When I first saw this text it too struck me as unclear and unnatural. The first problem has since been resolved, the second however remains. Another reply mentions Foster himself translating it as 'Insert your card--scidulam--so you can access the operations allowed.' - that's certainly not an exact rendering of what the Latin says, which is instead:
"I kindly ask that you then insert your card in order to learn what approach needs to be done."
From this follow my observations that will simultaneously try to answer the questions:
- inseritō: the future imperative is the standard form of instruction in manuals; however, I don't think it's appropriate in an immediate address:
"The present imperative differs from the future imperative in -to, the semantic value of which is, certainly in Early Latin comedy and in legal texts, ‘non-immediate realization of the action involved’. When the present and future imperatives
co-occur, the difference in immediacy becomes apparent..." (Pinkster 2015: 515)
- scidula: σχίδα~η seems to be a variant of σχέδη already in Greek; sc(h)eda looks to be reflected by Italian sc/ɛ/da (no diphthong would mean a native Tuscan survival).
- quaesō: I think it does anthrophomorphize the machine, and this is normal - we digital moderns anthropomorphize them all the time, and in Latin this is taken to eleven and one of the most common sources of neologisms. In this case, however, quaesō might be a little too friendly-conversational (Cicero in his letters reserves it for the most personal requests) and rogō might have been more appropriate - or in fact the even more impassionate rogāmus.
- I disagree that if an English translation does not, this means that the original doesn't either - in many cultures animal names are employed metaphorically to refer to certain objectionable human qualities, like "an ass=donkey" for dim-witted and obstinate people, and the fact that in English "ass" refers to the buttocks while "donkey" isn't used as an insult bears no relation to the fact that calling someone осёл in Russian is clearly zoomorphising, as is incidentally су́ка "bitch" - less so in English.
- ratiō faciunda uses ratiō in the sense "logical method, approach, way of proceding", but the use of facere seems unnatural to me, which I illustrate in the translation "to do an approach". I've found no instances of this collocation. This is the main reason the sentence is difficult to understand - since this meaning of the noun that exhibits a great variety of idiomatic uses doesn't work with a verb whose meaning is itself extremely bleached, and there's no clue as to what other meaning could have been intended.
- I don't think it can be "transaction", because the ATM has no business telling the user which monetary transaction they need to perform - it's the other way around.
- notice -und- instead of the more common -end- – their distribution was determined partly stylistically and partly word-by-word, and for facere in official contexts this form was indeed preferred, although this is not reflected by modern editions.
- cōgnōscās is simply "to get to know some information", which is it's primary meaning. It promises to tell you how to proceed next.
- The word order is the default one after a fronted faciundam, at least in written use. It exhibits what's commonly known in relation to Latin as 'hyperbaton' - a discontinuous noun phrase. In proper syntacticianese this is called 'movement', and in the case of leftwards movement 'fronting'. Here the underlying word order before fronting is cōgnōscās ratiōnem faciundam, while its presence adds a certain amount of poetic flavour.
- I suppose the most unmarked word order is ratiōnem faciundam cōgnōscās, with phrasal stress on the second word - the fronting of one member of the noun phrase is marked already, while faciundam ratiōnem cōgnōscās is doubly so and places stress on ratiōnem - or can be an instance of right-movement of cōgnōscās, thus delaying, suspending it (accompanied by a suspended intonation and possibly a pause).
My own rendering of 'Please insert your card to receive further instructions' would be:
Insere schedulam, rogāmus, ut agendī ratiōnem accipiās.
Notice the genitive nd-noun ("gerund") instead of the nominative nd-adjective ("gerundive") - this might be what Foster was going for, but he confused the two verbs and consequently the two constructions. Paradoxically enough I feel that this is the least marked word order in this case, since agendī ratiō is a single, quasi-compound noun phrase, quite regularly so when it comes to generic-reference objective genitive expressions - indeed, (Spevak 2010: 99 & 182) concurs that "genitives with generic referents [...] are often pre-nominal" and "objective genitives coming last are semantically prominent".
As for translating 'so you can access the operations allowed', I think I'd be stretching the idiomatic resources of Latin and/or my knowledge of its financial jargon, but I think this would be sufficiently clear:
...ut certior fīās quae ratiōnēs aut negōtia cūrārī possint.
- Pinkster H. (2015). The Oxford Latin Syntax
- Spevak O. (2010). The Noun Phrase in Classical Latin Prose