What does the phrase "pure descent" used for the Prophet (pbuh) mean?

What does the phrase "pure descent" used for the Prophet (pbuh) mean?

Dear Brother / Sister,

The Pride of the universe (pbuh) proclaimed this truth as,

“I am the supplication of my forefather Abraham (pbuh).” 1

Hazrat Ismail’s children and grandchildren continuously increased and they spread all over the Arabian Peninsula. From them, the sons of Adnan, and from them the sons of Mudar, and from them the tribe of Quraysh became superior and different from the others. The Hashim branch of the Quraysh tribe found the most honor and reputation them all. He himself described this reality as follows:

"Allah chose Ismael from the sons of Abraham, the sons of Kinana from the sons of Ismael, Quraysh from the sons of Kinane, Bani Hashim from Quraysh, and me from Bani Hashim."2

"I was transferred through the noblest race (from generation to generation, from family to family) of Adam’s lineage selected by Allah and at last I was born in the family of the sons of Bani Hashim."

"Allah made me born through my father and mother transferring me from the fathers who lived in accordance with Allah’s rules, lineage to the womb of the chaste mothers. From Adam to my father and mother, there is no one to have a relationship without marriage."

Footnotes:

1. Ibn Hisham, Sira: 1/175; Tabari, Tarikh: 2/128.
2. Ibn Sa'd, Tabaqat: 1/20. Muslim: 7/58.

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