The OED has hooray as a variant of hurrah meaning goodbye, from 1898. Hurrah and hurray are a shout or cheers of encouragement, from huzza of 1573.
Hip, also hep, is an exclamation or a call to another and the same as the Latin eho, heus!, according to Johnson. From 1752. It's also an exclamation, usually repeated three times to introduce a cheer, from The every-day book (1827):
To toss off the glass, and huzza after the ‘hip! hip! hip!’ of the toast giver.
Finally, derivatives of hip are hip-hurrah and hip-hip-hurrah, first quoted in The Examiner (1832):
One set of men ‘hip hurrah’ and rattle decanter stoppers.
Hip
Edit to answer question update: What's the source of the claim that "hip" stems from a medieval Latin acronym, "Hierosolyma Est Perdita", meaning "Jerusalem is lost", a term that gained notoriety in the German Hep hep riots? Is Gabay's Copywriter's Compendium (2006) the point of origin of the Hep-Hep connection?
It goes much further back than 2006.
The origin of hep used in the German riots is discussed in an 1869 Notes and Queries (imagine a Victorian precursor to Stack Exchange) and they believe it was from the Latin phrase "Hierosolyma Est Perdita" (Jerusalem is Lost) as both Germans and Jews accepted it. They note some derive it from Ziegen-Hep (goat's beard) referring to "the bearded Jews", and others say Hep was originally Heb for Hebrew. N&Q question the statement that the "Hep! Hep!" cry is as old as the Crusades, as it was first heard in Würzburg aronud 1819. It was much discussed in N&Q; Aug. 1853, Oct. 1853,
Brewer's Dictionary of Phrase and Fable (1898) repeats the hip-hep-Latin link and references Notes and Queries, which may have helped popularise it. But it seems to have been a well-known myth as early as 1841, when it's told in George Stanley's story Spencer Middleton; or the Squire of River Hill (published in The Metropolitan Magazine).
The "origin" is included in 1842's The Treasury of Wit and Anecdote and links it to Peter the Hermit:
While preaching the crusade, this furious zealot was accustomed to exhibit a banner emblazoned with the following letters, H. E. P., the initials of the Latin words, Hierosolyma est Perdita, Jerusalem is destroyed.
David Wilton discusses these links in Word Myths: Debunking Linguistic Urban Legends (2008), including the claim hep originates the Roman sacking of Jerusalem in 135 AD:
But despite these claims, no solid evidence of cries of Hep! or the phrase Hierosolyma Est Perdita can be found dating them to either Roman or Medieval times.
Wilton says the Würzburg students' Hep! Hep! could have been abbreviations from the Latin, or imitating the Hep! that 19th century German goatherds used to drive their goats.
Regardless of what the students of Würzburg meant by their shouts, it is not the origin of hip in Hip! Hip! Hurrah! English use of the cheer predates the 1819 riots.
He dates this English hip to the mid-18th century, hurrah to the late-17th century and concludes:
So there is a grain of truth to the legend in that the cry of Hep! has been associated with anti-Semitism since early nineteenth century, but the main point of the legend is false.
Finally, any pre-20th century acronyms should be treated with care. According to the Online Etymology Dictionary, acronyms were rare before the World War I, and didn't become popular until the World War II. Hep may not have derived from Hierosolyma Est Perdita during the crusades, but it's possible the German rioters did, and interesting a folk etymology was developed around this to describe hip in the 19th century.
Hooray
Edit 2 to answer question update: What's the source of the claim that Europeans picked up the Mongol exclamation "hooray" as an enthusiastic cry of bravado and mutual encouragement?
Is Jack Weatherford's book Genghis Khan and the Making of the Modern World (2004) the source?
It appears so.
Wikipedia says:
The origin of the word in its various forms is not clear, but it may have been influenced by war cries from various languages: the OED suggests Danish, Swedish, Dutch, Russian and Prussian words that may have played a part. Jack Weatherford asserts that it comes from the Mongolian Hurree, used by Mongol armies and spread throughout the world during the Mongol Empire of the 13th century, but he does not appear to present any supporting evidence. Weatherford says that in Mongolian Hurree is a sacred praise much like amen or hallelujah.
Dipping into the OED again, hooray is from hurrah which is a later substitute for huzza perhaps an onomatopoeic modification, or perhaps influenced by foreign shouts (Swedish, Danish, Low German, Dutch, Russian, Middle High German). It also mentions Prussian soldiers in the War of Liberation (1813-15).
Huzza goes back to 16th century (other forms hussa, hussaw, huzzah, huzzay, the oldest from the 15th century) and the etymology is given:
apparently a mere exclamation, the first syllable being a preparation for, and a means of securing simultaneous utterance of the final /ɑː/ .
