At the beginning of Dē frāctiōnibus continuīs dissertātiō, Euler writes the following:
Variī in Analysin receptum sunt modī quantitātēs.
in Analysin just means in Analysis but the rest of the sentence is a bit odd to me.
Variī receptum sunt modī quantitātēs.
Indeed receptum is singular while variī, sunt, quantitātēs are plural. How should I parse this sentence?
Edit. receptum should be receptī
You need the whole sentence. Reading from this scan, I get:
Varii in Analysin recepti sunt modi quantitates, quae alias difficulter assignari queant, commode exprimendi.
It might be easier to parse if I reorder it so that the words that belong together are actually close:
In Analysin recepti sunt varii modi commode exprimendi quantitates, quae alias difficulter assignari queant.
Now recepti (not -um!), varii, and modi are in the same form, and quantitates is the object of exprimere. This reads as:
In Analysis we have various ways to conveniently express quantities, which are otherwise difficult to assign.
I took some liberties translating. More literally, modi recepti sunt means "ways are received (back)" — I get the feeling that for Euler the prefix re- here did not necessarily mean getting something back as it did in classical times — but I translated it as "we have". This was just to conform to modern mathematical style and idiomatic English. The same applies to difficulter assignari queant, which would more literally be "are difficultly able to be assigned".
And this makes a lot of sense if the topic is continued fractions, a method of expressing quantities differently than one might first expect. And I should also add that I do like the way Euler constructed his opening sentence. It starts with emphasis on varii, and the convenience of expressing is only mentioned after the difficulty of expressing otherwise. It is a little slower to parse perhaps, but I find it to be dramatically correct in the more convoluted order.
