This tradition is known to us by the writings of the Church historian Eusebius of Caesarea who himself quotes the writing of Hegesippus (Ἡγήσιππος), a chronicler of the early Church. In his Ecclesiastical History (Ἐκκλησιαστικὴ Ἱστορία), Book II, Ch. XXIII, Eusebius wrote,
3 The words of Clement (already provided earlier) indicated the manner of James’ death, both being thrown from the pinnacle [of the Temple] and being beaten to death with a club. Indeed, Hegesippus, who lived during the first succession of the apostles, most accurately records his affairs. In his fifth commentary, he records this manner [of his death], saying,
Γʹ τὸν δὲ τῆς τοῦ Ἰακώβου τελευτῆς τρόπον ἤδη μὲν πρότερον αἱ παρατεθεῖσαι τοῦ Κλήμεντος φωναὶ δεδηλώκασιν, ἀπὸ τοῦ πτερυγίου βεβλῆσθαι ξύλῳ τε τὴν πρὸς θάνατον πεπλῆχθαι αὐτὸν ἱστορηκότος· ἀκριβέστατά γε μὴν τὰ κατ' αὐτὸν ὁ Ἡγήσιππος, ἐπὶ τῆς πρώτης τῶν ἀποστόλων γενόμενος διαδοχῆς, ἐν τῷ πέμπτῳ αὐτοῦ ὑπομνήματι τοῦτον λέγων ἱστορεῖ τὸν τρόπον·
4 "James, the brother of the Lord, who was called "Just" (since many were called "James") by everyone since the times of the Lord until even our times, succeeded [to the leadership of] the Church with the apostles.
Δʹ «διαδέχεται τὴν ἐκκλησίαν μετὰ τῶν ἀποστόλων ὁ ἀδελφὸς τοῦ κυρίου Ἰάκωβος, ὁ ὀνομασθεὶς ὑπὸ πάντων δίκαιος ἀπὸ τῶν τοῦ κυρίου χρόνων μέχρι καὶ ἡμῶν, ἐπεὶ πολλοὶ Ἰάκωβοι ἐκαλοῦντο,
5 And he was holy from his mother's womb. He did not drink wine or strong drink, nor did he even eat an animal. No razor came upon his head; he did not anoint himself with oil; and, he did not treat himself to a bath.
Εʹ οὗτος δὲ ἐκ κοιλίας μητρὸς αὐτοῦ ἅγιος ἦν, οἶνον καὶ σίκερα οὐκ ἔπιεν οὐδὲ ἔμψυχον ἔφαγεν, ξυρὸν ἐπὶ τὴν κεφαλὴν αὐτοῦ οὐκ ἀνέβη, ἔλαιον οὐκ ἠλείψατο, καὶ βαλανείῳ οὐκ ἐχρήσατο.
6 He alone was permitted to enter the holy place, for he did not wear woollen but linen garments. And he frequently entered the temple alone and was frequently found situated upon his knees asking forgiveness for the people, so that his knees became hard after the manner of a camel, on account of always bending down upon a knee while worshipping God and asking forgiveness for the people.
Ϛʹ τούτῳ μόνῳ ἐξῆν εἰς τὰ ἅγια εἰσιέναι. οὐδὲ γὰρ ἐρεοῦν ἐφόρει, ἀλλὰ σινδόνας. καὶ μόνος εἰσήρχετο εἰς τὸν ναὸν ηὑρίσκετό τε κείμενος ἐπὶ τοῖς γόνασιν καὶ αἰτούμενος ὑπὲρ τοῦ λαοῦ ἄφεσιν, ὡς ἀπεσκληκέναι τὰ γόνατα αὐτοῦ δίκην καμήλου, διὰ τὸ ἀεὶ κάμπτειν ἐπὶ γόνυ προσκυνοῦντα τῷ θεῷ καὶ αἰτεῖσθαι ἄφεσιν τῷ λαῷ.
7 Because of the preeminence of his justice, he was called "the Just," and "Oblias," which in Greek is "Bulwark of the people," and "Justice," as the prophets declare concerning him.
Ζʹ διά γέ τοι τὴν ὑπερβολὴν τῆς δικαιοσύνης αὐτοῦ ἐκαλεῖτο ὁ δίκαιος καὶ ὠβλίας, ὅ ἐστιν Ἑλληνιστὶ περιοχὴ τοῦ λαοῦ, καὶ δικαιοσύνη, ὡς οἱ προφῆται δηλοῦσιν περὶ αὐτοῦ.
Migne, Jacques-Paul. Patrologiae Cursus Completus, Series Graeca. Petit-Montrouge: Imprimerie Catholique, 1857. (Vol. 20, pp. 195-198)