on to the Indians" or perhaps even "The Taoists also had some early discussions of infinity" woudl do if it's at the end of the section. As it stands now, the reference to them leaves me confused, and wondering why we're bringing them up if we're not goign to say anythign specific. --Iustinus 18:29, 1 Februarii 2007 (UTC)

I'm wondering where the hell I got that from. I don't know a whit about Taoism, so it doesn't seem like something I could've invented...--Ioshus ^(disp) 20:49, 1 Februarii 2007 (UTC)

Was it you who wrote it? We should check the history. --Iustinus 21:06, 1 Februarii 2007 (UTC)

Aha! But it looks like all trace of that was removed from the English article. --Iustinus 06:50, 2 Februarii 2007 (UTC)

And aha! Not that this really tells us much of anything. But since the comment was unsourced, and looked hastily thrown in anyway, maybe we shoudl just cut it out. --Iustinus 07:08, 2 Februarii 2007 (UTC)

Agreed.--Ioshus ^(disp) 13:18, 2 Februarii 2007 (UTC)

My changes to the Midieval Europe section were a bit drastic in some places, so be sure to check if you approve of them. In particular I couldn't understand the last sentence as you had it written, so I checked it against the English and rephrased it. Let me know what you think. --Iustinus 19:45, 1 Februarii 2007 (UTC)

I will when I get home in an hour.--Ioshus ^(disp) 20:49, 1 Februarii 2007 (UTC)

I was just looking at this page to see if I coudl tease out an illustrative quote from Aquinas. It is a useful page, but the author seems to have some Latin troubles: the cited sections don't always seem to say what s/he says they do. --Iustinus 20:08, 1 Februarii 2007 (UTC)

I was looking through summa theologiae the other day. There was plenty on infinity, but I was having trouble gleaning a particularly poignant phrase. ANother thing I will work on in an hour when I get home.--Ioshus ^(disp) 20:49, 1 Februarii 2007 (UTC)

Well, there's "Sed contra, omne corpus superficiem habet. Sed omne corpus superficiem habens est finitum, quia superficies est terminus corporis finiti. Ergo omne corpus est finitum. Et similiter potest dici de superficie et linea. Nihil est ergo infinitum secundum magnitudinem." That's pretty good. --Iustinus 21:06, 1 Februarii 2007 (UTC)

This would go very well in the Torricelli section! The postulation, and the dispoof.--Ioshus ^(disp) 19:43, 10 Februarii 2007 (UTC)

Torricelli

Torricelli published at least Opera geometrica Latine. I wonder if we have it...--Ioshus ^(disp) 18:14, 1 Februarii 2007 (UTC)

Yes. --Iustinus 21:04, 1 Februarii 2007 (UTC)

OK, I found the relevant passage. It's in De solido Hyperobolico, scholium to lemma 5, p.116 = image #362 of Opera Geometrica:

Incredibile videri potest, cum solidum hoc infinitam longitudinem habeat, nullam tamen ex illis superficiebus cylindricis quas nos consideramus, infinitam longitudinem habere; sed vnamquamq' esse terminatam; vt vnicuiq; patebit, cui vel modicè familiaris sit doctrina Conicorum.

This passage seems to turn up a lot (in translation) when the horn is discussed. --Iustinus 22:25, 1 Februarii 2007 (UTC)

Real Number

I have no idea what the proper Latin for "real number" is, but Imaginary is indeed imaginarius. For a discussion, see http://members.aol.com/jeff570/constants.html (which is in general a very useful site for us) --Iustinus 22:49, 1 Februarii 2007 (UTC)

I wrote to Jeff Miller, who maintains that site, asking about this question. He replied that at http://members.aol.com/jeff570/i.html s.v. Imaginary there is a quote in English translation, but of Latin origin, that mentions "real" numbers. This is from the work of none other than John Wallis. The book is indeed online, at http://eebo.chadwyck.com/search/full_rec?ACTION=ByID&SOURCE=pgimages.cfg&ID=V37666 , but I have yet to find the relevant passage.

