Augustus
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Firstly Greek historian Diodorus Siculus was a non-muslim and this answers the first part of your question.
Secondly he mentions Mecca and the Kaaba as ""And a temple as been set up there,which is very holy and exceedingly revered by all Arabians"".
Does he mention Mecca, the Kaaba or the location? If so what is the quote.
Almost every mention I can find about this that equates it specifically with Mecca is from various Islamic sites and says almost exactly the same thing. From my experience, 9 times out of 10 this means they are copied from the same source who has added information to suit their agenda and simply repeated as fact without anyone actually checking it.
Does the original say anything other than there is a sacred temple somewhere in Arabia? If not why should I believe it is Mecca? If you can show me the original quote, then I might change my mind, if not it is inconclusive at best.
*edit: this source claims it is in South Jordan http://etheses.dur.ac.uk/1184/1/1184.pdf *
Finally do you know what is the meaning of Macoraba. Maco in arabic means house and raba means lord.
Macoraba simply means House of the God.Prophet Ibraham(PBBUH) built this house and called it the House of Allah.The Arabs pre-Islam called it the House of Allah and to this day we all call it "The House of allah".
Remember, you are trying to prove that Mecca was the undisputed centre of the Arab world where almost all Arabs went on regular pilgrimage. Ptolemy was not the first or the only person to write about Arabia. Even if we accept that Macoroba is Mecca, which is not certain, why did none of the others notice it? Why could Siculus find it 1stC BC, but the Romans couldn't find it during the next 7 centuries to even record its existence, except for a vague reference from Ptolemy?
Look at all the historical references to other places from that time, yet why would the undisputed centre of the Arab world, where tens of thousands of the Romans close allies visited every year, which was a major trade centre, which had the most famous, most Holy shrine in the region, not have been noticed, not once but many, many times? The Roman army would have had plenty of Arabs in it, never mind their tribal allies, but not even a rumour of the Holiest site in Arabia was recorded for hundreds of years after Ptolemy.
It should have dozens, if not hundreds of references if what you say is true. Even if we assume that all of your claims are correct (which is a pretty big leap), does 3 mentions in 800 years really make sense to you given the amazing importance of one of the most ancient and holy places on the planet?
Given their love of relics and holy things, if there was a site, right on the doorstep of the Romans, don't you think they would have at least looked at the place, if not captured it and stolen the sacred stone?
Your entire argument rests on 2 or three very vague references to a place that might or might not be Mecca, again, do you seriously believe that constitutes a significant body of evidence for such an important place?
*edit: Ptolemy identified Macoraba as being further East than Yathrib, whereas Mecca is further West. Your explanation? Also plenty of scholars doubt that your Arabic translation is likely to be a correct identification of a town called Mecca*
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