What is the latin name for the hasty generalization fallacy?

I've searched randomly on google, and "Dicto Simpliciter" comes up as the latin name for the hasty generalization fallacy, yet it also appears when I searchfor the latin name of the sweeping generalization fallacy. Is there a definite latin name for the hasty generalization fallacy?

It’s always been my understanding that the fallacy of “hasty generalization” is also known as secundum quid, its Latin name. The following excerpt is from Madsen Pirie’s book How to Win Every Argument: The Use and Abuse of Logic:

“ The fallacy of secundum quid is otherwise known as the hasty generalization. Whenever a generalization is reached on the basis of a very few and possibly unrepresentative cases, the fallacy is committed. It takes the argument from particular cases to a general rule on the basis of inadequate evidence. 

I was in Cambridge for ten minutes and I met three people, all drunk. The whole place must be in a state of perpetual inebriation.

 ( Not necessarily so. Saturday night outside Trinity College might be quite different from King’s on Sunday. A similar conclusion about London might have been drawn by a visitor who saw three people at midday outside a newspaper office.)

The fallacy lies in the assumption of material which ought to be established. There should be an attempt to establish that the sample is sufficiently large and sufficiently representative. One or two cases in particular circumstances do not justify the presumption of a general rule, any more than the sight of a penny coming down heads can justify a claim that it will always do so. Behind our identification of the fallacy lies our recognition that the few cases observed might be exceptional to any general rule which prevails. 

Don’t shop there. I once bought some cheese and it was mouldy. 

( This smells like a broad condemnation placed on a narrow base.) 

Clearly there is fine judgement required to distinguish between a secundum quid and a case where one or two instances do enable a valid judgement to be made. When assessing the fitness of a candidate for foster-parent, for example, it would be prudent to make a judgement on the basis of only one previous incident of child-molesting. In the film Dr Strangelove, when a psychotic commander sends his wing on a nuclear attack against the USSR, the General reassures the President: ‘You can’t condemn the whole system just because of one let-down.’ Both of these cases deal with systems which seek 100 per cent safety coverage, and in which one exception does validate a judgement. Secundum quid covers the more general circumstance in which it does not. 

A visitor who assesses the population of London from his experience of a royal wedding day is likely to be as wrong as one who makes a similar judgement about Aberdeen on a charity-collection day. The basic rule is ‘don’t jump to conclusions’. Opinion pollsters try to be very careful to avoid secundum quids. A famous American poll once wrongly predicted a Republican victory because it surveyed by telephone, not realizing that fewer Democrats owned telephones. Political parties everywhere are not averse to ‘talking up’ their support by quoting obviously unrepresentative poll-findings.

Scientific knowledge is like a battlefield mined with secundum quids . Scientific theories are often put forward with only a very few examples to back them up. The problem is one of knowing knowing when there are enough case-histories to be sure about the general rule put forward to explain them. Astonishingly, the answer is never. Science proceeds with the knowledge that a new case could suddenly appear to show that even its most solid theories are no good. A billion apples might have hit a billion heads since Newton’s, but it would still take only one apple going upward to force at least a modification to the general theory. Secundum quids will be very useful to you in persuading audiences to pass judgements which coincide with your own. You should appeal to one or two cases, well-known ones if possible, as proof of a general judgement. 

All actors are left-wing subversives. Let me give you a couple of examples . . . 

(You then spread over the entire profession the tar which your brush collected from two of them.)”

I’ve always referred to hasty generalizations as secundum quid and sweeping generalizations as dicto simpliciter. So I suppose a distinction is made between hasty generalizations and sweeping generalizations. 

Dicto simpliciter (literally: "said simply") is a shortened form of a dicto simpliciter ad dictum secundum quid (literally: "from said simply to saying 'according to' something")

To further complicate things, this fallacy is also sometimes called secundum quid or secundum quid et simpliciter.

Per Wikipedia: The fallacy "fails to recognize the difference between rules of thumb (soft generalizations, heuristics that hold true as a general rule but leave room for exceptions) and categorical propositions, rules that hold true universally. Since it ignores the limits, or qualifications, of rules of thumb(*), this fallacy is also named ignoring qualifications."

That's a good way of putting it. The dicto simpliciter is the simple, qualified statement. The secundum quid is the absolute, unqualified statement. Arguing that one supports the other is a logical fallacy.

The modifiers "hasty" and "sweeping" are other ways of adding color to the interpretation of this Latin phrase.

* I don't recall what the literal "rule of thumb" was, but I know of an analogous example. A human foot is about 12 inches. However, it would be fallacious to argue that my foot could be used to get an accurate measure of a room.