Also, on Mr. Miller's site, some Latin quotes pertaining to the origin of the lemniscate symbol are found on http://members.aol.com/jeff570/calculus.html . Mostly from the same book by Wallis, but again, no luck so far. --Iustinus 23:42, 1 Februarii 2007 (UTC)

OK! Definition of $\infty$ symbol is on this page! I'd better work out now, instead of trying to find that quote on real numbers. --Iustinus 23:50, 1 Februarii 2007 (UTC)

I'm not finding the "Real numbers" section in this at all. Maybe in the Latin version it was published in volume 1 instead? --Iustinus 06:42, 2 Februarii 2007 (UTC)

The Latin for "real" in the Mathematical sense is indeed realis. Descartes, Geometria III p. 76 (note that Descartes used a different equal sign, that looked rather like a backwards ∝, but I don't know of a unicode sign that will suffice for that).

Quemadmodum , tametsi tres imaginari possimus in hac , x³—6xx+13x—10 = 0 ; tamen una tantùm est realis; nempe 2; & quod ad reliquas duas attinet , quamvis illæ augeantur , diminuantur, aut multiplicentur, sicut jam exposui ; tamen non nisi imaginariæ fieri possunt.

--Iustinus 06:44, 5 Februarii 2007 (UTC)

Good lord, how did I miss all this? Great work. I guess that means I'll write the article on Numeri reales now =] --Ioshus ^(disp) 17:38, 6 Februarii 2007 (UTC)

Verus vs. Purus

In some places you translated "real" as verus, in others purus. It seems to me that your usage does seem to line up with a possible double meaning of the word: on the one hand there's "real number" as opposed to "imaginary number," on the other hand there's "real number" as opposed to "numerical concept." Now that we know the proper term for the former is realis, should I change instances like "Infinity is not a real number" as well, or is that really a subset of the same concept --Iustinus 17:51, 11 Februarii 2007 (UTC)

Hmm, a mathematically inclined friend tells me "Hmmm, well, when a mathematician says 'real number', it never means anything but an element of ℝ." And likewise, articles such as en:Affinely extended real number system seem to imply that "real" does indeed mean "real" in that sense. --Iustinus 18:08, 11 Februarii 2007 (UTC)

renaissance revisions

Iustine, a few things:

1. Nice find on the Galileo quote!

   Interpretis ignotis? Nonne Interpres ignotus? or ablative Interprete ingoto?

2. Elencho?
3. Why not narrare? (not arguing for it, just curious)

--Ioshus ^(disp) 17:33, 6 Februarii 2007 (UTC)

1. Thanks. I noticed it when I was looking for the main quote, but it didn't occur to add it to the article until now.

   You're right, I have been using ablative elsewhere, and that's likely better, since the work itself doesn't belong to the interpreter.

2. Elenchus, in this context, = Socratic dialog. It's not strictly necessary here, but I thought it would be nice.
3. I don't think narrare can mean "tell" in the sense we have here. We want something more like "inform."

--Iustinus 18:18, 8 Februarii 2007 (UTC)

Quo est Cantor?

I have to say, this is a very interesting article; in particular, while I had heard that Galileo had discussed equinumerosity, I don't recall ever seeing this (very lucid) exposition.

But there's a huge, glaring hole in the article! How is it possible to discuss Galilean equinumerosity, and his conclusion that all infinite quantities are the same, without mentioning Cantor's direct refutation of that claim, using precisely Galileo's definition?

It gets worse: Wittgenstein's reactionary little whine is faithfully reproduced, without any mention of what he was whinging about (namely Cantor's work)! Wittgenstein was, to say the least, undistinguished in mathematics; Cantor, on the other hand, initiated the absolutely dominant paradigm for the treatment of the infinite in mathematics since that time (and for much of the rest of mathematics, as far as that goes).

