In studying this issue, I've not found it mentioned by Ellis or anywhere else, the historic fulfillment of the 3 kings 'subdued'/'plucked up by the roots'. But, here is what I've found:
Daniel 2:40-43 And the fourth kingdom shall be strong as iron: forasmuch as iron breaketh in pieces and subdueth all things: and as iron that breaketh all these, shall it break in pieces and bruise. And whereas thou sawest the feet and toes, part of potters' clay, and part of iron, the kingdom shall be divided; but there shall be in it of the strength of the iron, forasmuch as thou sawest the iron mixed with miry clay. And as the toes of the feet were part of iron, and part of clay, so the kingdom shall be partly strong, and partly broken. And whereas thou sawest iron mixed with miry clay, they shall mingle themselves with the seed of men: but they shall not cleave one to another, even as iron is not mixed with clay.
Daniel 7:7b-8,24-25 [the fourth beast] was diverse from all the beasts that were before it; and it had ten horns. I considered the horns, and, behold, there came up among them another little horn, before whom there were three of the first horns plucked up by the roots: and, behold, in this horn were eyes like the eyes of man, and a mouth speaking great things...And the ten horns out of this kingdom are ten kings that shall arise: and another shall rise after them; and he shall be diverse from the first, and he shall subdue three kings. And he shall speak great words against the most High, and shall wear out the saints of the most High, and think to change times and laws: and they shall be given into his hand until a time and times and the dividing of time.
Keeping in mind that the passages above are images that parallel the same events:
History shows that the Roman kingdom divided into 2 halves (the two legs of iron). The Eastern Roman Empire, and the Western Roman Empire. The Western half of the Roman Empire would eventually fall, and the Eastern Roman Empire would later be known as the Byzantine Empire.
Both halves of the empire adhered to the idea of tetriarchal division (a division into 4 regions) with a capital in each region. But, each half of the empire also recognized a fifth capital that wasn't part of the tetriarchal division, but sort of sat in it's own independent 'perfect' or prefecture. In the West, Rome was recognized as the fifth, and in the East, Constantinople was recognized as the fifth.
Now, the Western Roman Empire collapsed in the 400's while the Eastern Roman Empire continued and morphed into the Byzantine Empire. Justinian (in the 500's just a few decades before the Muslim conquests) revived this idea of the division of the kingdom into five recognized regions.
So, here we have East and West, 5 toes each (10 horns).
Prior to the fall of the West, the 5 were recognized as: Nicomedia, Sirmium, Mediolanum, Augusta Treverorum, and Rome. After the fall of the West, Justinian I recognized the divisions as: Rome, Constantinople, Alexandria, Antioch, and Jerusalem.
History is very muddled as to what was recognized by whom, because even after the fall of the Western Empire, and subsequent reconquering/reacquisition by the East, the state-established religion caused a religious division between the East and the West.
Never-the-less, it is recognized that there were 2 distinct divisions in the Roman Empire (East and West). This represents the 2 legs of iron.
And, never-the-less, within each historical era, the Empire was divided into 5 regions with 5 capitals.
Now moving forward into the Muslim conquests, we recognize that the 3 toes subdued by the Islamic conquests in the early 600's as Jerusalem, Antioch, and Alexandria. The remaining toes/horns were never subdued completely by Islam, because the prior 5 disappeared with the disappearance of Western Roman power (possibly a fulfillment of Daniel 8:25?) and I don't believe Islam ever successfully subdued Rome and Constantinople.
Sources:
http://www.ucalgary.ca/applied_history/tutor/islam/beginnings/roman.htmlhttps://en.wikipedia.org/wiki/Muslim_conquests#Byzantine.E2.80.93Arab_Wars:_634.E2.80.93750https://en.wikipedia.org/wiki/Pentarchyhttps://en.wikipedia.org/wiki/Tetrarchyhttps://en.wikipedia.org/wiki/Outline_of_the_Byzantine_Empirehttps://en.wikipedia.org/wiki/Western_Roman_Empirehttps://en.wikipedia.org/wiki/Roman_Empire