no muslims come through Ishmael who was the brother of Isaac the father of Esau and Jacob/Israel, NOT Esau
The chart does fall a little short on Ishmael's genealogy, whose seed also had twelve tribes. Though Muhammad himself was likely a Hamite or Cushite because his tribe the Quraish migrated from Yemen to Mecca somewhere around the 4th century AD, and the kaaba was likely built in the early 5th century. Evidence suggests that the Yemeni Quraish pagan's ancestors arrived from across the strait from Ethiopia, in the horn of Africa.
It's important to note that there is no historical or archaeological evidence that suggests that Mecca ever existed before the 4th century, and any notion of Abraham, Hagar or Ishmael ever having been within 1,000 kilometers of Mecca, is geographically preposterous.
The Old Testament falls silent on what happened to the Ishmaelites but as Islamic conquest of the Arabian peninsula moved north they overran the Ishmaelites for the hottest trading location in northern Arabia, and the Ishmaelites moved north into the fertile crescent and/or were absorbed into the Muslims from the south. A source I like is Dr. Rafat Amari whose first language is Arabic and who spent 20 years in full time study, 8-10 hours a day, 6 days a week investigating, including original source material and archaeology. Much of the material he covers in his book is available free online in the left sidebar of his website:
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All that said, those that do proudly self-proclaim a heritage from Ishmael's seed may well be, as we see how they are revealed in scripture, and thus in the world today:
Genesis 16:12 And he will be a wild man;
his hand [will be] against every man, and every man's hand against him; and he shall dwell in the presence of all his brethren.
In the New Testament:
Galatians 4:22 For it is written, that Abraham had two sons, the one by a bondmaid, the other by a freewoman. 23
But he [who was] of the bondwoman was born after the flesh; but he of the freewoman [was] by promise. 24 Which things are an allegory: for these are the two covenants; the one from the mount Sinai, which gendereth to bondage, which is Agar. 25 For this Agar is mount Sinai in Arabia, and answereth to Jerusalem which now is,
and is in bondage with her children. 26 But Jerusalem which is above is free, which is the mother of us all.
Romans 9:7 Neither, because they are the seed of Abraham, [are they] all children: but,
In Isaac shall thy seed be called. 8 That is,
They which are the children of the flesh, these [are] not the children of God: but the children of the promise are counted for the seed.
But of course any self-proclaimed "Ishmaelite", or any Muslim, or any other gentile that is not of the seed of Isaac, can come to Christ, through a circumcision of the heart by being born again. The shed blood of Jesus Christ is for all and God does not wish that any should perish.
It is interesting to note that Muhammad adopted and then adapted the moon, sun, star and jinn-devil worship rituals of his tribe the Quraish, having gotten rid of 364 idols that were in and around the Kaaba. However he kept the Quraish pagan's black stone idol, and perhaps an interest in the income generated from the annual pagan pilgrimmage (or Hajj) to "Kaaba Inc", some profits from which Muhammad's uncle had formerly enjoyed.
Indeed the pagan's and Muslims circumambulated the kaaba during the Hajj shoulder to shoulder, right up until the year before Muhammad's last Hajj, when he kicked the poor pagans out of their own ritual!
Sahih Bukhari Volume 1, Book 8, Number 365: Narrated Abu Huraira: On the Day of Nahr (10th of Dhul-Hijja,
in the year prior to the last Hajj of the Prophet when Abu Bakr was the leader of the pilgrims in that Hajj)
Abu Bakr sent me along with other announcers to Mina
to make a public announcement: "No pagan is allowed to perform Hajj after this year and no naked person is allowed to perform the Tawaf around the Ka'ba. Then Allah's Apostle sent 'All to read out the Surat Bara'a (At-Tauba) to the people; so he made the announcement along with us on the day of Nahr in Mina: "No pagan is allowed to perform Hajj after this year and no naked person is allowed to perform the Tawaf around the Ka'ba."
The Saudis profit from Kaaba Inc. today as every Muslim is obligated to travel to Mecca and "perform" the "Hajj" as it is one of the pillars of Islam. They also kiss the Quraish pagan's black stone idol as Muhammad did, or if it is too crowded, at least point to it on each trip around. Muslims also travel to Mecca to run back and forth between the two hills of Al-Safa and Al-Marwah 7 times as the Arabian jinn-devil worshipers did, which hills had formerly contained idols of the most venerated priest and priestess of the Arabian jinn-devil religion.
Every Muslim is required to prostrate toward the Quraish pagan's kaaba (that houses the black stone idol in one corner) five times a day, while performing "Salat".
From the book "Infidel": "You say Praise be to Allah thirty-three times; God forgive me thirty-three times; Allah is great thirty-three times; and then, if you choose, you may also say Gratitude to Allah."
That's 495 repetitions of those phrases every day. Here's how the Gospel weighs in on such prayer:
Matthew 6:7 But when ye pray,
use not vain repetitions, as the heathen [do]: for they think that they shall be heard for their much speaking.
Any surprise that the self-proclaimed seed of Ishmael are referred to as "children of the flesh" particularly since, while Christians are in the kingdom of God, Muhammad's followers have maintained a 1400 year lust for all kingdoms of the world, and
subjugation of all people to DISbelieving the crucifixion of Christ, DENYING the Son of God, and REJECTING the shed blood of the Lamb of God as articles of their faith in the false prophet Muhammad alone.
[video=youtube;-4PMvVKrb_Y]http://www.youtube.com/watch?v=-4PMvVKrb_Y[/video]