Unfortunately my Latin is not up to the task. I hope someone will quickly rectify this omission. The Cantorian concepts, given their proven fruitfulness, should deserve easily as much screen space as those of Galileo, Locke, Wittgenstein, and Blake, all put together; the notions of those four never really went anywhere. --Trovatore 04:16, 7 Februarii 2007 (UTC)

I leave that decision to Ioshus, who is the principle author of this article. Have you read the english version of this article? What do you think of their presentation of Cantor?

I see Cantor published threeish works in Latin,but I can't find what Latin name he used. --Iustinus 05:21, 7 Februarii 2007 (UTC)

The English exposition is pretty decent, as far as it goes. --Trovatore 05:40, 7 Februarii 2007 (UTC)

Interesting: [2]... both that Cantor apparently wrote that, and that they expand his G.C. signature to G. Cantoris... but that could just be speculation. --Iustinus 05:42, 7 Februarii 2007 (UTC)

It's Georg (so presumably Georgius), and the Library of Congress has one of his Latin volumes, but the online catalogue doesn't specify the Latin form of the name. If only a Vicipaedian worked in the library and could go handle the volume and find out! IacobusAmor 05:51, 7 Februarii 2007 (UTC)

Yeah, one of the books is at my university, but it's the GC one, and presumably he doesn't give his name in any fully form there. One of the others is his dissertation, and as you know, getting latin names from dissertations is next to impossible. --Iustinus 06:09, 7 Februarii 2007 (UTC)

Hi Trovatore, please consider this article a work in progress and nowhere near a finished product. Also realize that it really doesn't prescribe to any one school of thought regarding infinity, so Cantor isn't left out. I ask you to visit this page frequently as iustinus and I are constantly coming up with new material for it. Also, i noticed on your english page that you speak a bit of Italian. You'll want to check out the Italian version of this article, it has a completely different but also very interesting representation of historical views. I plan to incorporate all.--Ioshus ^(disp) 06:04, 7 Februarii 2007 (UTC)

OK, cool. Of course not everything has to be done at once; it just seemed like such an obvious huge hole.

I think Cantor's take ought to go in the "Renaissance to today" section as well as in the mathematics section. What I'd do is put the more philosophical part in "Renaissance to today", mentioning for example the refutation of Galileo on his own terms, and maybe even Cantor's attempt to convince the Catholic Church. The backlash against his ideas (Kronecker, Wittgenstein) should also be mentioned, of course. Then something should be said in the mathematics section about aleph numbers and large cardinals. --Trovatore 07:42, 7 Februarii 2007 (UTC)

Hey, could you point me in the direction of some sources on the refutation of Galilaeus and his attempts to convince the catholic church? The mathematical fonts are easier to find...--Ioshus ^(disp) 02:40, 8 Februarii 2007 (UTC)

You can find the refutation at en:Cantor's diagonal argument (Galileo is not mentioned and I don't actually know whether Cantor had him specifically in mind, but you can see that it's precisely the Galilean notion of equinumerosity that's refuted, between the naturals and the reals). As for the Church stuff, I think it's mentioned in Dauben's biography. I haven't seen my copy since my last move; actually I'm not sure I ever got it back from the girl I lent it to. --Trovatore 04:08, 8 Februarii 2007 (UTC)

What do you think so far, Trovatore? What could be better/worse/different? And I didn't put him in Renaissance, I put him in modern thoughts...--Ioshus ^(disp) 03:33, 12 Februarii 2007 (UTC)

Qyitavkes

That's right, qyitavkes! Er... sorry, I meant "quotables," but I'm tired! Anyway, I'm generally not correcting things if they don't really need it, and your translation of the Einstein quote is fine. Buuut, were I Ioshus, here is how I would have said it: "Duo tantum sunt infinita: universum et stultitia hominum. De illa autem, haud cetus sum." ... just wanted to say that. Please resume what you were doing. --Iustinus 06:51, 8 Februarii 2007 (UTC)

