Thus, I attempted to trace the origins of these quotes, as best I could. For the first quote, ending in "dictatorship," I have chosen to adopt the title "Why Democracies Fail," or WDF for short, which is perhaps the most common title given the quote. The last sentence of the first paragraph does not appear alongside the earliest instances of the quote. For the second quote, I have chosen to use the title "Fatal Sequence," or FS, which was the name given to it in a 1989 newspaper.
Frequently, "Why Democracies Fail" is quoted alongside "Fatal Sequence," often as a single passage attributed to Professor Tytler/Tyler. But all indications point to the two having separate origins. Firstly, unlike "WDF," "Fatal Sequence" is attributed to a wide variety of authors. In addition to Tytler/Tyler or Anonymous, I have seen the quote credited to Benjamin Disraeli (1804-1881), Arnold Toynbee (1889-1975), Ezra Taft Benson (1899-1994), Davis Paschall (1911-2001), Bernard Weatherill (1920-present) and Robert Muntzel (?-?). Secondly, while I have tracked both quotes back to the mid-20th century, the first instance I have found of them used together was in 1979.
None of Prentis' uses of the Fatal Sequence that I have read include the Why Democracies Fail passage. Not that Prentis, a clear free-market advocate, didn't express vaguely similar sentiments, though. Later in his 1946 speech, Prentis said "The three legs of our tripod of freedom stand or fall together. Destroy constitutional representative self-government, and pure democracy - the unmitigated rule of the current majority - soon degenerates into despotism and tyranny."
The earliest anonymous attribution of the "Fatal Sequence" I have found was in an October 27, 1950 speech delivered by Eugene E. Wilson at a special United Nations Convocation at Hillyer College in Hartford, Connecticut, but Wilson expresses disagreement with the quote's sentiments. An anonymous attribution tends to suggest an author who was not particularly notable, which is true of Prentis.