This is delightful! Finally I can learn how those bina, quina etc. words work. I was wondering . . . why "essent" and not "sint"? Also, "triginta" is missing the letter "n" on page 28.
Thanks for noting the typo! I have fixed that, and also let Evan know about your comment to see how this fits in with Comenius's usage in general.
My guess is that it has to do with the hypothetical nature of this kind of math: semel quina is not quite the same as when we say "one times five" in English; it is more like saying "if one time you had five OF SOMETHING" or "one time a group of five" (since quina is a group of five things, not just a pure number, like quinque, 5). So, in this hypothetical calculation, we don't have five of anything really; we are just pretending to have these groups of five when we do the math - but if we DID have five of something, then here is the calculation.
Just my quess, though - let's see what Evan says! I had no idea how math was done out loud in Latin before Evan started posting these nifty readers for us to read!
I have scratched my head over this one. I could find very few attestations of mathematical language in the classical authors. The first question, was, should I use a singular verb when multiplying by semel. I still have not resolved this question....i.e. five times one IS, or five times one ARE....
The second was, the form of the subjunctive verb in the dependent question.
I had found in Riddle's dictionary " Non didicit bis bina qvot sint" , elsewhere this is rendered ' non didicit bis bina qvot essent' (Which is a qvote from Cicero - so I went with the version that was attested....). In Sonnenschein's grammar, we also find both: Here is one example: "Nescit quot bis bina sint" "Nesciebat qvot bis bina essent" Here the agreement of the subjunctive seems to be more clear..... Now, these are both dependent questions, but have the same structure as "Scisne bis bina quot essent". Scisne has the same structure as nescis (with the difference of person only) in the quote from Cicero. Cicero did not write 'nesciebat qvot bis bina essent', but 'Nescit bis bina qvot essent'. This appears to break the rule of agreement.....so I understand the question being asked.
Krebs offers "Qvot sunt bis bina?" as a direct question.
I still think it's still a hypothetical subjunctive rather than an indirect question one (the didicit example, and the nescit/nesciebat examples are clearly indirect questions) - we are pretending that we have a group of five things (as opposed to just the cardinal number five), and so we need the subjunctive eo engage in that pretense, since we don't have a five things at all (like all those hypothetical word problems in math class: If a train going 45 miles per hour leaves the station heading due east at 2pm, etc. etc.). Anyway, I really am fascinated by this question. Just this week we started a reading group at Fireside on the history of Greek math and this use of the distributive words in Latin to pose a mathematical problem really reminds me of the definition of arithmos as a number in Greek, i.e. a number of COUNTED things, a group of things. I don't know how they did oral multiplication questions in Greek; I'll see if I can find out!
This is delightful! Finally I can learn how those bina, quina etc. words work.
ReplyDeleteI was wondering . . . why "essent" and not "sint"?
Also, "triginta" is missing the letter "n" on page 28.
Thanks for noting the typo! I have fixed that, and also let Evan know about your comment to see how this fits in with Comenius's usage in general.
ReplyDeleteMy guess is that it has to do with the hypothetical nature of this kind of math: semel quina is not quite the same as when we say "one times five" in English; it is more like saying "if one time you had five OF SOMETHING" or "one time a group of five" (since quina is a group of five things, not just a pure number, like quinque, 5). So, in this hypothetical calculation, we don't have five of anything really; we are just pretending to have these groups of five when we do the math - but if we DID have five of something, then here is the calculation.
Just my quess, though - let's see what Evan says! I had no idea how math was done out loud in Latin before Evan started posting these nifty readers for us to read!
I have scratched my head over this one. I could find very few attestations of mathematical language in the classical authors.
ReplyDeleteThe first question, was, should I use a singular verb when multiplying by semel. I still have not resolved this question....i.e. five times one IS, or five times one ARE....
The second was, the form of the subjunctive verb in the dependent question.
I had found in Riddle's dictionary " Non didicit bis bina qvot sint" , elsewhere this is rendered ' non didicit bis bina qvot essent' (Which is a qvote from Cicero - so I went with the version that was attested....).
In Sonnenschein's grammar, we also find both:
Here is one example: "Nescit quot bis bina sint"
"Nesciebat qvot bis bina essent"
Here the agreement of the subjunctive seems to be more clear.....
Now, these are both dependent questions, but have the same structure as "Scisne bis bina quot essent". Scisne has the same structure as nescis (with the difference of person only) in the quote from Cicero. Cicero did not write 'nesciebat qvot bis bina essent', but 'Nescit bis bina qvot essent'. This appears to break the rule of agreement.....so I understand the question being asked.
Krebs offers "Qvot sunt bis bina?" as a direct question.
I still think it's still a hypothetical subjunctive rather than an indirect question one (the didicit example, and the nescit/nesciebat examples are clearly indirect questions) - we are pretending that we have a group of five things (as opposed to just the cardinal number five), and so we need the subjunctive eo engage in that pretense, since we don't have a five things at all (like all those hypothetical word problems in math class: If a train going 45 miles per hour leaves the station heading due east at 2pm, etc. etc.). Anyway, I really am fascinated by this question. Just this week we started a reading group at Fireside on the history of Greek math and this use of the distributive words in Latin to pose a mathematical problem really reminds me of the definition of arithmos as a number in Greek, i.e. a number of COUNTED things, a group of things. I don't know how they did oral multiplication questions in Greek; I'll see if I can find out!
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