Sententiae Hodiernae

I can't for the life of me figure out what kind of conditional that Blake quote is, even after looking up the context in the original poem. Anyway, you can ask about my latest edit here. --Iustinus 08:22, 9 Februarii 2007 (UTC)

Regarding "If X were, Y would," I think you've got it right: Bradley's Arnold's example is Si hoc dicat, erret 'If he were to say this, he would be wrong' (#450). IacobusAmor 19:54, 10 Februarii 2007 (UTC)

Well, it's trickier than that:

• si purgentur, omnia videantur "If the doors should be cleansed, every thing would appear", i.e. if it should happen.
• "si purgarentur, omnia viderentur "If the doors were (being) cleansed, every thing would appear", i.e. they aren't (being) cleansed, but if they were...
• si purgatae essent, omnia viderentur "If the doors were (already) cleansed, every thing would appear" i.e. they have not been cleansed, but if they were...

I'm not really sure which of these is closest to what Blake had in mind. --Iustinus 20:09, 10 Februarii 2007 (UTC)

As I understand Blake, he meant the first one. It has potential, "when the doors will have been cleaned, everything will be infinite".--Ioshus ^(disp) 20:14, 10 Februarii 2007 (UTC)

Sicut ait Ioshus, credo Blake primam significationem intendisse. IacobusAmor 20:18, 10 Februarii 2007 (UTC)

ordo

Locutionem Einstein in animo habui esse epigramma, non partem veram. Et theoria serierum bene ducta est ex quibus super scriptis. At bene dicis, ordo sit per tempus.--Ioshus ^(disp) 19:48, 10 Februarii 2007 (UTC)

Limit

According to [3]:

Gregory of St. Vincent (1584-1667) used terminus to mean the limit of a progression, according to Carl B. Boyer in The History of the Calculus and its Conceptual Development.

But then it goes on to quote Newton's Principia, 1.1 ad fin. The quote is given in translation, but I looked up the original Latin and got:

Ultimae rationes illae quibuscum quantitates evanescunt, revera non sunt rationes quantitatum ultimarum, sed limites ad quos quantitatum sine limite decrescentium rationes semper appropinquant; & quas propius assequi possunt quam pro data quavis differentia, nunquam vero transgredi, neque prius attingere quam quantitates diminuuntur in infinitum. (etc.)

So looks like Newton used limes. I guess that's more likely to be the "official" word. --Iustinus 06:59, 11 Februarii 2007 (UTC)

zenonis paradoxa

In anticipation of Iustinus coming through witht eh greek text:

"You can never catch up." "In a race, the quickest runner can never overtake the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead." (Aristotle Physics VI:9, 239b15)

--Ioshus ^(disp) 06:03, 12 Februarii 2007 (UTC)

The Greek I can five you immediately. It's the Latin that will be difficult. ANd there's more good stuff in the quote than what you have here, so I'll give you the whole paragraph:

