FOXBORO, Mass. — Try to imagine if Leonardo da Vinci had painted the Mona Lisa, but without the smile.

Suppose, at the end of “Casablanca,” Bogey had simply walked away from Claude Rains at the airport, into the rainy night, with only a wave, and a “See you around the Casbah, Captain Renault.”

That’s what it’ll be like if the Patriots, having won their first 16 games, don’t win three more.

The Pats have been perfect so far. Now, they need to complete this memorable masterpiece of what has been a record-setting season for the ages, or they’ll be remembered for the wrong reason.

These playoff games, starting with tomorrow’s American Football Conference semifinal against the Jacksonville Jaguars at Gillette Stadium, are “must-win” games in more ways than one.

It’s not only that, in the playoffs, it’s one-and-done. It’s that a loss now by the Patriots would diminish what they have done.

Just one other team in the history of the National Football League has finished the regular season undefeated – the 1972 Miami Dolphins, coached by the legendary Don Shula. The Dolphins won 14 games that year. The Patriots have won 16 this season. Now, they need to win three more, just as the Dolphins did in the playoffs in ‘72, when they completed a perfect, 17-0 season with a win over Washington in Super Bowl VII.

Win three more – tomorrow night against the Jags, the AFC championship game next Sunday in Foxboro, and the Super Bowl in Phoenix on Feb. 3, and the Patriots can legitimately lay claim to being the NFL’s greatest team ever.

The ’72 Dolphins will become a footnote, as football fans worship at the feet of the Patriots of 2007.

Win three more, and the Pats will have achieved pigskin perfection – 19-0, undefeated, untied, and, in many games, virtually unchallenged, champions.

They’d be remembered, and revered, forever.

They’ll also be remembered forever if they lose.

And that’s the problem.

If they lose in the playoffs, the Patriots will be remembered as the team that couldn’t finish. They’d be recalled as a club that won ‘em all during the regular season, but didn’t win when it mattered most, when everything was on the line, in the postseason.

They’d be remembered, not as champions, but as chokers – especially by the not-insignificant portion of NFL fandom that would love to see them, and their less-than-lovable coach, Bill Belichick, lose.

That would be a shame, because this Patriots team is unquestionably the best in franchise history, and deserves to be ranked among the very best – arguably, the best — in NFL history.

The list of records set by the 2007 Patriots extends from Bar Harbor to Block Island.

They have scored more points (589) and more touchdowns (75) than any NFL team, ever. They have outscored their opponents by 315 points, also a league record. If you don’t want to do the math, that means the Pats have won their league-record, 16 games by an average score of 37-17.

Quarterback Tom Brady threw for 50 touchdowns – an NFL record. Wide receiver Randy Moss caught 23 of those TD passes, also an NFL record. Counting the last three games of the 2006 season, the Patriots have won 19 consecutive regular-season games, breaking their own league record of 18 set in 2003-04.

The Patriots haven’t just defeated their opponents, they’ve demolished them – winning 10 of their games by at least three touchdowns.

They haven’t been merely excellent, they’ve been dominant.

Now, they have perfection in sight, although not quite within their grasp.

They’re three outs away from pitching a perfect game. They need one more strike to bowl 300. Win three more games, and even the Russian judge would have to give the Patriots a perfect 6.0 score.

The first 16 games were ones the Patriots wanted to win. The next three are games they have to win.

“The difference between the regular season and the playoffs,” Pats wide receiver Donte Stallworth said this week, “is that you can lose a game in the regular season and be all right. You lose in the playoffs – that’s it. Everybody knows that. Everybody understands that. You make mistakes, and that’s it for you. You’re home for the rest of the time.”

Make no mistake, the goal in New England always has been to win another championship, to add a fourth Lombardi Trophy to the three (from 2001, 2003, and 2004) that already reside in the trophy case in Foxboro.

If, when training camp opened last July, you’d asked any of the Patriots if they’d rather go 16-0, but lose in the playoffs, or go 10-6 and win the Super Bowl, the answer would have been instant, and unanimous.

It’s the title they want.

Now, to get it, they have to be perfect.

So smile, Louie — tonight’s game could be the beginning of a beautiful playoff run.

jdonalds@projo.com