I'm following an ancient Teach Yourself Ancient Greek course. This is from a (presumably highly simplified) version of Xenophon's account of Spartan education:
βελτιον γαρ ἐστιν, ὡς φασιν, ὀλιγον χρονον ἀλγησαντα, πολυν χρονον εὐδοκιμουντα εὐφραινεσθαι.
This book's explanation of the participles ἀλγησαντα (and εὐδοκιμουντα as well, I surmise) is as follows:
ἀλγησαντα is accusative, agreeing with "one" understood, and subject of εὐφραινεσθαι. "It is better, as they say, for one having suffered a short time (acc.) to enjoy having a good reputation for a long time". This is called the accusative and infinitive construction, and corresponds to a noun clause in English.
Firstly, unless I'm much mistaken, ἀλγησαντα is acc. m. s. (could be nom./acc. n. pl. but the explanation seems to say not). So why is it described as the "subject" of εὐφραινεσθαι, rather than its "object"? Also, εὐφραινεσθαι means "to enjoy", so I'm a bit baffled that you would "enjoy suffering" (although can't rule it out, given the notoriously kinky nature of the Spartans generally). Also, the English translation given by the author does not have "having suffered" as the subject/object of "to enjoy" and thus seems at variance with the explanation.
Clearly though, there does appear to be a sense of "better it is X ... in order to Y" conveyed by the entire sentence, though I'm not clear whether "in order to" is entirely implicit from "βελτιον ἐστιν...[participle 1], [participle 2]" or conveyed by some other element here.
But can someone say why these participles are in the acc. m. s. (if indeed they are)? What then is the implicit subject in the case of ἀλγησαντα: is it (a masculine) "one" as the book says? And what has turned it accusative?
I've also found what I hope is the real text, from here.
...καὶ ὡς πλείστους δὴ ἁρπάσαι τυροὺς παρ’ Ὀρθίας καλὸν θείς, μαστιγοῦν τούτους ἄλλοις ἐπέταξε, τοῦτο δηλῶσαι καὶ ἐν τούτῳ βουλόμενος ὅτι ἔστιν ὀλίγον χρόνον ἀλγήσαντα πολὺν χρόνον εὐδοκιμοῦντα εὐφραίνεσθαι.