The first published edition of Le Jeu des Eschets dates to 1669, but Lewis may have worked from a more widely available version published later. Greco kept notebooks of games, as was the habit of chess players in his day, and made copies of portions of his notes for patrons. What we know of Greco's chess comes from these manuscripts and published compilations, such as Le Jeu des Eschets.
Lewis did not simply translate the French text. Rather, he rearranged the games by opening. Greco's games in Lewis amount to 168 variations of 47 games with 15 the maximum number of variations in a single game. His arrangement was modified by Angelo Lewis who wrote under the pen name of Professor Louis Hoffmann (The Games of Greco [London: George Routledge & Sons, 1900]), which is likely the source for a frequent claim (found in Wikipedia, for instance) that Greco's collection consists of 77 games. Lewis's first game appears as games I and II in Hoffmann.
In Lewis's and Hoffmann's books are games credited to Gioachino Greco that are not accessible through today's modern databases.
The first game in Lewis begins 1.e4 e5 2.Nf3 Nc6 3.Bc4 Bc5 4.c3 Nf6 5.d4 exd4 6.cxd4 Bb4+ 7.Nc3 Nxe4 8.0–0 Nxc3 9.bxc3 Bxc3 10.Qb3
Black to move
A search for this position in ChessBase Online turns up 203 games, including three by Greco (two of which are identical, albeit with different dates). The continuation 10...Bxa1 is given as first game and the first two variations in Lewis. 10...Bxd4 is in variations three and four.
Lewis's first game concludes:
10...Bxa1 11.Bxf7+ Kf8 12.Bg5 Ne7 13.Ne5 Bxd4 14.Bg6 d5 15.Qf3+ Bf5 16.Bxf5 Bxe5 17.Be6+ Bf6 18.Bxf6 gxf6 19.Qxf6+ Ke8 20.Qf7# 1–0
The ChessBase database deviates at Black's move 18 ending with 18...Ke8 19.Bxg7. The final position of this game also appears in what must have been an arranged draw: Shumiakina -- Litinskaya, Svetlogorsk 1997.
Game one, first variation offers a line that includes what appears as a 1990 novelty in the ChessBase database: 13...d5.
10...Bxa1 11.Bxf7+ Kf8 12.Bg5 Ne7 13.Ne5
Black to move
13...d5 14.Qf3 Bf5 15.Be6 g6 16.Bh6+ Ke8 17.Bf7# 1–0
ChessBase credits Paul Oostheim with Greco's 12...Nxd4 in Lewis's variation two.
10...Bxa1 11.Bxf7+ Kf8 12.Bg5 Nxd4 13.Qa3+ Kxf7 14.Bxd8 Rxd8 15.Rxa1 Nc2 16.Qb3+ Kf8 17.Qxc2 1–0
Oostheim's move has been played often enough that White has stumbled several times with 13.Qb4+ giving Black the opportunity to recover the otherwise lost game.
Variation three introduces 10...Bxd4 after which Black seems to hold on a few moves longer than when grabbing the rook on a1.
10...Bxd4 11.Bxf7+ Kf8 12.Bg5 Bf6 13.Rae1 Ne7 14.Bh5
Black to move
14...Ng6 15.Ne5 Nxe5 16.Rxe5 g6 17.Bh6+ Bg7 18.Rf5+ gxf5 19.Qf7# 1–0
Lewis offers the diagram after White's 14.Bh5, which serves to guide readers through several possibilities outlined in variation four. Variation three is found in the database, but variation four appears only as a curious game from 1962.
Black to move
15...Kxe7 is presented in three lines and 15...Qxe7 is presented in two.
15...Kxe7 16.Re1+ Kf8 17.Qb4+ Kg8 18.Re8+ 1–0 is first offered by Lewis, then four A offers 15...Qxe7 16.Re1 Qd7 17.Qb4+ Kg8 18.Re8+ 1–0
The most interesting line is Lewis's variation four D, and it deserves a place in the database as part of Greco's oeuvre.
15...Qxe7 16.Re1 Be6 17.Nd4 Bxg5 18.Nxe6+ Kg8 19.Qxd5 c6 20.Qb3 Qf6
White to move
Lewis notes that 21.Nd8+ would have been superior to Greco's analysis. It may have been played in Amsterdam in 1962.
21...Kf8 22.Qb4+ Kg8 23.Bf7+ Qxf7 24.Nxf7 1–0
In a game found in the ChessBase database, an improvement to Greco's game that was suggested by William Lewis appears to have been played over the board. However, while the loser has a few other games in the database from 1989-1990, this game is the sole example of the winner's play. The game omits Greco's 19...c6 20.Qb3 and offers Qd6 in place of Qf6.
[Event "IBM Reserve F"]
[White "Schippers, H."]
[Black "Lagendijk, J."]
1. e4 e5 2. Nf3 Nc6 3. Bc4 Bc5 4. c3 Nf6 5. d4 exd4 6. cxd4 Bb4+ 7. Nc3 Nxe4 8.O-O Nxc3 9. bxc3 Bxc3 10. Qb3 Bxd4 11. Bxf7+ Kf8 12. Bg5 Bf6 13. Rae1 Ne7 14.Bh5 d5 15. Rxe7 Qxe7 16. Re1 Be6 17. Nd4 Bxg5 18. Nxe6+ Kg8 19. Qxd5 Qd6 20.Nd8+ Qxd5 21. Re8# 1-0
A recent work in economic history juxtaposes the names Schipper and Lagendijk as co-authors: Frank Schipper, Vincent Lagendijk, and Irene Anastasiadou, “New Connections for an Old Continent: Rail, Road and Electricity in the League of Nations’ Organisation for Communications and Transit,” in Materialising Europe: Transnational Infrastructures and the Project of Europe, ed. Alexander Badenoch and Andreas Fickers (London: Palgrave, 2010), 113-143.