What are the earliest known uses of vicious circle, in its two senses, and vicious cycle? And can we tell anything of what motivated the variant vicious cycle?
Merriam-Webster and Etymoline are fairly detailed about the origin of vicious circle but say little (M-W) or nothing (Etymoline, cycle) about the origin of vicious cycle. And neither quotes the actual earliest known uses. From Etymoline:
vicious […] In law, “marred by some inherent fault” (late 14c.), hence also this sense in logic (c. 1600), as in vicious circle in reasoning (c. 1792, Latin circulus vitiosus), which was given a general sense of “a situation in which action and reaction intensify one another” by 1839.
From Merriam-Webster:
Vicious circle originally referred to a circular argument, that is, an argument that assumes the conclusion as one of its premises. That sense was first documented around the end of the 18th century. Approximately 50 years later, vicious circle acquired the now more common “chain of events” sense as people began to think of the circle as a metaphorical circle rather than a circular argument. Today, vicious cycle is a common variant for the “chain of events” sense. Vicious spiral, in which the ill effects are cumulative as well as self-aggravating, puts in an occasional appearance as well.
Google Books Ngram suggests vicious cycle appears early in the 20th century.
My second question, can we tell anything about what motivated the variant vicious cycle, is a lot harder, but maybe someone wrote about it in the early days, either condemning or defending vicious cycle. I can think of two possibilities: people mixed up circle and circle; or someone thought cycle was a better metaphor than cycle for the ‘chain of problems’ sense. To my mind circle is the more appropriate metaphor for ‘circular reasoning’. Well it isn’t for nothing we call that reasoning circular: it ends where it had began. The chain of ill effects we name ‘vicious circe/cycle’ is especially vicious because it keeps recurring (say poor sales, firms lay off people, income and demand falls, sales get poor, firms lay off more people, and on and on). Cycles recur too, so maybe some people thought cycle was a better metaphor.
Best Answer
'Vicious circle' as an error in reasoning
The earliest match for "vicious [or rather, vitious] circle" that I've been able to find appears in Edward Maihew, A Treatise of the Groundes of the Old and Newe Religion (1608). Unfortunately, I haven't been able to gain access to the contents of this book beyond its table of contents, so I can't provide the actual quotation here.
However, the term appears multiple times just seven years later in John Ainsworth & Henry Ainsworth, The Trying Out of the Truth Begunn and Prosequuted in Certayn Letters and Passages Between Iohn Aynsworth and Henry Aynsworth; the One Pleading for, the Other Against the Present Religion of the Church of Rome (1615):
Throughout this series of dueling arguments, the Ainsworths agree in defining a "vicious circle" (evidently on the authority of Aristotle) as a form of pseudo-logic that uses its parts to prove each other. The vice in a "vicious circle" thus lies in its inadequacy and deceptiveness as a claim to offer real proof of a proposition and, secondarily, in its entrapment of the deluded person's mind, which renders him incapable of seeing the falsity of the argument.
A number of other seventeenth-century religious polemicists use "vicious circle" in a similar way. In all, searches for the terms "vicious circle" and "vitious circle" at Early English Books Online yield some three dozen matches, all of them using it in the rhetorical sense of a logical argument that purports to prove its conclusion by citing an assumption whose validity depends on the validity of the conclusion.
A century after the Ainsworths, Charles Leslie, The Case Stated Between the Church of Rome and the Church of England in a Second Conversation Betwixt a Roman Catholick Lord and a Gentleman of the Church of England (1721) provides a helpful definition of the term "vicious circle":
'Vicious circle' as a recurring series of unfortunate events
The earliest instance that I've been able to find of "vicious circle" in the sense of "undesirable or evil recurring chain of events" occurs much later, in "The Provincial Contest," in the Madison [Indiana] Republican (July 19, 1817):
And from "Letter from Sydney," in the Sydney [New South Wales] Gazette And New South Wales Advertiser (March 18, 1830):
'Vicious cycle'
The phrase "vicious cycle" doesn't appear at all in the Early English Books Online database. The earliest occurrence of it that I am aware of is from Isaac Newton, Observation upon the Prophecies of Daniel, and the Apocalypse of St John (1733), page 246:
This interesting example involves use of "vicious cycle" as a kind of short form for "vicious lunar cycle"—Newton's chief interest being to corroborate or refute Epiphanius's claim that the Jewish calendar was two days out of synch with the actual lunar cycle. As with the original sense of "vicious circle," the sense of vicious" here seems to be "fundamentally flawed" or "ill-reasoned," not "wicked" or "deplorable" or "reprehensible."
The next instance of "vicious cycle" that I found was much later, however. From an untitled item in the [Melbourne, Victoria] Argus (June 8, 1877):
Here we have "vicious cycle" as sense 2 of "vicious circle": a recurring series of unfortunate events.
Usage commentators on 'vicious circle' and 'vicious cycle'
Here is an Ngram chart tracking the relative frequency of "vicious circle" (blue line) and "vicious cycle" (red line) over the period 1750–2005:
The most striking thing about this chart is how close the frequencies of the two phrases has become during the period from 1979 to 2005. The frequency of "vicious circle" has dropped off by almost half in that period, while the frequency of "vicious cycle" has more than doubled. As a result, "vicious circle" was only slightly more frequent than "vicious cycle" in works published in 2005.
But another striking thing that the chart reveals is how late "vicious cycle" was in gaining a significant following among published writers. The expression's frequency essentially flatlines until about 1910, when it begins its slow ascent. Because it is rather late to the party of everyday English "vicious cycle" doesn't show up in the works of early commentators who focused on correcting what they considered errors in usage.
Even as late as Bergen Evans & Cornelia Evans, A Dictionary of Contemporary American Usage (1957), a two-paragraph entry for "vicious circle" doesn't mention "vicious cycle" at all:
William Morris & Mary Morris, Harper Dictionary of Contemporary Usage, second edition (1985) does include an entry on the two terms but seems to have little use for "vicious cycle":
But eighteen years later, Bryan Garner, Garner's Modern American Usage, second edition (2003) accepts "vicious cycle" as legitimate alternative to "vicious cycle":
Conclusions
As a term in logic, "vicious circle" is very old indeed, dating to the early 1600s at least. Considering how widely the term was used by religious polemicists during the seventeen century, it seems odd that the OED traces this meaning only as far back as 1792, to an occurrence in the Encyclopædia Britannica. Here, at greater length, is that occurrence, from the entry for "Lightning" in the 1798 edition of the Encyclopædia Britannica:
The same term used in the sense of an undesirable and inescapable series of recurring events, in which each event is triggered by a reaction to a prior event, with the result that all stages repeat themselves indefinitely, emerged much more recently, but certainly no later than 1817.
As for "vicious cycle," Isaac Newton used that term to describe supposed calculation of a "vicious lunar cycle" by ancient Jewish astronomers; but the term may not have appeared in its modern sense, as an alternative to "vicious circle" in contexts unrelated to logic, until perhaps the second half of the nineteenth century (user66974's answer points to a New York Times instance of relevant usage from 1858, which is nineteen years earlier than the earliest such instance that I was able to find).
My impression is that "vicious cycle" didn't appeal to English writers until people stopped thinking of the primary sense of "vicious circle" as being "a logical error involving a self-referential quasi-proof." Once the sense of "vicious circle" became more widely associated with "a recurring sequence of bad events," the variant "vicious cycle" gained a following because such a recurring sequence seems at least as cyclical as it is circular.