"Ζήνων δὲ παραλογίζεται· εἰ γὰρ αἰεί, φησίν, ἠρεμεῖ πᾶν [ἢ κινεῖται] ὅταν ᾖ κατὰ τὸ ἴσον, ἔστιν δ’ αἰεὶ τὸ φερόμενον ἐν τῷ νῦν, ἀκίνητον τὴν φερομένην εἶναι ὀϊστόν. τοῦτο δ’ ἐστὶ ψεῦδος· οὐ γὰρ σύγκειται ὁ χρόνος ἐκ τῶν νῦν τῶν ἀδιαιρέτων, ὥσπερ οὐδ’ ἄλλο μέγεθος οὐδέν. τέτταρες δ’ εἰσὶν οἱ λόγοι περὶ κινήσεως Ζήνωνος οἱ παρέχοντες τὰς δυσκολίας τοῖς λύουσιν, πρῶτος μὲν ὁ περὶ τοῦ μὴ κινεῖσθαι διὰ τὸ πρότερον εἰς τὸ ἥμισυ δεῖν ἀφικέσθαι τὸ φερόμενον ἢ πρὸς τὸ τέλος, περὶ οὗ διείλομεν ἐν τοῖς πρότερον λόγοις. δεύτερος δ’ ὁ καλούμενος Ἀχιλλεύς· ἔστι δ’ οὗτος, ὅτι τὸ βραδύτατον οὐδέποτε καταληφθήσεται θέον ὑπὸ τοῦ ταχίστου· ἔμπροσθεν γὰρ ἀναγκαῖον ἐλθεῖν τὸ διῶκον ὅθεν ὥρμησεν τὸ φεῦγον, ὥστε ἀεί τι προέχειν ἀναγκαῖον τὸ βραδύτερον. ἔστιν δὲ καὶ οὗτος ὁ αὐτὸς λόγος τῷ διχοτομεῖν, διαφέρει δ’ ἐν τῷ διαιρεῖν μὴ δίχα τὸ προσλαμβανόμενον μέγεθος. τὸ μὲν οὖν μὴ καταλαμβάνεσθαι τὸ βραδύτερον συμβέβηκεν ἐκ τοῦ λόγου, γίγνεται δὲ παρὰ ταὐτὸ τῇ διχοτομίᾳ (ἐν ἀμφοτέροις γὰρ συμβαίνει μὴ ἀφικνεῖσθαι πρὸς τὸ πέρας διαιρουμένου πως τοῦ μεγέθους· ἀλλὰ πρόσκειται ἐν τούτῳ ὅτι οὐδὲ τὸ τάχιστον τετραγῳδημένον ἐν τῷ διώκειν τὸ βραδύτατον), ὥστ’ ἀνάγκη καὶ τὴν λύσιν εἶναι τὴν αὐτήν. τὸ δ’ ἀξιοῦν ὅτι τὸ προέχον οὐ καταλαμβάνεται, ψεῦδος· ὅτε γὰρ προέχει, οὐ καταλαμβάνεται· ἀλλ’ ὅμως καταλαμβάνεται, εἴπερ δώσει διεξιέναι τὴν πεπερασμένην. οὗτοι μὲν οὖν οἱ δύο λόγοι, τρίτος δ’ ὁ νῦν ῥηθείς, ὅτι ἡ ὀϊστὸς φερομένη ἕστηκεν. συμβαίνει δὲ παρὰ τὸ λαμβάνειν τὸν χρόνον συγκεῖσθαι ἐκ τῶν νῦν· μὴ διδομένου γὰρ τούτου οὐκ ἔσται ὁ συλλογισμός."

Hmm... maybe that was more than you needed ;) --Iustinus 06:27, 12 Februarii 2007 (UTC)

Again, from the translation of Argytopylus:

"Zeno vero prave ratiocinatur. dicit enim, si semper omne quiescit aut movetur, cum est in sibi aequali, id autem quod fertur, est sibi aequali spatio, in ipso nunc semper, immobilem eam esse sagittam quae fertur. hoc autem est falsum: tempus enim non ex ipsis nunc indivisibilibus constat, quemadmodum nec ulla alia magnitudo. quattuor autem Zenonis de motu sunt rationes, quae difficultatem solventibus afferunt. at prima quidem est ea qua motus ex eo tollitur, quia prius ad medium quam ad finem id quod fertur pervenire oportet: de qua distinximus antea. secunda vero est ea quae nuncupatur Achilles, qua motus rursus ex eo tollitur, quia nunquam id quod celerrime currit, id consequetur quod tardius currit: id enim quod persequitur eo perveniat ante necesse est, unde id quod fugit fugam arripuit; quare tardius ipsum semper aliquo spatio praecedat necesse est. est autem et huius rationis eadem vis quae in partes aequales sectionis; sed hoc differt, quod magnitudinem quae accipitur non in dimidia dividit. accidit igitur ut tardius ipsum non attingatur ex ratione nimirum ipsa. fit autem ob divisionem, qua quidem et antecedens utitur ratio. in utrisque namque fit ut non perveniatur ad finem magnitudine subeuntem et si non eodem modo, divisionem. sed in hac additur tamquam tragice decantatum, ne celerrimum quidem unquam tardissimum attingere persequendo. quare solutionem utriusque eandem esse necesse est. id vero, quod censet nunquam id attingi quod antecedit, falsum est: nam cum antecedit, non attingitur, attamen attingitur tandem, si dabit magnitudinem finitam id quod movetur transire. hae igitur duae sunt rationes Zenonis. tertia vero est ea quae quiescere dicit sagittam, cum fertur; de qua paulo ante diximus. Accidit autem id ex eo quia tempus sumitur ex suis punctis constare; quod si non dederis, ratio continuo exspirabit.

