Was Rishi Vyasa the great grandson of Rishi Vashishtha?
There is a verse Attributed to Great Sage Vyasa which goes like this
vyAsam vasishta-naptAram Sakteh pautram akalmasham
parAsarAtmajam vande Suka-tAtam tapo-nidhim.
vyAsa is the Great-Grandson of vasishta and the grandson of Sakti. He is the son of parAsara and the father of Suka. I offer my obeisance to that vyAsa who is free from all defects and is a mine of austerities.
Adi parva of Mahabharata about Vyasa's Birth
And it was thus that Vyasa was born of Satyavati through Parasara. And because he was born on an island, he was called Dwaipayana (Dwaipa or islandborn). And the learned Dwaipayana, beholding that virtue is destined to become lame by one leg each yuga (she having four legs in all) and that the period of life and the strength of men followed the yugas, and moved by the desire of obtaining the favour of Brahman and the Brahmanas, arranged the Vedas. And for this, he came to be called Vyasa (the arranger or compiler)
Vasishtha did not restrain him from this slaughter of the Rakshasa, from the determination of not obstructing this second vow (of his grandson). And in that sacrifice, the great Muni Parasarasat before three blazing fires, himself like unto a fourth fire. And the son of Saktri, like the Sun just emerging from the clouds, illuminated the whole firmament by that stainless sacrifice of his into which large were the libations poured of clarified butter.
So Vyasa is Great-Grand-Son of Rishi Vasishta who in turn is Son of Brahma.
By the way,
Vasistha, Shakti, Parashara and Krishna Dwaipayana are Vyasas for 8th, 25th, 26th and 28th Mahayuga of Vaivasvara (current) Manvantara respectively.
Chapter 24 of Linga Purana.(Pg No-90)
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