By so much also (kata tosouto kai). Correlative demonstrative corresponding to kath' hoson (the relative clause) in Heb 7:20.
The surety (egguos). Vulgate sponsor. Old word, here only in the N.T., adjective (one pledged, betrothed), from egguē, a pledge, here used as substantive like egguētēs, one who gives a pledge or guarantee. There may be a play on the word eggizō in Heb 7:19. Egguaō is to give a pledge, eggualizō, to put a pledge in the hollow of the hand. It is not clear whether the author means that Jesus is God’s pledge to man, or man’s to God, or both. He is both in fact, as the Mediator (ho mesitēs, Heb 8:6) between God and man (Son of God and Son of man).