Whew, that was long, and we are certain to only use a small part of it. There are bound to be errors too, set let me know if you catch any. --Iustinus 00:58, 21 Februarii 2007 (UTC)

archimedes quote

"There are some, King Gelon, who think that the number of the sand is infinite in multitude; and I mean by the sand not only that which exists about Syracuse and the rest of Sicily but also that which is found in every region whether inhabited or uninhabited." (I'll try and find the location)--Ioshus ^(disp) 04:22, 13 Februarii 2007 (UTC)

• Archemedis Arenarius (!) 2.134:

Οἴονταί τινες, βασιλεῦ Γέλων, τοῦ ψάμμου τὸν ἀριθμὸν ἄπειρον εἶμεν τῷ πλήθει· λέγω δὲ οὐ μόνον τοῦ περὶ Συρακούσας τε καὶ τὰν ἄλλαν Σικελίαν ὑπάρχοντος, ἀλλὰ καὶ τοῦ κατὰ πᾶσαν χώραν τάν τε οἰκημέναν καὶ τὰν ἀοίκητον.

• --Iustinus 06:06, 16 Februarii 2007 (UTC)

Close translation:

Opinantur quidam, Gelon Rex, harenae numerum infinitum esse multitudine: dico autem non solum quae et circa Syracusas et alias partes Siceliae sunt, sed etiam per omnes terras et habitatas et desertas.

--Iustinus 21:15, 18 Februarii 2007 (UTC)

Actual published translation:

Sunt, qui existement, rex Gelo, numerum arenae infinitum esse magnitudine; dico autem, non solum eius, quae circa Syracusas et reliquam Siciliam est, sed etiam quae in qualibet regione siue culta siue inculta.

A footnote after the word magnitudine specifies "Hoc tritum prouerbium erat Graecis; Pindarus Ol. II, 98; Paroemiogr. Gr. p. 11, 167, 250 ed. Gaisford"

The author's name is given as J. L. Heiberg. The only one of Dr. Heiberg's Latin works I can find in which his name is given in full says "Iterum edidit Iohan Ludvig Heiberg," but I don't think it's too much of a stretch for us to say Iohannes Ludovicus, do you? --Iustinus 01:17, 21 Februarii 2007 (UTC)

Hardly a stretch at all, barely a lean... Your translation was pretty close.--Ioshus ^(disp) 01:46, 21 Februarii 2007 (UTC)

End of Infinity

The end of Infinitas' reign as article of the month is drawing near. I'll need to finish proofing it for good before the time is up. In the meantime, Ioshus, I'll be on campus again this afternoon. Anything else you want me to look for? --Iustinus 18:07, 27 Februarii 2007 (UTC)

Well, it's over. Congratulations! --Iustinus 18:36, 1 Martii 2007 (UTC)

Thanks! That was fun. =] --Ioshus ^(disp) 19:28, 1 Martii 2007 (UTC)