It notes 17-18th century writers said it was a sailor's cheer or salute when friends came aboard, and may be the same as the hauling or hoisting cry heisau! hissa!, from heeze and hissa. (It parenthetically mentions German hunting and, later, exultation cry ˈhussa.)
In 2005, Joe Murphy, a member of the Usenet group sci.lang wrote to Weatherford to ask his sources, and I'll quote it in full:
Dear Prof. Weatherford:
I am a semi-retired lawyer in Indianapolis. I am also a history buff
and something of an amateur linguist. I am presently reading your
book, "Genghis Khan and the Making of the Modern World". In reading
it, I came across this, in the introductory pages of the paperback
version at page xxiv of your Introduction:
"The Europeans even picked up the Mongol exclamation "hooray" as an
enthusiastic cry of bravado and mutual encouragement."
This piqued my interest. I checked my Merriam-Webster Collegiate
dictionary for the etymology of "Hurrah" and "Hurray" and found the
word listed as of probable German origin. A Google search on the
etymology revealed this:
Hurrah: 1686, alteration of huzza, apparently infl. by similar shouts
in Ger., Dan., Swed. May have been picked up during Thirty Years'
War. According to Moriz Heyne, this was the battle-cry of Prussian
soldiers during the War of Liberation (1812-13). Hooray is its
popular form and is almost as old.
I'm a long-time member of the Usenet group, sci.lang and yesterday
broached the matter of the origin of "Hurray" with the group (which
includes a lot of practicing linguists). One of them, Peter T.
Daniels, suggested that I write you and ask if you had any sourcing
for the Mongol origin of the word. So, that's the reason for this
email. I couldn't find anything on it in the Source Notes provided at
the back of your book and was wondering where you came up with your
contention that the origin of the word is Mongolian.
By the way, I'm enjoying the book. You really write well. I was
unaware of the historical background surrounding "The Secret History
of the Mongols" until I read what you had to say on the subject. I'm
looking forward to finishing your book.
I've been interested in the Mongols, by the way, since I was a kid and
read Harold Lamb's Landmark Books biography of Genghis Khan.
Anyway, if you have a source for the Mongol origin of "hurray" I'd
appreciate your sharing it with me. I've got a lot of my friends on
sci.lang interested in this. Believe it or not, some there actually
speak Mongolian!
Joe Murphy
Weatherford replied:
Many thanks for the note and your interest.
Like most etymologies that do not come through the standard sources,
many scholars will reject this, but in my mind there is absolutely no
question.
The Germans (or really, the Prussians) picked it up from the Russians
who picked it up from the Mongols. A little more of the etymology can
be found in the Oxford English Dictionary than in Webster's, but the
OED only traces it as far as Russia and the Cossacks (if my memory is
correct) but then leaves it unknown before that time.
In Mongolian the phrase is used today much the way Christians use
"amen." At the end of a prayer, Mongols hold both hands out with
palms up and move them in a clockwise circle three times saying
"hurray, hurray, hurray." Earlier the phrase was used for all types
of official occasions -- it is sacred in that it is calling on the
Sky for aid.
The root of the word is the same as Khuraltai -- the great gathering
of Mongolians that I mention in the book. In fact, the modern
parliament is called the Ih Hural where, I believe, President Bush
will be speaking for the first time in about 12 hours from now.
I will check back in the OED as well, but I hope that this gives a
little more information.
Jack
P.S.
I forgot one of the most important points.
It is unclear whether the Mongols actually used the cry in war when
mounted on horses. They used it at all group gatherings and almost
certainly for the ceremonial prayer before the attack. It may have
been the Russians who, in their many years of fighting with and for
the Mongols, began using it at the moment of attack.
Best Answer
From Phrases, Cliches, Expressions on www.joe-ks.com:
...and then there are the following two quotes from the Bible which if interpreted the same way, would put the usage way before the 20th century:
Isaiah 18:4 For this is what the Lord has told me: “I will wait and watch from my place, like scorching heat produced by the sunlight, like a cloud of mist in the heat of harvest.” 18:5 For before the harvest, when the bud has sprouted, and the ripening fruit appears, he will cut off the unproductive shoots with pruning knives; he will prune the tendrils. 18:6 They will all be left for the birds of the hills and the wild animals; the birds will eat them during the summer, and all the wild animals will eat them during the winter.
Jeremiah 16:4 They will die of deadly diseases. No one will mourn for them. And they will not be buried. Their dead bodies will lie like manure spread on the ground. They will be killed in war or die of starvation. And their corpses will be food for the birds and the wild animals.
(from the website: 10000birds.com as an answer to the question, "Why is 'for-the-birds' a bad thing?")