What is the meaning of Matthew 1:17?

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References

So all the generations from Abraham to David are fourteen generations; and from David until the carrying away into Babylon are fourteen generations; and from the carrying away into Babylon unto Christ are fourteen generations. (Matthew 1:17 KJV)

So all the generations from Abraham unto David are fourteen generations; and from David unto the carrying away to Babylon fourteen generations; and from the carrying away to Babylon unto the Christ fourteen generations. (Matthew 1:17 ASV)

All the generations, therefore, from Abraham to David were fourteen generations; and from David until the carrying away of Babylon, fourteen generations; and from the carrying away of Babylon unto the Christ, fourteen generations. (Matthew 1:17 DBY)

All the generations, therefore, from Abraham unto David are fourteen generations, and from David unto the Babylonian removal fourteen generations, and from the Babylonian removal unto the Christ, fourteen generations. (Matthew 1:17 YLT)

So all the generations from Abraham to David are fourteen generations; from David to the exile to Babylon fourteen generations; and from the carrying away to Babylon to the Christ, fourteen generations. (Matthew 1:17 WEB)

Interlinear

Mt 1:17 So /oun/ all /pas/ the generations /genea/ from /apo/ Abraham /Abraam/ to /heos/ David /Dabid/ are fourteen /dekatessares/ generations; /genea/ and /kai/ from /apo/ David /Dabid/ until /heos/ the carrying away /metoikesia/ into Babylon /Babulon/ are fourteen /dekatessares/ generations; /genea/ and /kai/ from /apo/ the carrying away /metoikesia/ into Babylon /Babulon/ unto /heos/ Christ /Christos/ are fourteen /dekatessares/ generations. /genea/

Albert Barnes’ Commentary

Verse 17.  All the generations, etc. This division of the names in their genealogy was doubtless adopted for the purpose of aiding the memory. It was common among the Jews; and other similar instances are preserved. They were destitute of other books beside the Old Testament, and had but few copies of that among them, and those chiefly in their synagogues. They would, therefore, naturally devise plans to keep up the remembrance of the principal facts in their history. One method of doing this was to divide the tables of genealogy into portions of equal length, to be committed to memory. This greatly facilitated the remembrance of the names. A man who wished to commit to memory the names of a regiment of soldiers, would naturally divide it into companies and platoons, and this would greatly facilitate his work. This was doubtless the reason in the case before us. And though it is not strictly accurate, yet it was the Jewish way of keeping their records, and answered their purpose. There were three leading persons and events that nearly, or quite, divided their history into equal portions–Abraham, David, and the Babylonish captivity. From one to the other was about fourteen generations, and, by omitting a few names, it was sufficiently accurate to be made a general guide or directory in remembering their history.  

In counting these divisions, however, it will be seen that there is some difficulty in making out the number fourteen in each division. This may be explained in the following manner. In the first division, Abraham is the first, and David the last, making together fourteen In the second series, David would naturally be placed first, and the fourteen was completed in Josiah, about the time of the captivity, as sufficiently near for the purpose of convenient computation, 2 Chron xxxv. In the third division, Josiah would naturally be placed first, and the number was completed in Joseph. So that David and Josiah would be reckoned twice. This may be shown by the following table of the names:  

First
Division
Second
Division
Third
Division
AbrahamDavidJosias
IsaacSolomonJechonias
JacobRoboamSalathiel
JudasAbiaZorobabel
PharesAsaAbiud
EsromJosaphatEliakim
AramJoramAzor
AminadabOziasSadoc
NaassonJoathamAchim
SalmonAchazEliud
BoazEzekiasEleazar
ObedManassesMatthan
JesseAmonJacob
DavidJosiasJoseph
141414

Carrying away into Babylon. This refers to the captivity of Jerusalem, and the removal of the Jews to Babylon by Nebuchadnezzar, 588 years before Christ. See 2 Chron. xxxvi. Josiah was king when these calamities began to come upon the Jews; but the exact time of the seventy years of captivity did not commence until the eleventh year of Zedekiah’s reign, or 32 years after the death of Josiah. Babylon was situated on the, Euphrates, and was encompassed with walls which were about 60 miles in circuit, 87 feet broad, and 350 feet high; and the city was entered by a hundred brazen gates, 25 on each side. It was the capital of a vast empire, and the Jews remained there for seventy years. See Barnes for Isa 13:1 and following.