An 18th century dissertation

[Alatius]

Salve(te)! As a part of a paper, I'm setting out to translate an 18th century mathematical dissertation, but I must admit I'm a bit humbled by the many problems I have encountered in only the very first paragraphs... It was a while since I studied Latin actively, and so I feel I bit rusty. Perhaps you can give me some help? The text begins:

"Quamvis hominum felicitati terrestri promovendæ, vix aliud excellentius ac usibus eorum magis accommodatum videatur, quam divinæ studium Matheseos; non tamen defuere, qui huic scientiæ debitam detrahere laudem non fuerint veriti, nec qui 'apicem eruditionis humanæ', Analysin Mathemathicam, a cavillationibus intactum relinquere voluerunt."

("Matheseos" is a Greek genitive, ἡ μάθησις -εως.)

First, what to do with the isolated "quamvis ... promovendae"? Based on what the sentence ought to mean, it feels like I have to supply "sit accomodatum" from the following main clause, and I would then translate it as "However much it may serve to promote the humans' earthly happiness, hardly any other study seems more excellent and more suitable to their use, than that of the divine Mathematics". Other opinions?

"However, there has been no shortage of people who did not hesitate to deprieve this science of the glory it deserves..." So far, so good. But does the rest translate to "... and who did not want to leave the mathematical analysis intact from scoffings"? The thing is, I can also imagine that it might mean the opposite: "... nor was there a shortage of people who wanted to leave it intact." Is that a possibility? (The context, I might add, points to the first meaning.) What is the significance of the fact that we have "fuerint" in the subjunctive, but "voluerunt" in the indicative?

[adrianus]

I'd say this, Alatius // Hoc, Alati, propono:

Although scarcely anything would seem more excellent for the advancement of people's earthly happiness and more suitable for their benefits than study of heavenly mathematics [astrology, depending on context / quod e contextu pendet], there was not however any lack of those who would not have feared to withhold the praise [potential thing // res possibilis] due to this science, nor of those* [sic] who were willing that Mathematical Analysis, the "pinnacle of human learning", should be left unscathed by [their] scoffing[s] [done thing // res facta].

Corrigendum. Vide infrá: non "of those" sed "were there those".

[modus.irrealis]

If that comma weren't there after "promovendae", that would make the most sense as the subjunctive "videatur" would belong to the quamvis-clause, like in adrianus's translation. And what else could the subjunctive be doing?

"However, there has been no shortage of people who did not hesitate to deprieve this science of the glory it deserves..." So far, so good. But does the rest translate to "... and who did not want to leave the mathematical analysis intact from scoffings"? The thing is, I can also imagine that it might mean the opposite: "... nor was there a shortage of people who wanted to leave it intact." Is that a possibility? (The context, I might add, points to the first meaning.) What is the significance of the fact that we have "fuerint" in the subjunctive, but "voluerunt" in the indicative?

I think it can only be the latter and that "nec qui..." = "et non defuere qui...". I'm not sure that "nec qui..." = "et qui non..." is possible. But you're right that the context requires a negative sense. I understand it as saying "although math is so great, there was no shortage of people who wanted to leave it untouched from their sophistires (i.e. ignore it)", taking "cavillatio" with that meaning and seeing it as a criticism of those people by the author.

[adrianus]

I think it best to translate this way // Melius est sic vertere, ut opinor: "nor were there those [who wanted mathematics to remain untouched by scoffing]"
instead of (as I previously wrote) // non (ut priùs verti) "nor of those [i.e., no shortage of those who wanted mathematics to remain untouched by scoffing]"